Experimental Investigation of Natural Convection

Experimental Investigation of Natural Convection Heat Transfer in Heated Vertical Tubes with Discrete Rings R. C. Nayak, M. K. Roul & S. K. Sarangi

Experimental Techniques ISSN 0732-8818 Volume 41 Number 6 Exp Tech (2017) 41:585-603 DOI 10.1007/s40799-017-0201-6

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Author's personal copy Exp Tech (2017) 41:585–603 DOI 10.1007/s40799-017-0201-6

Experimental Investigation of Natural Convection Heat Transfer in Heated Vertical Tubes with Discrete Rings R. C. Nayak 1 & M. K. Roul 2 & S. K. Sarangi 1

Received: 12 April 2017 / Accepted: 30 July 2017 / Published online: 16 August 2017 # The Society for Experimental Mechanics, Inc 2017

Abstract Natural convection heat transfer from heated vertical pipes has been investigated experimentally. The pipes are open-ended and circular in cross section. The test sections are electrically heated imposing the circumferentially and axially constant wall heat flux. The outer surface of the test section is insulated and heat is allowed to dissipate from the internal surface. Experiments are carried out for four different channels of 45 mm internal diameter and 3.8 mm thickness with length varying from 450 mm to 850 mm. Ratios of length to diameter of the channel are taken as L/D = 10, 12.22, 15.56, and 18.89. Wall heat fluxes are maintained at q// = 250 to 3341 W/m2. Experiments are also carried out on intensified tubes of the same geometrical sizes with the discrete rings of rectangular cross section provided on the internal surface. Thickness of the rings are taken as t = 4, 6 and 8 mm; step size (s) of the rings are varying from 75 mm to 283.3 mm and the other ratios are taken as s/D = 1.67 to 6.29, t/D = 0.088 to 0.178 and s / t = 9.38 to 70.82. The effects of L/D ratio, ring thickness, ring spacing and wall heating conditions on local steady-state heat transfer phenomena are studied. A correlation is developed for average Nusselt number and modified Rayleigh number and another correlation is also developed for modified Rayleigh number and modified Reynolds number. These correlations predict the data accurately within ±10% error.

* R. C. Nayak [email protected]

1

Department of Mechanical Engineering, SOA University, Bhubaneswar PIN-751030, India

2

Department of Mechanical Engineering, GITA, Bhubaneswar, Odisha PIN-752054, India

Keywords Heat flux . Heat transfer . Natural convection . Ring spacing . Ring thickness . Correlation

Introduction Natural convection problem has received increasing attention in the literature in recent years due to its wide applications. At present, flow of gaseous heat carriers in vertical channels with natural convection is widely encountered in science and engineering such as in domestic convectors, cooling systems of electronic and electrical equipment, nuclear reactors with passive cooling systems, dry cooling towers, ground thermo siphons, etc. The heat released by these equipments should be transferred from the surface to the surrounding not only to protect them but also for their longer life. The internal surfaces of vertical open-ended pipes are generally cooled by natural convection, despite the low rates of heat transfer that this convection process affords. Thus information on the behaviour of natural convection flow through confined spaces has been found useful especially in the thermal fluid systems encountered in the diverse fields of nuclear and solar energy. Natural or free convection is observed as a result of the motion of the fluid due to density changes arising from the heating process. The movement of the fluid in free convection, whether it is a gas or liquid, results from the buoyancy forces imposed on the fluid when its density in the proximity of the heat transfer surface is decreased as a result of the heating process. The buoyant forces play an important role in freeconvection, in addition to the viscous and inertia forces encountered in forced convection. When a vertical plate is heated a free-convection boundary layer is formed over the surface, as shown in Fig. 1. Inertial, viscous and buoyant forces are predominant in this layer. The velocity profile in this boundary layer is quite unlike the

Author's personal copy 586

Exp Tech (2017) 41:585–603

(a)

Turbulent

u TW

δ

T∞ Laminar

(b) TW T T∞

T, u

u

δ Fig. 1 (a) Boundary layer on a vertical flat plate (b) Velocity and Temperature distribution in the boundary layer

velocity profile in a forced convection boundary layer. At the wall the velocity is zero because of no slip condition; it increases to some maximum value and then decreases to zero at the edge of the boundary layer since the free stream conditions are at rest in the free-convection system. The initial boundary layer development is laminar; but at some distance from the leading edge, depending on the fluid properties and temperature levels to which the wall is subjected, turbulent eddies are formed, and transition to a turbulent boundary layer begins. Father up the plate the boundary layer may become fully turbulent. Although extensive work has been done on the study of natural convection hydrodynamics and heat transfer in vertical open-ended channels without internal rings, but the works on internal heat transfer with presence of internal rings are not adequate in literature. Investigations are still going on to determine the effects of various parameters on hydrodynamics and heat transfer coefficients. Tanda [1] studied experimentally natural convection heat transfer characteristics of an array

of four staggered vertical plates. The thermal input at each plate was the same or differed from plate to plate depending on various heating modes. The effects of the interplate spacing and the plate-to-ambient temperature difference were investigated. The experiments were performed in air. Convective interactions among the plates were identified by examining the per-plate heat transfer coefficients and the local heat transfer coefficients along the vertical sides of plates. Local heat transfer results were obtained by means of the schlieren quantitative technique. Comparison of local heat transfer coefficients along the plate assembly with those of a continuous vertical plate (having the same height) showed enhancements up to a factor of two. Sparrow and Prakash [2] have analyzed the free convection heat transfer from a staggered array of discrete vertical plates. They compared the performance of a staggered array of discrete vertical plates with that of a parallel flat channel, considering the wall at uniform temperature. Their results indicated that larger spacing, shorter plate and smaller heights of the channels provide enhancement of heat transfer. Anug et al. [3] attempted to derive a general expression to account for the effect of flow restriction, while still considering the governing equation to be parabolic. Flow restrictions encountered in Aung’s study are in the form of staggered cards and baffles. Capobianchi and Aziz [4] analyzed natural convective flows over vertical surfaces and found that the local Nusselt number is an implicit function of the Biot number characterizing the convective heating on the backside of the plate. The order of magnitude of the local Nusselt number was therefore evaluated numerically for three values each of the Boussinesq, Prandtl, and Biot number. Jha and Ajibade [5] investigated the natural convection flow of viscous incompressible fluid in a channel formed by two infinite vertical parallel plates. Fully developed laminar flow has been considered in a vertical channel with steady–periodic temperature regime on the boundaries. The effect of internal heating by viscous dissipation is taken into consideration. Separating the velocity and temperature fields into steady and periodic parts, the resulting second order ordinary differential equations are solved to obtain the expressions for velocity, and temperature. The amplitudes and phases of temperature and velocity as well as the rate of heat transfer and the skin-friction on the plates are also obtained. The critical Grashof number has been observed by Eckert and Soehngen [6] to be approximately equal to 4 × 108. Critical Grashof number Values ranging between 108 and 109 are observed for different fluids and environment. Elenbass [7] carried out extensive analytical and experimental work on natural convection flow in such cross sectional geometries as the equilateral triangle, square, rectangle, circle and infinite parallel plates and his results are often compared with analytical results for those channels. Natural convection heat transfer measurements for vertical channels with

Author's personal copy Exp Tech (2017) 41:585–603

isothermal walls of different temperature are presented in the work of Sernas et al. [8]. Experimental study of Sparrow and Bahrami [9] encompasses three types of hydrodynamic boundary conditions along the lateral edges of the channel. Akbari and Borges [10] solved numerically the two dimensional, laminar flow in the Trombe wall channel, while Tichy [11] solved the same problem using the Oseen type approximation. Levy et al. [12] address the problem of optimum plate spacing for laminar natural convection flow between two plates. Capobianchi and Aziz [4] presented a scale analysis for natural convection from the face of a vertical plate. Three types of thermal boundary conditions are considered: (1) constant surface temperature; (2) constant surface heat flux, and (3) plate heated from its back surface. Fully developed laminar flow is considered in a vertical channel with steady– periodic temperature regime on the boundaries. The effect of internal heating by viscous dissipation is taken into consideration. Separating the velocity and temperature fields into steady and periodic parts, the resulting second order ordinary differential equations are solved to obtain the expressions for velocity, and temperature. Sankar et al. [13] investigated natural convection flows in a vertical annulus filled with a fluid-saturated porous medium when the inner wall is subjected to discrete heating. The outer wall is maintained isothermally at a lower temperature, while the top and bottom walls, and the unheated portions of the inner wall are kept adiabatic. Through the Brinkmanextended Darcy equation, the relative importance of discrete heating on natural convection in the porous annulus is examined. An implicit finite difference method has been used to solve the governing equations of the flow system. The analysis is carried out for a wide range of modified Rayleigh and Darcy numbers for different heat source, lengths and locations. It is observed that placing of the heater in lower half of the inner wall rather than placing the heater near the top and bottom portions of the inner wall produces maximum heat transfer. The numerical results reveal that an increase in the radius ratio, modified Rayleigh number and Darcy number increases the heat transfer, while the heat transfer decreases with an increase in the length of the heater. The maximum temperature at the heater surface increases with an increase in the heater length, while it decreases when the modified Rayleigh number and Darcy number increases. Du et al. [14] have developed a mathematical separated flow model of annular upward flow to predict the critical heat flux (CHF) in uniformly heated vertical narrow rectangular channels. The theoretical model is based on fundamental conservation principles: the mass, momentum, and energy conservation equation of the liquid film and the momentum conservation equation of the vapor core together with a set of closure relationships.

587

Kang and Chung [15] have conducted Natural convection experiments inside a vertical pipe for Grashof number of 5.2 × 106 to 3 × 1010 to seek the proper transition criteria. In order to achieve high Grashof number easily, the analogy concept has been employed and a cupric acid–copper sulfate electroplating system has been adopted as the mass transfer system. Nusselt numbers measured for laminar natural convection for all Prandtl numbers showed good agreement with the existing heat transfer correlation. Dey and Chakraborty [16] found that the local flow field around a fin can substantially enhance the forced convection heat transfer from a conventional heat sink. A fin is set into oscillation leading to rupture of the thermal boundary layer developed on either side of the fin. This enhancement in heat transfer is demonstrated through an increase in the timeaveraged Nusselt Number (Nu) on the fin surfaces. Buonomo and Manca [17] studied natural convection in a vertical micro channel heated at uniform heat flux and found. that the highest mass flow rate was obtained at the highest Knudsen number. This is due to the same driving force corresponding to a lower viscous resistance at increasing Kn value, Heat transfer results showed a different behaviour because the average Nusselt number is increased with increase in Kn value for lower Ra values (Ra < 10), where as the trend changed for Ra > 100. The average Nu was higher at lower Kn and the highest Nu value was attained for Kn = 0.0. El-Morshedy et al. [18] investigated experimentally the natural convection heat transfer in narrow vertical rectangular channel heated from both sides. They compared the measured local Nusselt number values with the predictions of two correlations for both natural and combined natural and forced convection regimes respectively. The comparison shows the need for developing new correlation to represent the obtained experimental results and to be utilized for the prediction of the local Nusselt number in thermal–hydraulics and safety analysis of the reactor. The developed correlation fits the experimental data within 5.8% relative standard deviation. Nayak et al. [19] studied natural convection heat transfer in heated vertical pipes dissipating heat from the internal surface. They found that average heat transfer rate from the internal surfaces of heated vertical pipes increases when discrete rings are provided on the internal surface of the pipes. Over the years it has been found that average freeconvection heat transfer coefficients can be represented in the following functional form for a variety of circumstances: m Nu f ¼ C Gr f Pr f

ð1Þ

Where the subscript f indicates that the properties in the dimensionless groups are evaluated at the film temperature, which is given by: Tf ¼

Tw þ T∞ 2

ð2Þ


Exp Tech (2017) 41:585–603

The product of the Grashof and Prandtl number is called Rayleigh number: Ra ¼ Gr Pr

ð3Þ

The characteristic lengths used in the Nusselt and Grashof numbers depend on the geometry of the problem. For a vertical plate characteristic length is the height of the plate L and for a horizontal cylinder characteristic length is the diameter D. For vertical surfaces, the Nusselt and Grashof numbers are formed with L, the height of the surface as the characteristic dimension. If the boundary layer thickness is not large compared to the diameter of the cylinder, the heat transfer may be calculated with the same relations used for vertical plates. The general criterion is that a vertical cylinder may be treated as a vertical flat plate when, D 35 ≥ L Gr1 =4 L

ð4Þ

Where, D is the diameter of the cylinder. For isothermal surfaces, the values of the constants are given by Vliet [20]. There are some indications from the analytical work of various investigators that the following relation may be preferable. 1 Nu f ¼ 0:10 Gr f Pr f =3

ð5Þ

More complete relations have been provided by Churchill and Chu [21] and are applicable over wider ranges of the Rayleigh numbers: 0:670Ra =4 9 . 9 =16 4 =9 for RaL < 10 ð6Þ 1 þ 0:492 Pr 1

Nu ¼ 0:68 þ

1

Nu

=2

0:387Ra =6 −1 . 9 =16 8 =27 for 10 1 þ 0:492 Pr 1

¼ 0:825 þ

< RaL < 1012

ð7Þ

Equation (6) is also a satisfactory representation for constant heat flux. Properties for these equations are evaluated at the film temperature. Extensive experiments have been reported by Vliet [20] for free convection from vertical and inclined surfaces to water under constant heat-flux conditions. In such experiments, the results are presented in terms of a modified Grashof number, Gr*: Gr*x ¼ Grx Nux ¼

gβ qw x4 kυ2

ð8Þ

Where qw is the wall heat flux in watts per square meter. The subscript x indicates distance from the bottom end of the

test section. The local heat transfer coefficient (hx) is correlated by the following relation for the laminar flow range: Nuxf ¼

1 = hx x ¼ 0:60 Gr*x Pr f 5 for 105 < G*x < 1011 ; ð9Þ kf

For the turbulent region, the local heat-transfer coefficients are correlated with 1 = Nux ¼ 0:17 Gr*x Pr 4 for 2 103 < Gr*x Pr < 1016 ; ð10Þ All properties in the above correlation are evaluated at the local film temperature. Although these experiments were conducted for water, the resulting correlations are shown to work for air as well. Writing equation (1) as a local heat transfer form we have, Nux ¼ C ðGrx PrÞm

ð11Þ

Substituting the value of Grx: 1 m = Nux ¼ C =ð1þmÞ Gr*x Pr ð1þmÞ

ð12Þ

The value of m for laminar and turbulent flow are taken as 1/4 and 1/3 respectively. Churchill and Chu [21] show that equation (6) may be modified to apply to the constant heat flux case if the average Nusselt number is based on the wall heat flux and the temperature difference at the center of the plate (x = L/2). The result is h i 1 0:67 Gr*L =4 N uL NuL −0:68 ¼ h ð13Þ i4=9 1 þ ð0:492=PrÞ9=16 Where NuL ¼ qw L= k ΔT and ΔT . ¼ T w at L 2 −T ∞ ð14Þ The purpose of this work is to study experimentally the natural convection heat transfer from the internal surface of heated vertical pipes at different heating levels. The test section is a vertical, open-ended cylindrical pipe dissipating heat from the internal surface. The test section is electrically heated imposing circumferentially and axially constant wall heat flux. As a result of the heat transfer to air from the internal surface of the pipe, the temperature of the air increases. The resulting density non-uniformity causes the air in the pipe to rise. Heat transfer experiment is carried out for four different test sections of 45 mm internal diameter and 3.8 mm thickness with length varying from 450 mm to 850 mm. Ratios of length to diameter of the channel are taken as L/D = 10, 12.22, 15.56, and 18.89. Wall heat fluxes are maintained at q// = 250 to 3341 W/m2. The studies are also carried out on intensified channels of the same geometrical sizes with the discrete rings of rectangular section. Thickness of the rings are taken as t = 4,


589

3

7

6, 8 mm; step size (s) of the rings are varying from 75 mm to 283.3 mm and the other ratios are taken as: s / D = 1.67 to 6.29, t / D = 0.088 to 0.178 and s / t = 9.38 to 70.82.

2

5

10

Experimental Set-up and Procedure Figure 2, shows the overall experimental set-up, which consists of the entire apparatus and the main instruments. The experimental set-up consists of a test section, an electrical circuit of heating and a measuring system. The test section is a cylindrical open ended tube. The cross-sectional view of the test section is shown in Fig. 3. In this study a hollow tube is made of aluminium which is 45 mm in diameter and 3.8 mm thick. Eight Copper-Constantan thermocouples are fixed to monitor temperatures on the internal surface at various locations as shown in the Fig. 2. Holes of 0.8 mm diameter are drilled at these locations for inserting the thermocouples. After inserting the thermocouple beads, the holes are filled with aluminium powder for getting good thermal contact with the tube. Then the opening of the thermocouple wells are closed by punching with a dot punch. Epoxy is used for sealing the opening of the thermocouple wells and for holding the thermocouples in position. After mounting the thermocouples a layer of asbestos paste (10 mm thick) is provided on the outer surface of the tube. A layer of glass tape is provided over the asbestos paste and then the nichrome wire heater coil is helically wound around the external surface with equal spacing. Then asbestos rope of 3

12

6 1

4

7 13

2

11

5

8 9 10

Fig. 2 Experimental Set-up. 1. Test section, 2. System of thermocouples, 3. Selector switch, 4. Millivoltmeter, 5. Thermometer, 6. Ammeter, 7 & 9. Volt meter, 8. Variac, 10. Transformer, 11-13. Traversing type thermocouples

8

9

4

1

6

Fig. 3 Cross sectional view of test section. 1. Aluminium tube, 2. Position of thermocouples, 3. Heater coil, 4. Glass tape, 5. Asbestos rope, 6. Asbestos paste, 7. Glass fibre, 8. Cotton cloth, 9. Aluminium foil. 10. Internal rings

diameter approximately 7 mm is wound over the heater coil with close fitting. After that another layer of asbestos paste is provided. A layer of glass-fibers of approximately 15 mm thickness is wrapped around it. A thick cotton cloth is wrapped over the glass fibers. It is covered with a very thin aluminium foil for reducing the radiation heat transfer. Two traversing type thermocouples are provided; one at the entrance and the other at the exit, to determine the temperature profile of fluid entering and leaving the tube at different radial distances. Another traversing type thermocouple is also used for measuring the external surface temperature of the test section to find out the heat loss from the external surface. Four different channels of similar construction with height varying from 450 mm to 850 mm are considered. Ratio of length to diameter of the channel are taken as L/D = 10, 12.2, 15.6, and 18.89. Rings of rectangular section of thickness varying from 4 mm to 8 mm are used. Wall temperatures at different locations are found out from the mill voltmeter readings to which thermocouples are connected. The fluid temperatures at the channel exit and entrance are found out at various radial distances by two traversing type thermocouples provided at the top and bottom of the channel


Exp Tech (2017) 41:585–603

respectively. The electric power input to the test section is determined from the measured voltage drop across the test section and the current along the test section. Though adequate thermal insulation is provided on the outer surface of the tube, there is still some heat rejection from the external surface and this heat loss by natural convection from the test section through the insulation is evaluated by measuring the outer surface temperature of the insulation and the ambient temperature. At different axial locations along the pipe the outer surface temperature of the insulator are measured by thermocouples and the average insulation temperature is determined. Heat loss from the external surface is then computed by the suggested correlation for natural convection from a vertical cylinder in air. Now heat dissipated from the internal surface can be found out by subtracting this heat loss from the heat input to the test section. The wall heat flux q// can be found out by dividing this heat by the internal surface area. From the measured temperature profiles at the channel entrance and exit, the approximate temperature profile at any other axial distance can be calculated. Here; q1 ¼ Heat input to the test section ¼ V x I And q2 ¼ Heat rejected from external surface ¼ h π D1 L ΔT

Where D 1 = Outer diameter of test section and ΔT = Difference between outer surface temperature of the insulation and the ambient temperature. Let the local wall temperatures at different axial distance along the pipe be Tw1, Tw2, Tw3,…etc., and the fluid temperature at these distances be Tb1, Tb2, Tb3,... etc. respectively, then local heat transfer coefficient at these locations can be calculated by the relation: h1 ¼

qn ðT w1 −T b1 Þ

ð15Þ

Similarly, h2, h3, h4, … can be calculated and from which average heat transfer coefficient is found out. The average Nusselt number can be found out from the average heat transfer coefficient by using the relation [22]

Re# ¼

ρuD2 μL

ð19Þ

Thermal boundary conditions of uniform wall heat flux q// = constant is considered. Wall heat fluxes are maintained at q// = 250 to 3341 W/m2. Spatial variations of the measured local wall temperatures are plotted for the smooth channel for different wall heat fluxes and non dimensional channel length. Measured temperature profiles at the channel exit for various heat fluxes and for different channel length are plotted. A correlation is developed for average Nusselt number and modified Rayleigh number. And another correlation is also developed for modified Rayleigh number and modified Reynolds number. Similarly studies are also carried out on intensified channels of the same geometrical sizes with providing the discrete rings of height t = 4, 6 and 8 mm; step size (s) of the rings are varying from75mm to 283.3 mm and the different non-dimensional ratios are taken as: s / D = 1.67 to 6.29, t / D = 0.088 to 0.178 and s / t = 9.38 to 70.82. Four test sections with length varying from 450 mm to 850 mm were considered. For each test section experiments were conducted for eight different heat flux values. Internal rings are provided at different locations with thickness varying from 4 mm to 8 mm, spacing varying from 75 mm to 283.3 and heat flux varying from 250 to 3341 W/m2. Total 320 numbers of experiments were conducted and to perform each experiment around 4 h were required for steady state conditions to be reached (Tables 1, 2, 3 and 4). Sample Calculations For q // = 2188 W/m2, L = 450 mm, L/D = 10;

hD Nu ¼ k

ð16Þ

Now modified Rayleigh number [23] based on constant heat flux and average wall temperature can be calculated by using the following two formula. D gβq== D5 ¼ αυkL L gρ2 cp β T w −T b D4

Ra# ¼ Gr Pr Ra# ¼

Since constant wall temperature is difficult to be maintained, we will consider the constant wall heat flux case only. A vane type anemometer is used to measure the velocity of fluid [24] at the exit of the channel. The modified Reynolds number can be calculated by multiplying non dimensional number D/L with Re:

Lkμ

(a) Heat loss from external surface, q2:

ð17Þ

Average surface temperature excess over ambient, ΔT = 180 C, T∞ = 270 C. Average temperature of fluid, Tf = 27 + 18/2 = 360C. The different property values of air at one atm. Pressure can be found out from the data table as follows:

ð18Þ

β ¼ 1=T f ¼

1 ¼ 3:236 10−3 =K 36 þ 273

Author's personal copy Exp Tech (2017) 41:585–603 Table 1

591

(a) - (d) variations of local wall temperatures for various L/D ratios and for various heat fluxes

(a) L = 450 mm, L/D = 10 mm 409 W/m2 0 30.4

762 W/m2 47.2

1012 W/m2 65.4

1377 W/m2 86.2

1723 W/m2 101.8

2188 W/m2 128.1

2655 W/m2 156.4

3158 W/m2 176.8

65 129

32.8 35.2

50 53.5

70.2 74.8

96.8 105.4

109.8 118.2

137.2 144.2

167.6 176.2

190.5 200.6

193

36

54.5

76.2

108.2

120.6

147.8

180

205.1

225 257

36.8 37.3

55.8 56.6

77.6 79.3

109.1 110.4

122.4 124.2

150.8 153.3

182.5 186.3

208.8 211.7

321

38

58

80.4

111.8

127.7

155.5

188.9

215.5

385 450

37.9 37.4

57.6 57

80.4 79.2

111.5 111

127.7 126.5

155.8 155

189.2 188.4

215.6 214.4

(b) L = 550 mm, L/D = 12.22 mm 0 80 158

401 W/m2 38.9 40.8 42.2

899 W/m2 77.8 82.2 85.6

1219 W/m2 91.2 98.8 105.4

1490 W/m2 115.8 122.9 128.2

1707 W/m2 140.8 150 157.4

2090 W/m2 167.6 178.4 187.2

2557 W/m2 200.8 214.5 224.4

3341 W/m2 218 233.2 244.4

236 275 314 392 470

44.4 45 45.8 46.2 46.5

88.6 90.5 92.8 93.2 94

111.6 114.3 116.7 117.2 118

132.6 135.8 138 139.7 141.6

163.7 167.4 170.3 172.8 175.2

194.2 199 203 205.7 207.5

232.6 238.3 243.4 244.5 247

250.4 258.2 265.5 266.7 268.6

550

45.6

92.8

116.9

139.2

173.2

205.2

244

266.3

576 W/m2 45.2 49.8 54.4

978 W/m2 61.2 67.8 74.3

1271 W/m2 89 98.6 108.2

1398 W/m2 101.2 111.4 121.5

1612 W/m2 118.2 128.8 141.3

2045 W/m2 147.2 161.5 176.4

2504 W/m2 189 202.5 217.5

58.2 59.8 60.6 61.4 61 58.9

79.2 81 82 82.4 82 79.8

116.1 118.8 121.2 122.3 122 120.5

129.8 132.9 135.3 136.2 136.4 134.2

149.7 153.5 156.6 157.4 157.6 155.7

187.8 191.2 194.5 196 196.8 195.2

227.8 232.2 235.4 236.7 236.9 234.6

892 W/m2 66.7 76.4 84.6

1128 W/m2 72.2 83.4 92.8

1227 W/m2 84 97.5 109.4

1460 W/m2 97 113.4 126.8

1637 W/m2 108 126.4 140.5

1880 W/m2 127.20 148.8 165.8

2596 W/m2 139.6 162.8 184

93.2 97 101 102.2 103 97.8

102.7 107.4 111.5 112.8 113.6 109.8

121.5 126 132 132.8 133 128.2

140.2 146.6 153.4 154.8 155.7 149.8

156.4 163 169.6 170.8 171 167.5

185.3 191 199 201.4 201.8 195

201.6 211.8 219.5 229.4 227.5 221.8

(c) L = 700 mm, L/D = 15.56 mm 250 W/m2 0 22 100 24 200 26.6 300 28 350 28.8 400 29 500 29.2 600 29.2 700 28.5 (d) L = 850 mm, L/D = 18.89 mm 664 W/m2 0 52.8 123 59.9 244 66 365 425 486 607 728 850

72.6 75.8 78.4 79.7 80 74.9

Author's personal copy 592 Table 2

Exp Tech (2017) 41:585–603 (a) – (d) Fluid temperatures at channel exit at various radial distances for different heat fluxes and different L/D ratio for smooth tubes

(a) L = 450 mm, L/D = 10 mm 409 W/m2 0 4.4 2 5.2 4 6.8 6 9.9 8 12 10 14.8 12 16.3 14 19.5 16 21.8 18 25 20 27.2 22 30.4 22.5 37 (b) L = 550 mm, L/D = 12.22 mm 250 W/m2 0 3.25 2 3.25 4 3.25 6 4 8 4.8 10 6.4 12 8 14 10 16 12 18 14.8 20 18.5 22 23 22.5 28.5 (c) L = 700 mm, L/D = 15.56 mm 401 W/m2 0 11.4 2 12 4 13.6 6 15.6 8 18.4 10 21.3 12 23.6 14 26.4 16 29.2 18 31.8 20 34.5 22 38 22.5 45.6 (d) L = 850 mm, L/D = 18.89 mm 664 W/m2 0 20.8 2 20.8 4 21.6 6 23 8 25.2 10 27.8 12 31 14 34.6 16 39.5 18 46 20 54.4 22 64 22.5 74.9

762 W/m2 7.3 9 11.5 14.2 17.4 21.2 25.8 29.8 33.4 37.7 44.2 49.2 57

1012 W/m2 11 12.3 13.8 16.7 20.4 23.2 29.6 37.5 40.2 46.4 54.8 61.3 79.2

1377 W/m2 22 25 26.9 29 31.8 35.5 45.8 52.6 57 63.9 72.5 90.6 111

1723 W/m2 29.5 33.8 38.8 45 51.2 55.8 62 69 74.2 78.2 92.7 100.4 126.5

2188 W/m2 34 36.8 39.4 42 44.8 49 53 58.8 67 86.2 95.6 117 155

2655 W/m2 37.2 39.3 42 45.2 48.5 53 57.4 65.4 75.5 100 117 138.4 188.4

3158 W/m2 40 44.3 47.2 52.6 57.4 64.5 74.8 86.3 96.7 114.8 138.4 165.2 214.4

576 W/m2 8.3 8.3 9 10.2 12.4 15.5 20.4 25.4 31 35.8 41.8 49 58.9

978 W/m2 13 13 14.5 16.4 18.4 21 24.5 28.6 34 42.5 52 64.5 79.8

1271 W/m2 19 20 22.2 25 28.5 32.5 37.4 44.6 52.4 62 74.5 90.5 120.5

1398 W/m2 22.4 24.4 27.6 32 36.5 41.5 48.3 56.4 66.5 78 92.8 108 134.2

1612 W/m2 29.5 31.4 34.5 39.5 46 55.6 64.3 74 84.6 96.6 109.4 125 155.7

2045 W/m2 35.6 39.6 45.4 52.5 60.8 70.8 81 93.8 105.4 122 139.4 159 195.2

2504 W/m2 40.4 46.8 54 63.4 73.6 84.4 96.8 109.5 125.8 145 167 193.5 234.6

899 W/m2 15.8 16.8 19 22.4 25.4 29.4 33.3 37.5 45.2 54.8 64.6 77.4 92.8

1219 W/m2 19.6 21 23.8 27.3 31.4 36.4 44 52 60.4 69.6 81.5 96.4 116.9

1490 W/m2 28.5 33.8 36.2 39 42.3 45.8 52.6 61.5 71.4 82.8 94.4 110.6 139.2

1707 W/m2 34 36.3 39.4 42.3 45.5 50.3 56 67.5 75.5 90.6 108.7 148.6 173.2

2090 W/m2 39.4 40.5 43 46.5 51 60.4 72 84.8 99.6 119.6 144.5 176 205.2

2557 W/m2 43.5 48.5 54 61.6 71.6 82.3 96 112 130 141.4 168 204.5 234

3341 W/m2 50.4 53 58.5 66.8 77.4 88.4 102 118.4 136.8 148.6 173.4 223 266.3

892 W/m2 24.2 24.5 25 26.5 28.4 30.8 35 42 50.3 61.4 71.6 81.8 94.4

1128 W/m2 29 29.5 32 34 37.4 43.4 50.2 57.5 65.4 73.6 82.5 92.8 109.8

1227 W/m2 34.5 35 35.8 37.5 41 46.8 52.5 58.4 67.5 78.6 90.4 106.8 128.2

1460 W/m2 39.6 40 41.4 43.5 46.8 51 58 67.2 77.4 90 105.8 125.6 147

1637 W/m2 43 44 46.6 50.5 55.8 63 72.4 82.2 93.8 107.5 123.6 143 167.5

1880 W/m2 47.5 50.4 56 63.5 72 81.6 92.5 104 119 134.5 149.5 171.4 195

2596 W/m2 52.4 55 59.6 66 75.4 85 97 113 128.4 146.4 167.6 193.6 221.8

Author's personal copy Exp Tech (2017) 41:585–603 Table 3

593

(a)-(k) Fluid temperature at the exit with discrete rings for different heat fluxes and different L/D ratio

(a) L = 450 mm, L/D = 10, t = 6 mm, s = 225 mm mm 409 762 1012 W/m2 W/m2 W/m2 0 9.6 14.2 19 2 9.6 14.2 20 4 10 14.8 21.5 6 10.8 15.6 23.8 8 12 17 26 10 13.5 19.3 28.5 12 15.3 23 31 14 17.5 27 34.2 16 19.8 30.6 38.6 18 22.4 35 45 20 26 40.6 53.8 22 30 47.8 63.4 22.5 35.8 55 76.5 (b) L = 450 mm, L/D = 10, t = 6 mm, s = 150 mm 762 1012 mm 409 W/m2 W/m2 W/m2 0 12.5 18 23.6 2 12.5 18 24 4 12.8 18.8 24.8 6 13.5 19.5 26 8 14.8 21 28 10 16.8 23.3 30.5 12 19.4 26 33.6 14 22.6 29.5 38.5 16 23.8 34.5 44.2 18 25.4 38.6 49.5 20 27.2 43.2 56.5 22 29.8 47.8 63.8 22.5 35 54 74.2 (c) L = 450 mm, L/D = 10, t = 6 mm, s = 112.5 mm 762 1012 mm 409 W/m2 W/m2 W/m2 0 14 20.3 26.5 2 14 20.3 26.8 4 14.4 21 27.4 6 15 22.4 28.2 8 15.8 24 29.4 10 17 25.8 33 12 18.5 27.8 36.8 14 20 30 40.5 16 23 32.4 45 18 25.2 35.4 49.8 20 27.2 39 54 22 29.4 45.8 61.4 22.5 34 52.4 72.3 (d) L = 450 mm, L/D = 10, t = 6 mm, s = 75 mm 762 W/m2 1012 W/m2 mm 409 W/m2 0 11.5 17 22 2 11.5 18 23 4 12 18.8 24.6 6 13.4 19.5 26

1377 W/m2 28 29 30.4 32.6 35.6 40 45.5 52 59.2 68.8 79.5 92.5 107.6

1723 W/m2 37 39.8 43 47.5 52.4 58 63.8 70.5 77.6 84 94.8 108 123.8

2188 W/m2 41.5 44.8 48.3 53.4 60.8 68 76.5 83.6 91 103.4 116.5 134 150

2655 W/m2 47 50.8 55 60.5 66 75.4 85.8 96.4 109 124.8 141 163 184

3158 W/m2 54 55.4 58.5 63.4 72.8 82.5 94.8 107.4 121.6 135.4 154 184.5 210

1377 W/m2 32 33 34.5 36.5 39 43 48.5 54.5 61.6 69.6 78 90.5 105

1723 W/m2 39.8 40.5 42.5 45 47.4 51.6 56.8 63.8 72.8 83 95.4 110 121.5

2188 W/m2 46.5 47 48.5 50.8 54 58.8 65 74.5 86.6 101.8 114 132.8 147.8

2655 W/m2 53.5 54.5 57 60.8 66.5 74 83.5 94.5 106.3 121 137.5 159.8 181.5

3158 W/m2 63 64.8 68.4 71.5 76.5 83.4 92 104.4 119 136.2 154.8 182.5 207

1377 W/m2 35.6 35.6 36 37.3 39.8 43.4 47.5 54 59.4 66.6 74.5 88.8 103

1723 W/m2 42.4 42.8 43.6 46.6 51 57 62.8 69.5 76 84 92.5 106.5 119

2188 W/m2 50 51.5 53 54.8 58 63.8 71 80.4 90 100.3 111.5 126 145.3

2655 W/m2 58.4 59.8 61.3 64.5 69.8 75.8 82.4 91.8 103.8 115.4 132.8 159.6 179

3158 W/m2 68.6 69.8 72.4 76.5 82 88 94.5 102.5 117 134 154.5 181 204.6

1377 W/m2 31.5 32.5 34.5 36.5

1723 W/m2 38 39 40.6 44

2188 W/m2 45.5 47 48.5 50.8

2655 W/m2 51.6 52.5 54.6 58.8

3158 W/m2 61.5 63 67.4 71


Exp Tech (2017) 41:585–603

Table 3 (continued) 8 14.8 21 28 10 16.8 23.3 30.5 12 19.4 26 33.6 14 22.6 29.5 38.5 16 23.8 34.5 44.2 18 25.4 38.6 49.5 20 27.2 43.2 56.5 22 30 48 64.4 22.5 36 55.4 76 (e) L = 850 mm, L/D = 18.89, t = 4 mm, s = 425 mm mm 664 W/m2 892 W/m2 1128 W/m2 0 23.6 28.4 34 2 23.6 28.4 34 4 23.6 29.5 35.4 6 24.4 31 37.5 8 26.6 34.4 41 10 29 38.6 45.6 12 33.4 43 50.8 14 37 49 55.6 16 42.6 54.2 61.4 18 49 61.4 70.8 20 56.3 70.6 80.5 22 64 80.8 91 22.5 73 91.6 105.5 (f) L = 850 mm, L/D = 18.89, t = 4 mm, s = 283.33 mm mm 664 892 1128 W/m2 W/m2 W/m2 0 24.5 30 35.4 2 24.5 30 35.4 4 24.5 30.6 36 6 25.6 31.5 37.5 8 27 33.6 39.6 10 30.6 37 42 12 35 41.8 46 14 38.4 47 51.3 16 42.5 53.4 58 18 46.4 59.5 67.6 20 52.4 68 78.5 22 61 78.6 89 22.5 71.4 90.5 104.3 (g) L = 850 mm, L/D = 18.89, t = 4 mm, s = 212.5 mm mm 664 892 1128 W/m2 W/m2 W/m2 0 25.6 31.5 37.4 2 25.6 31.5 38 4 26 32.4 39.4 6 27.4 34.5 41.5 8 29.5 37.5 44.5 10 33 41 47.8 12 37.6 46.4 52.4 14 42 52 57 16 47 58.6 64 18 52.5 66 72 20 57.8 73.6 81.4 22 63 80.4 91 22.5 70.5 89 102.4 (h) L = 850 mm, L/D = 18.89, t = 6 mm, s = 425 mm mm 664 892 1128 W/m2 W/m2 W/m2 0 27 34 40

39 43 48.5 54.5 61.6 69.6 78 92 105

46.5 51.7 57 64 73 84.4 97.4 112 123

54 58.8 65 74.5 86.6 101.8 114 134.6 149.6

63.4 70 79.5 90.5 104 120.6 138 166.7 184

77 83.7 93 107 121 138 155.4 186 207.6

1227 W/m2 40.6 41 42.4 44 46.6 49.5 54 61.6 70.5 80.6 93.4 107.6 123.4

1460 W/m2 47 48.4 50.6 54 57.8 62.4 67.2 73.4 82 93.4 105.8 123 141.6

1637 W/m2 51.4 52.6 54 57 61.5 66.6 75 85.4 96.8 109.6 124.5 141 161

1880 W/m2 58 60.4 64.6 71 79.4 87.6 96 109.6 121 134 147.5 165.6 187.6

2596 W/m2 64.4 67 71.6 78 85.4 93.6 104 116.4 132 149.4 168 189 214

1227 W/m2 43 43.6 44.5 46 48 51.4 56 61.5 67.4 76 87.6 102.6 121

1460 W/m2 49.5 50 51 52.4 54.5 57.6 64 69.4 76 86.5 103.4 118.5 139.6

1637 W/m2 54.6 55.6 57.4 60.6 64 68.2 73.4 79.4 87 98 112.5 132.4 158.4

1880 W/m2 61 62.5 64.6 68 73.4 79.8 86.4 96 108 122.6 139.6 159 184

2596 W/m2 68.6 71 75.6 81 88.5 97.6 107.8 118 131.4 146.4 164.6 184 210

1227 W/m2 46 46.6 47.4 49.5 53 57 62.4 69.6 77 86.4 96 107 118.6

1460 W/m2 53.6 54.4 56 58.4 62 67.8 74 82.4 91 101.4 112 124 137.4

1637 W/m2 58 59 60.6 63 67 73 80.5 90 101.5 113 126.5 140 156

1880 W/m2 65.6 67 69.5 73 78 84.4 91.2 102.4 115 130.4 147 163 181.8

2596 W/m2 72 75.4 79.6 84 90 98.4 108 119.2 132 147 164 184.5 207.4

1227 W/m2 49

1460 W/m2 57

1637 W/m2 62.4

1880 W/m2 70

2596 W/m2 77


595

Table 3 (continued) 2 4 6 8 10 12 14 16 18 20 22 22.5

27 27.6 28.6 30 32 35 39 44 49 55.4 62 70

34 34.6 35.8 38 42.6 47.5 53.4 59.6 65 72.4 78.6 88

40 41 42.5 44.5 47.8 52.4 57 64 72 81.4 90.4 100.8

(i) L = 850 mm, L/D = 18.89, t = 6 mm, s = 212.5 mm mm 664 892 1128 W/m2 W/m2 W/m2 0 27.8 35 41.4 2 27.8 35 41.4 4 27.8 35.6 42 6 28.4 36.6 43.6 8 29.4 39 45.4 10 31 42 48.4 12 33.4 46 51.6 14 39 51.6 55 16 43 57 62 18 48 63.4 69.6 20 53.4 70.4 78.4 22 61 77 88.2 22.5 69 86.4 99 (j) L = 850 mm, L/D = 18.89, t = 6 mm, s = 425 mm mm 664 892 1128 W/m2 W/m2 W/m2 0 28.6 36.2 41.5 2 28.6 37 42 4 29 37.8 42.8 6 29.8 39 44 8 30.6 40.4 45.4 10 32 43 47.8 12 33.4 47 51.4 14 36 52.5 56 16 40 58.6 61.5 18 45 63.6 68.6 20 52 69.6 76.4 22 61.4 76 86 22.5 68 85.4 97.5 (k) L = 850 mm, L/D = 18.89, t = 8 mm, s = 212.5 mm mm 664 892 1128 W/m2 W/m2 W/m2 0 27.5 34.4 40.5 2 27.5 35 41 4 28.4 35.6 42.5 6 30 36.6 43.6 8 31.5 39 45.4 10 31 42 48.4 12 33.4 46 51.6 14 39 51.6 55 16 43.4 57 62 18 48.7 63.4 69.6 20 54.3 70.4 78.4 22 62 78 89.6 22.5 69.5 87.2 100

49 50 51.6 54 57 61.4 68.6 75 84.6 95 104 116

57.6 58.8 60.5 63 63.6 68 75.4 83.6 94 107.4 120 134.4

63 64.5 66.4 69 72.4 77.6 86 96.4 108.4 122.6 136.4 152

71.5 73.6 77 81.5 87 94.4 104.6 116.4 130 143.4 158.4 176

78 81.6 85.4 92 101 111.6 123 135.6 148 163 181.6 201

1227 W/m2 50.6 51 52.5 54.6 57.4 60.6 64.5 69.6 75 82.4 90.6 101 114

1460 W/m2 58.8 59.6 61.8 65 68.4 73 77.6 83 90 97.6 105.8 116 131.3

1637 W/m2 64.4 65 67 70.4 74.4 79 85 92.4 100.4 108 118.6 132.6 149.6

1880 W/m2 72.6 73.5 75 78 82.6 89 97 106.6 116 127 139 154.4 173.4

2596 W/m2 79.6 80.5 83 87.6 93 102 113.6 124.8 136 149 163 178 197.5

1227 W/m2 51.5 52 53.5 56 59.4 63.5 67.7 71 76 81.4 87.7 99 112.6

1460 W/m2 60 60.8 62 64 66.5 69.6 72.4 76.6 83 92.4 102.4 115 130

1637 W/m2 65.6 66 67.5 71 75.4 80 86 93 101.4 109.8 119.4 130.8 147.6

1880 W/m2 74 76 78.6 81.4 85 91.8 98 106.6 116 127 138.5 152.8 171

2596 W/m2 81 82.6 84 87.4 94 102.6 114 125.4 137 152.4 164 179 195.5

1227 W/m2

1460 W/m2 57 58.4 61.8 65 68.4 73 77 83.4 91 98.6 106 118.6 132.5

1637 W/m2 62.8 64 66.6 70 74 79.3 85.5 93.4 102.4 112.4 123.4 135.6 151

1880 W/m2 70.4 72.4 74.5 77.6 82.5 88.4 96 106.5 117.4 128 142 157.5 175

2596 W/m2 76.8 78.4 81 85.5 91.5 98 108.7 120.4 132 147 164 181 199.5

49.6 50.5 51.6 53 56.4 59.6 63.5 69.5 76 83.4 92 102.5 115.4


Exp Tech (2017) 41:585–603 Fluid temperature at corresponding thermocouple locations

Table 4

Fluid temp. Thermocouple Local wall temp. positions in mm Excess over amb. in Excess over 0 amb. in 0C C

Now Rayleigh number,

==

h ¼ ðT w1q−T b1 Þ

Ra¼Gr:Pr ¼

in W/m2. 0C

0

128.1

0

17.08

65 129

137.2 144.2

5 9.5

16.55 16.244

193

147.8

14

16.353

257 321

153.3 155.5

18 23.5

16.17 16.5757

385 450

155.8 155

28.5 34

17.1877 18.083

¼

gβ ðT w −T ∞ ÞD31 Pr υ2

9:81 3:236 10−3 18 ð0:12Þ3 0:6998 2 16:576 10−6

1 1 0:387 Ra =6 2 ¼ 2:515 106 Nu ¼ 0:825 þ h 9 =16 i8 =27 1 þ 0:494 Pr

¼ 4:604Nu ¼ 21:198h ¼

Nu:k 21:198 0:027236 ¼ D1 0:12

¼ 4:811

Heat lost fron the external surface, q2 ¼ h π D1 L ΔT ¼ 4:811 π 0:12 0:45 18 ¼ 14:69 W

(a)

(c) 250

250 2

250 W/m 2 576 W/m 2 978 W/m 2 1271 W/m 2 1398 W/m 2 1612 W/m 2 2045 W/m 2 2504 W/m

2

150

100

200 0

0

Temperature in c

200

Temperature in c


150

100

50

50

0

0 0

50 100 150 200 250 300 350 400 450 500 550 600

0

100

200

300

400

500

600

(b)

900 1000

250 2

150 100


200 0

200

2

Temperature in c

401 W/m 2 899 W/m 2 1219 W/m 2 1490 W/m 2 1707W/m 2 2090 W/m 2 2557 W/m 2 3341 W/m

250 0

800

(d) 300

Temperature in c

700

Distance in mm

Distance in mm

150

100

50

50 0

0 0

100

200

300

400

500

600

700

Distance in mm

Fig. 4 (a) Variation of wall temperature for different heat fluxes for L = 450 mm, (b) Variation of wall temperature for different heat fluxes for L = 550 mm, (c) Variation of wall temperature for different heat fluxes

0

100 200 300 400 500 600 700 800 900 1000 1100

Distance in mm

for L = 700 mm, (d) Variation of wall temperature for different heat fluxes for L = 850 mm


597

(a)

(c) 250

250 2

150

o

100

150

100

50

0 0.0


200

Temperature in c

o

Temperature in c

200

2


50

2.5

5.0

7.5

0 0.0

10.0 12.5 15.0 17.5 20.0 22.5 25.0

2.5

5.0

7.5

Radial distance in mm

(b)

(d) 250

300

2

2

150

200 o

o

200


Temperature in c

250

Temperature in c

10.0 12.5 15.0 17.5 20.0 22.5 25.0

Radial Distance in mm

100

100

50

50

0 0.0

150

664 W/m 2 892W/m 2 1028 W/m 2 1227 W/m 2 1460 W/m 2 1637 W/m 2 1980 W/m 2 2596 W/m

2.5

5.0

7.5

10.0 12.5 15.0 17.5 20.0 22.5 25.0

0 0.0

2.5

5.0


7.5

10.0 12.5 15.0 17.5 20.0 22.5 25.0


Fig. 5 (a) Temperature profile at channel exit for different wall heat fluxes for smooth tubes with L = 450 mm, (b) Temperature profile at channel exit for different wall heat fluxes for smooth tubes with L = 550 mm, (c) Temperature

profile at channel exit for different wall heat fluxes for smooth tubes with L = 700 mm, (d) Temperature profile at channel exit for different wall heat fluxes for smooth tubes with L = 800 mm

(b) Wall heat flux:

(d) Different non-dimensional numbers:

Heat input, q1 = V x I = 90 × 1.71 = 153.9 W. Heat rejected from the internal surface, q = q1 – q2 = 153.9– 14.69 = 139.21 W. Wall heat flux = Aq ¼ Aq ¼ 2188 W=m2 (c) Heat transfer coefficient: The local and average heat transfer coefficient is calculated in a tabular form as given in

T w ¼ 147:520 C T b ¼ 170 C 134:243 ¼ 16:78 W=m2 : 0 C h¼ 8

T f 1 ¼ 27 þ

T w −T b 147:52−17 ¼ 27 þ ¼ 92:260 C 2 2

The properties of air corresponding to this temperature are: υ ¼ 22:3328 10−6 m2 =s α ¼ 32:2845 10−6 m2 =s k ¼ 0:031465 W=m:K 1 ¼ 2:7378 10−3 =K β¼ 92:26 þ 273 hD Nusselt Number, Nu ¼ hD k ¼ k ¼ 23:998.


Exp Tech (2017) 41:585–603

(d)

(a)

250

250 2

150

100

2

200 o

Temperature in c

o

Temperature in c

200


100

50

50

0 0.0

150


2.5

5.0

0 0.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


(b)


(e) 250

250

2

2

150

100

200 o

Temperature in c

o

Temperature in c

200


100

50

50

0 0.0

150

664 W/m 2 892 W/m 2 1028 W/m 2 1227 W/m 2 1460W/m 2 1637 W/m 2 1980 W/m 2 2596 W/m

2.5

5.0

0 0.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0



(c)

(f) 250

2

2

150

100

o

150

100


50

50

0 0.0

200

Temperature in c

o

Temperature in c

200


2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0


0 0.0

2.5

5.0

7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0



599

(g)

(j) 250

250

2

2


150

200 o

Temperature in c

o

Temperature in c

200


100

150

100

50

50

0 0.0

0 2.5

5.0

7.5

10.0 12.5 15.0 17.5 20.0 22.5 25.0

0.0

2.5

5.0

7.5


(h)

(k)

250

250

2

150

o

100

50

150

100

50

0 0.0

0 2.5

5.0

7.5

10.0 12.5 15.0 17.5 20.0 22.5 25.0


(i) 250 2


200 o

Temperature in c


200

Temperature in c

o

Temperature in c

2

664 W/m 2 892 W/m 2 1028 W/m 2 1227 W/m ) 2 1460 W/m 2 1637 W/m 2 1980 W/m 2 2596 W/m

200

10.0 12.5 15.0 17.5 20.0 22.5 25.0


150

100

50

0 0.0

2.5

5.0

7.5

10.0 12.5 15.0 17.5 20.0 22.5 25.0


Fig. 6 (continued)

0.0

2.5

5.0

7.5

10.0 12.5 15.0 17.5 20.0 22.5 25.0



Exp Tech (2017) 41:585–603

Fig. 6

(a) Distribution of temperature of flow at the exit of the tube with discrete rings (L/D = 10, t = 6 mm, s = 250 mm). (b) Distribution of temperature of flow at the exit of the tube with discrete rings (L/D = 10, t = 6 mm, s = 150 mm). (c) Distribution of temperature of flow at the exit of the tube with discrete rings (L/D = 10, t = 6 mm, s = 112.5 mm). (d) Distribution of temperature of flow at the exit of the tube with discrete rings (L/D = 10, t = 6 mm, s = 75 mm). (e) Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 4 mm, s = 425 mm). (f) Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 4 mm, s = 283.33 mm). (g) Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 4 mm, s = 212.5 mm). (h) Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 6 mm, s = 425 mm). (i) Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 6 mm, s = 283.33 mm). (j) Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 6 mm, s = 212.5 mm). (k). Distribution of temperature of flow at the exit of the smooth tube with discrete rings (L/D = 18.89, t = 8 mm, s = 212.5 mm)

Modified Rayleigh number, gβq== D5 αυkL 9:81 2:7378 10−3 2188 ð0:045Þ5 ¼ 0:45 22:3328 10−6 32:2845 10−6 0:031465

Ra# ¼

¼ 1:062182 106

Mean stream velocity, u = 13.5 m/min = 0.225 m/s. 2 uD2 Modified Reynolds number, Re# ¼ uD υL ¼ υL ¼ 45:337.

Results and Discussion Typical axial variations of local wall temperatures for various L/D ratios and for various heat fluxes are shown in plotted in Fig. 4(a) to (d) for smooth tubes. It increases along the height of the cylinder, which is in accordance with the theoretical predictions done by various investigators. But it slightly decreases towards the end, which may be due to the heat rejection from the end of the tubes. Experimental temperature profiles at the channel exit for different heat fluxes and for different L/D ratio for smooth tubes are indicated in Fig. 5(a), (b), (c), (d). The radial distances are taken as abscissa whereas the fluid temperatures are taken as the ordinate. Here the distances are measured from the center of the pipe towards the wall at the exit of the test section. At the center r = 0 and at the wall r = R = 22.5 mm. It is evident from these figures that the fluid temperature is maximum at the wall which is nearly equal to the wall temperature at the exit of the pipe and it minimum at the center of the pipe. This is due to the fact that heat is transferred from the wall of the heated pipe to the air by natural convection. So, the air in the vicinity of the wall is hotter as compared to the air farther the wall.

Similarly, studies are also carried out on intensified channels of the same geometrical sizes by providing internal rings of same material of different heights such as t = 4 mm, 6 mm, and 8 mm. Step size (s) of the rings are varying from75mm to 283.3 mm. Other non-dimensional ratios are taken as: s / D = 1.67 to 6.29, t / D = 0.089 to 0.178 and s / t = 9.375 to 70.82. Experimental temperature profiles at the channel exit for different heat fluxes and for different L/D ratio for tubes with discrete rings are indicated in Fig. 6(a) to (k). It is evident from these figures that the fluid temperature is maximum at the wall which is nearly equal to the wall temperature and minimum at the center of the pipe. It can also be seen from these figures that the air temperature at the center of the pipe is more in case of pipes with internal rings as compared to that of smooth pipes. This is due to the fact that there is enhancement of heat transfer from the wall to the air when internal rings are provided. As hot layers diffuse to the center of flow, and the cold ones move to wall area, the gradient of temperature in the boundary layer increases, and thus heat transfer increases. It can also be seen that the average heat transfer rate increases with increasing the thickness of the rings up to a certain limit, beyond which it decreases. When ring thickness increases from 4 mm to 6 mm there is enhancement of heat transfer from the wall to air. But by further increasing the ring thickness from 6 mm to 8 mm there is slight decrease in heat transfer. This may be due to the fact that when the ring thickness increases, the intensity of pulsation will increase and the pulsation arising behind the ring will have no time to fade sufficiently on the way to the following ring and will defuse to the flow core. Thus intensity of pulsation will increase and consequently the turbulence of flow will occur. This results in significant growth of hydraulic resistance with small increase of heat transfer. The Fig. 7 shows the distribution of temperatures of flow at outlet of channels for various L/D ratio, i.e.; for different length of the tube. It is clear from the graph that heat transfer increases with increase in tube length. This is because by increasing the length of the test sections the surface area increases as a result of which the heat transfer from the wall to air increases. The Figs. 8 and 9 shows the distribution of temperatures of flow at outlet of channels for various heat fluxes and various thickness and spacing of rings inside the tube. It can be seen that the average heat transfer rate increases with increasing the thickness of the rings up to a certain limits, beyond which it decreases, which is shown in the Fig. 9. Figure 8 shows that when the spacing between the rings decreases beyond a certain limit, the heat transfer rate decreases. This may be due to the fact that with an


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L/D = 10 L/D = 12.22 L/D = 15.56 L/D = 18.89

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often arrangement of rings the pulsation arising behind the intensifier will have no time to fade sufficiently on the way to the following intensifier and will defuse to the flow core. Thus intensity of pulsation will increase and consequently the turbulence of flow will occur. This results in significant growth of hydraulic resistance with small increase of heat transfer. As hot layers diffuse to the center of flow, and the cold ones move to wall area, the gradient of temperature in the boundary layer decreases, and thus heat transfer decreases.

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Distance in mm

Fig. 7 Temperature profiles at the channel exit for smooth tubes with different length

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Fig. 9 Temperature profiles at the channel exit for different ring spacing

for laminar natural convection in smooth vertical tubes can be expressed as: 0:31 N u ¼ 0:33 Ra#

ð20Þ

Relationship Between Reynolds Number and Rayleigh Number: Figure 11 shows the relationship between experimentally obtained modified Reynolds number and modified Rayleigh number, which are plotted with logarithmic scales. This correlation can be obtained as:

Relationship Between Nusselt Number and Rayleigh Number: Figure 10 shows the relationships between the experimentally obtained average Nusselt number and modified Rayleigh number, which is plotted with log-log scale. This correlation

1 = Re# ¼ 0:49 Ra# 3

ð21Þ

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Empty s = 225mm s = 150mm s = 112mm s = 75mm

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L/D = 10 L/D = 12.22 L/D = 15.56 L/D = 18.89 Eq. 20 Upper Line + 10 % Lower Line - 10 %

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Fig. 8 Temperature profiles at the channel exit for tubes with discrete rings

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Fig. 10 Relationships between the experimentally obtained average Nusselt number and modified Rayleigh number


Exp Tech (2017) 41:585–603

Modified Reynolds Number

100

(vii). Another correlation between modified Rayleigh number and modified Reynolds number was found as: 1 = Re# ¼ 0:49 Ra# 3 , which can predict the data accurately within ±10% error. L/D = 10 L/D = 12.22 L/D = 15.56 L/D = 18.89 Eq. 21 Upper Line + 10 % Lower Line - 10 %

10

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References 1. 2. 1E7

Modified Rayleigh Number

Fig. 11 Relationship between experimentally obtained modified Reynolds number and modified Rayleigh number

Conclusions The natural convection heat transfer in heated vertical pipes has been studied experimentally, both for smooth tubes and for tubes with internal rings. The effects of channel length, imposed wall heat flux and also the effects of ring thickness and ring spacing on the characteristics of natural convection heat transfer are examined in detail. The following conclusions are drawn from the present investigation.

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(i). Axial variation of local wall temperature increases along the height of the cylinder but decreases slightly towards the end, which may be due to heat rejection from the end of the tubes. (ii). Temperature of air at channel exit is minimum at the center of the pipe and increases towards the wall of the pipe for cases considered in this experimental investigation. (iii). Average heat transfer rate from the internal surfaces of a heated vertical pipe increases with providing discrete rings. (iv). Average heat transfer rate increases with increasing the thickness of the rings up to a certain limits, beyond which it decreases. (v). Average heat transfer rate increases with increasing the number of rings i.e. reducing the spacing between the rings up to a certain value of spacing, but further reduction in spacing, reduces the heat transfer rate from the internal wall to air. (vi). A correlation between average Nusselt number and modified Rayleigh number was found as: Nu = 0.33 x (Ra#)0.31, which can predict the data accurately within ±10% error.

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Tanda G (1993) Natural convection heat transfer from a staggered vertical plate Array. J Heat Transf 115:938–945 Sparrow EM, Prakash C (1980) Enhancement of natural convection heat transfer by a staggered Array of discrete vertical plates. ASME J Heat Transf 102:215–220 Anug W, Beith KI, Kessler TJ (1972) Natural convection cooling of electronic cabinets containing arrays of vertical circuit cards. ASME Paper No.72-WA/HT-40, 26–30 Capobianchi M, Aziz A (2012) A scale analysis for natural convective flows over vertical surfaces. Int J Therm Sci 54: 82–88 Jha BK, Ajibade AO (2012) Effect of viscous dissipation on natural convection flow between vertical parallel plates with time-periodic boundary conditions. Commun Nonlinear Sci Numer Simul 17: 1576–1587 Eckert ERG, Soehngen E (1951) Interferometric studies on the stability and transition to turbulence of a free convection boundary layer. Heat Transfer ASME-IME. London, 321–323 Elenbaas W (1942) Heat dissipation of parallel plates by free convection. Physica 9:1–28 Sernas V, Fletcher LS, Aung W (1972) Heat transfer measurements with a Wallaston prism Schlieren interferometer. ASME Paper No.72-HT-9, Presented at the AIChE-ASME Heat Transfer Conf, Denver, 6–9 Sparrow EM, Bahrami PA (1980) Experiments in natural convection from vertical parallel plates with either open or closed edges. ASME J Heat Transf 102:221–227 Akbari H, Borges TR (1979) Free convective laminar flow within Trombe wall channel. Sol Energy 22:165–174 Tichy JA (1983) The effect of inlet and exit losses on free convective laminar flow in the Trombe Wall channel. J Sol Energy Eng 105(2):187–193 Levy EK, Eichen PA, Cintani WR, Shaw RR (1975) Optimum plate spacing for laminar natural convection heat transfer from parallel vertical isothermal flat plates, experimental verification. ASME J Heat Transfer 97:474–476 Sankar M, Park Y, Lopez JM, Do Y (2011) Numerical study of natural convection in a vertical porous annulus with discrete heating. Int J Heat Mass Transf 54:1493– 1505 Du DX, Tian WX, Su GH, Qiu SZ, Huang YP, Yan X (2012) Theoretical study on the characteristics of critical heat flux in vertical narrow rectangular channels. Appl Therm Eng 36:21–31 Kang GU, Chung BJ (2010) The experimental study on transition criteria of natural convection inside a vertical pipe. Int Commun Heat Mass Transfer 37:1057–1063 Dey S, Chakrborty D (2009) Enhancement of convective cooling using oscillating fins. Int Commun Heat Mass Transfer 36:508–512 Buonomo B, Manca O (2010) Natural convection slip flow in a vertical micro channel heated at uniform heat flux. Int J Therm Sci 49:1333–1344

Author's personal copy Exp Tech (2017) 41:585–603 18.

19.

20. 21.

Morshedy SEE, Alyan A, Shouman L (2012) Experimental investigation of natural convection heat transfer in narrow vertical rectangular channel heated from both sides. Exp Thermal Fluid Sci 36: 72–77 Nayak RC, Roul MK, Sarangi SK (2017) Experimental investigation of natural convection heat transfer in heated vertical tubes. Int J Appl Eng Res 12:2538–2550 Vliet GC (1969) Natural convection local heat transfer on constantheat-flux inclined surfaces. J Heat Transf 91:511–516 Churchill SW, Chu HHS (1975) Correlating equations for laminar and turbulent free convection from a vertical plate. Int J Heat Mass Transf 18:1323–1329

603 22.

23.

24.

Gbadebo SA, Said SAM, Habib MA (1999) Average Nusselt number correlation in the thermal entrance region of steady and pulsating turbulent pipe flows. Heat Mass Transf 35: 377–381 Hernandez J, Zamora B (2005) Effects of variable properties and non-uniform heating on natural convection flows in vertical channels. Int J Heat Mass Transf 48:793–807 Velmurugan P, Kalaivanan R (2016) Energy and exergy analysis in double-pass solar air heater. Sadhana 41:369–376