Quantitative and Qualitative Energy Assessments of

Quantitative and Qualitative Energy Assessments of Floor Heating and Skirting Board Heating Systems in a Room

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Morteza Abdolzadeh 1; Mohammad Saleh Sargazizadeh 2; and Mohammad Hadi Dehghan 3

Abstract: In the present study, energy and exergy analyses of two commonly used heating systems, including floor heating and skirting board heating, were investigated in a room. For this purpose, first the energy analysis of each heating system was carried out using an in-house computer code along with the computational fluid dynamics (CFD) method. The room temperature distributions as well as the energy efficiencies of the both heating systems were found and compared with each other in the same conditions. Second, the exergy analyses of the both systems were evaluated. Then, the exergy destructions of these two systems were obtained and discussed. Results showed that with equally generated heat flux in the both systems, the total thermal efficiency of the skirting board heating system was 8% more than that of the floor heating system. However, the skirting board heating system could not provide good thermal conditions in the room, especially when there was a window on the room’s walls. The exergy analysis also showed that the thermodynamic second law efficiency of the thermal skirt system was 4% higher than that of the floor heating system. Although the exergy destruction between the supplied hot water and the room air in the skirting board heating system was more than that of the floor heating system (i.e., 40%), the overall exergy performances of these two systems were still close to each other. Furthermore, it was concluded that the floor heating system followed more closely the criteria of thermal conditions in comparison with the skirting board heating system. DOI: 10.1061/(ASCE)EY.1943-7897.0000385. © 2016 American Society of Civil Engineers. Author keywords: Exergy; Energy; Floor heating; Skirting board; Efficiency; Exergy destruction.

Introduction Nowadays, water-based heating systems are widely used to heat indoor spaces of buildings. Water is first heated in the heat exchanger of the heating system and then piped to spaces. After heating the spaces, the exit water from the room is returned to the heat exchanger for starting a new heating cycle. In this system, the radiation heat transfer has a significant portion of the supplied heat transfer of heating systems in the room. Generally, heating systems are divided into two categories based on the temperature of their radiant surfaces, namely high temperature and low temperature (Watson and Chapman 2001). The low-temperature radiant heating systems, such as floor heating, mainly provide a larger area for heat transfer rather than a high temperature difference between the radiant surface and room air. The floor heating system is an energy-efficient system compared to other heating systems. It provides better thermal conditions for the residents of a building. In recent years, floor heating systems have been extensively used in many North American and European countries owing to low energy consumption and good level of thermal conditions. The other advantages of floor heating system are no noise owing to the absence 1

Assistant Professor, Dept. of Mechanical Engineering, Graduate Univ. of Advanced Technology, End of Haft Bagh Highway, 7631133131 Kerman, Iran (corresponding author). E-mail: [email protected] 2 M.Sc. Student, Dept. of Mechanical Engineering, Graduate Univ. of Advanced Technology, End of Haft Bagh Highway, 7631133131 Kerman, Iran. E-mail: [email protected] 3 M.Sc. Student, Dept. of Mechanical Engineering, Graduate Univ. of Advanced Technology, End of Haft Bagh Highway, 7631133131 Kerman, Iran. E-mail: [email protected] Note. This manuscript was submitted on December 10, 2015; approved on April 13, 2016; published online on June 27, 2016. Discussion period open until November 27, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Energy Engineering, © ASCE, ISSN 0733-9402. © ASCE

of a mechanical blower, small difference between the temperature of supplied hot water and room set-point temperature, and nearly uniform temperature distribution all over the heated space (Miriel et al. 2002). These advantages drew the attention of researchers and engineers to consider these systems for heating spaces. So far, many studies have been carried out in this regard. Meir et al. (2003) developed a method to control the temperature of floor heating systems in buildings. They showed that this method decreased the response time and provided a closer following of outdoor temperature changes. They also showed that this method was more efficient than the traditional thermostat systems. Laouadi (2004) developed a semianalytical model for radiant heating and cooling systems to calculate the heat transfer inside the building construction assemblies. His model predicted the performance of heating systems and tracked the results of a full twodimensional numerical model. Strand and Baumgartner (2005) studied cooling and radiant systems and summarized the issues of past studies and then provided a model that resolved the concerned issues like modeling of a building with any size as well as its associated HVAC system. Weitzamann et al. (2005) presented a two-dimensional computational model of heat losses and temperatures in a slab on a grade floor with floor heating system. They investigated the influences of the floor construction and foundation characteristics (i.e., materials used and layer arrangement) on the performance of the floor heating system. They found that the foundation had a large impact on the energy consumption of buildings heated by the floor heating. Sattari and Farahaneie (2006) numerically studied the effects of design parameters on the performance of a typical radiant floor heating system. They revealed that the type and thickness of the floor cover were the most important parameters in the design of radiant heating systems because these parameters greatly impacted on heat transfer exchanged between the floor and the room air. Zukowski (2007) developed an analytical model to predict a minimum required

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air jet velocity to block downdrafts in a room. He showed that the draft discomfort inside the occupied room was less than the upper limit value recommended by the international standard. Myhren and Hoimberg (2008) investigated the interaction between a conventional two-panel and air supply ventilation. They showed that the radiators supplying with low-temperature water flows had approximately the same output heat as the conventional hightemperature radiators. Hasan et al. (2009) studied the thermal performance of an apartment building with a combined system that included radiators in rooms and floor heating in bathrooms. They indicated that the combined low-temperature water heating system performed well and was able to maintain the zones within the required temperature levels. Jin et al. (2010) proposed a calculation method for the prediction of the floor surface temperature in radiant floor heating–cooling system. They developed a new formula to estimate the floor surface temperature. Their model predicted the experimental and numerical results with reasonable accuracy. Ren et al. (2010) studied a very low-temperature radiant heating–cooling indoor end system for efficient use of renewable energies. They showed that 50 W per meter of tube length could be achieved with the medium temperature of 30°C for heating and 15°C for cooling. Hewitt et al. (2011) assessed the performance of an air source heat pump that was connected to a radiator system. They showed that the pump efficiency would increase using a low temperature radiator. Pinard et al. (2012) investigated the effect of induced stack on the enhancement of the heat output from a room heater. They showed that this method could enhance the total output heat by 24%. Wu et al. (2015) proposed a simplified model to calculate the temperature and heat transfer coefficient of a floor heating system. Their results showed that the surface temperature and heat transfer of radiant floor calculated by the proposed model agreed very well with the simulated data. Xia and Zhang (2016) proposed a new doublelayer radiant floor system with phase change material. Their results showed that the double-layer radiant floor system with phase change material could hit the required thermal conditions of users under heating mode. They also indicated that the energy consumption of the system was lowered during thermal storage process. The skirting board heating system is a revolution in the central heating systems, which combines packed piping and bulky radiators into one clean, good looking, space-saving, and easy-to-clean unit. A thermal skirt looks like a slightly larger skirting board around the edge of the room. It is made from a hi-tech extruded heat-radiating alloy polymer or metal alloys that come in a variety of colors which can be matched with any room. Two pipes are behind the facial skirting board to transfer the generated hot water into the heating system. The heat of flowing water is conducted in the face of the board and radiated into the room. This heat is evenly radiated into the room, because the skirting board goes right around the edges of the room. It should be stated that skirting board heaters supplied by 75–90°C temperatures of water flow are normally considered as high-temperature heating systems, and 45–55°C water temperatures are known as medium- and low-temperature systems, respectively. Ploskićand and Holmberg (2010a) studied the performance of three hydronic skirting board heating systems. The main target of their study was to show whether thermal skirting boards worked with low-temperature water supply and were able to suppress strong downdrafts or not. They showed that the thermal performance of the hydronic skirt heaters with low-temperature water supply must be improved in order to reverse a strong downdraft. Ploskić and Holmberg (2010b) investigated the thermal performance of a low-temperature baseboard heating system when airflow of cold outdoor air (ventilation) was blown through the baseboard heater. The performance of the system was studied with different ventilation rates at typical outdoor temperatures during the © ASCE

Swedish winter season. They showed that the low-temperature baseboard heating systems integrated with air supply could meet the international comfort requirements, and lead to energy savings in cold climates. These authors later (Ploskić and Holmberg 2014) investigated the thermal performance of the hydronic radiant baseboards used for space heating in built environments and compared its performance with five conventional radiator systems. They revealed that the mean heat transfer coefficient of the investigated radiant baseboards was approximately 50% higher than the mean heat transfer coefficient of the conventional radiator heating systems. As stated previously, skirting board and floor heating systems are known as high-temperature and low-temperature heating systems, respectively. It seems that the higher exergy destruction due to the high temperature difference between the skirting board and room air, which is a sign of exchanging low quality of thermal energy into the room, would be happening in skirting board heating system compared to floor heating system. Thus, it is essential to carry out a combined energy and exergy analysis of skirting board and floor heating systems, as well as their comparison to further clarify the advantages and disadvantages of these two systems. It should be pointed out, based on the reviewed literature, this comparison has not been done yet. For doing this purpose, energy performances of these two systems were first obtained in a room (e.g., a study room or an office room) having a door and a window. Then the exergy analyses of the systems were evaluated and finally, based on the energy and exergy assessments, the system with better thermal conditions was introduced.

Description of the Studied Systems Fig. 1 is a schematic plan of the room that was selected in order to study the energy and exergy analyses of both the heating systems computationally. The room dimensions were 4 × 4 × 2.7 m. The two introduced heating systems are shown in Fig. 2. In this study, the outdoor temperature was assumed as −5°C and the materials of the room components, including door, window, and walls were selected based on the materials recommended in the ASHRAE handbook. The thermal resistances and dimensions of all the room components are given in Table 1. The piping sketches of the two heating systems are also shown in Fig. 1. The characteristics of the piping system, as well as the inlet and outlet temperatures of water and the water mass flow rate of each system, are given in Table 2. All the piping information and thermal characteristics of the systems were chosen based on the EN-1264 ASHRAE standard (ANSI/ ASHRAE 2001). It should be pointed out that the piping system characteristics as well as the water mass flow rate for each system in the studied room were obtained using the LoopCAD version 14 software. To obtain the specified information in this software, the room temperature was assumed as 21°C and then the supplied heat fluxes for heating the room in each system were calculated based on the data in Tables 1 and 2. It should be stated that the heat transfer rates were found in two cases, namely the room with no door and window (Case 1) and the room with a door and window (Case 2; Table 3). The room space is not ventilated, thus the effect of the downdraft was ignored. In the mean time, Case 1 was considered to investigate the effect of the door and window on the room temperature distribution.

Governing Equations Energy The air temperature distribution inside the room was determined in order to evaluate the room thermal performance. Thus, the

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Fig. 1. Schematic of thermal skirt boarding and floor heating systems in the study room

Fig. 2. Schematic of heating systems in the present study

Table 1. Thermal Resistances and Dimensions of the Room Components Component Wall Ceiling Window Door

Code in ASHRAE

Thermal resistance (m2 · K=W)

Dimension (m2 )

RW28 RR11 30424C 3063D

2.3 2.7 0.2 0.4

2.7 × 4 4×4 2 × 1.5 2.7 × 1.2

governing differential equations of air were solved to find the room temperature distributions in Cases 1 and 2. These equations were mass, momentum, and energy. The following assumptions were used to solve these airflow equations: laminar flow, incompressible flow, three-dimensional flow, and the gravity act in the vertical direction. The equations are as follows: ∂ui ¼0 ∂xi

Table 2. Piping System Characteristics and Inlet and Outlet Water Temperatures in the Floor Heating and Skirting Board Heating Systems Selected Based on Wu et al. (2015) Parameter Diameter of pipes (mm) Length of piping (m) T in (°C)-Case 1 T in (°C)-Case 2 T out (°C)-Case 1 T out (°C)-Case 2 T surr (°C) ˙ w (kg=s) m © ASCE

Floor heating

Skirt heating

20 51 50 36 40 30 −5 0.0344

15 29.6 70 60 60 54 −5 0.0316

ρ

ð1Þ

∂ui ∂u ∂ ∂ui ∂p − þ ρuj i ¼ μ þ gi βðT room − T outdoor Þ ∂xj ∂xj ∂xi ∂t ∂xj ð2Þ

ρ

∂T room ∂T ∂ ∂T þ ρuj room ¼ kair room ∂xj ∂t ∂xj ∂xj

ð3Þ

where u = air velocity; p = air pressure; g = gravitational acceleration; β = coefficient of thermal expansion; k = thermal

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Table 3. Heat Transfer Rates of the Walls, Ceiling, Floor, Door, and Window in Two Heating Systems Based on T outdoor ¼ −5°C and T room ¼ 21°C for the Ventilated Room Space Case number 1 2

Heating system

Ceiling

Wall 1

Wall 2

Wall 3

Wall 4

Door

Window

Total heat loss

Floor

Skirt

Floor (W) Skirt (W) Floor (W) Skirt (W)

−296 −296 −296 −296

−115 −110 −115 −110

−140.4 −140 −140.4 −140

−140.4 −140 −140.4 −140

−104.2 −110 −104.2 −110

−198 −198 0 0

−328 −328 0 0

−1,322 −1,322 800 800

1,322 — 800 —

— 1,322 — 800


conductivity; ρ = air density; μ = air viscosity; T = temperature; T out = outdoor air temperature; and xi = x, y, z directions. Exergy

S˙ gen;total ¼ S˙ gen1 þ S˙ gen2

ð11Þ

where S˙ gen1 = entropy generation between the supplied hot water and the radiant surface and S˙ gen2 = entropy generation between the radiant surface and the room air. They are calculated as follows:

In this section, the room exergy equations are presented and discussed. The exergy balance of the room is as follows:

˙ HL =T s ˙ pipe C lnðT out =T in Þ þ Q S˙ gen1 ¼ m

ð12Þ

˙ out − EX ˙ destruct ¼ dEX st ˙ in − EX EX dt

˙ HL ð1=T room − 1=T s Þ S˙ gen2 ¼ Q

ð13Þ

ð4Þ

For steady-state condition, the new equation is ˙ in − EX ˙ out − EX ˙ destruction ¼ 0 EX

ð5Þ

˙ HL = total heat loss of the room; T in = inlet temperature of where Q hot water; T out = outlet temperature of hot water; and T s = radiant surface temperature. The exergy of heat losses is calculated as follows: ˙ HL ¼ EX ˙ W − T room S˙ gen;total EX

The inlet exergy of the room is ˙ in ¼ EX ˙ W EX

ð6Þ

˙ W¼m ˙ pipe ðΔhw − T surr Δsw Þ EX

ð7Þ

˙ W = exergy of the supplied hot water into the room; m ˙ pipe where EX = water flow rate inside the pipe; Δhw = enthalpy difference between the inlet and outlet water; and Δsw = entropy difference between the inlet and outlet water. The outlet exergy is ˙ out ¼ EX ˙ HL EX

ð8Þ

˙ HL = exergy of heat losses. The destruction exergy is as where EX follows: ˙ destruction ¼ EX ˙ W − EX ˙ HL EX

ð9Þ

˙ destruction ¼ T room S˙ gen;total EX

ð10Þ

where S˙ gen;total = total entropy generation between the supplied hot water in the room and the room air (Fig. 3). It is as follows:

ð14Þ

The exergetic efficiency is ηII ¼

EX HL EX F

ð15Þ

where EX F = exergy of fuel thermal energy. It should be pointed out that exergy of CH4 thermal energy at the stochiometric conditions was 51,859 kJ=kg-Fuel (Winterbone 1987). It also should be stated that the room temperature required for finding the dependent temperature properties in Eqs. (4)–(15) were calculated based on the average temperature obtained by computational fluid dynamics (CFD) previously. Boundary Conditions Fig. 4 shows the room modeled in the present research. The room was simulated in two cases, namely with (Case 1) and without (Case 2) a door and window. It was assumed that an equal heat flux enters into the room in each heating system. The air change rate was assumed to be zero in the room and the supplied heat and

Fig. 3. Sketch of entropy generations and exergy destruction between the supplied hot water and the room air © ASCE

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˙ F = released heat from where ηWH = water heater efficiency and Q the fuel. All the heat fluxes were calculated based on the information given previously. The heat fluxes given to the surrounding air were calculated using the wall materials (details given in Table 1), T amb ¼ −5°C, and hair;outdoor ¼ 20 W=m2 · K. The effects of surface radiation exchanged between the room walls were not considered here. The simulation was done in night hours, when no solar radiation existed over the room. Moreover, 1,596 W of thermal power was delivered to the room by the skirting boards using the equation proposed by Ploskic and Holmberg (2014) and the skirting board’s information (i.e., 14.4 m length, 0.1 m height, 70°C inlet water temperature, and 60°C outlet water temperature). This heat power was 21% higher than the demand heat of room in Case 1. Fig 4. Study system modeled in the software

Numerical Method total heat loss are the same in the both heating systems. The total heat losses from all the walls as well as the floor and ceiling for Cases 1 and 2 are calculated as follows: ˙ HL ¼ U wallþceiling ðT room − T outdoor Þ þ U floor ðT room − T ground Þ Q ð16Þ where U wallþceiling = total heat transfer coefficient of walls and ceiling; U floor = floor total heat transfer coefficient; T outdoor = outdoor temperature; T ground = ground temperature; and T room = room temperature. The supplied heat is calculated as follows: ˙w ¼Q ˙ wall þ Q ˙ floor þ Q ˙ ceiling ¼ Q ˙ HL Q

ð17Þ

˙w ¼m ˙ pipe ðhin − hout Þ ¼ m ˙ pipe Cp ðT in − T out Þ Q

ð18Þ

˙ wall = total heat loss of ˙ HL = total heat loss from the room; Q where Q ˙ floor = floor heat loss to the ground; Q ˙ ceiling = ceiling the walls; Q ˙ w = supplied heat to the water by the gas water heater; heat loss; Q ˙ w = supplied heat to the water from the water heater; and hin and Q hout = inlet and outlet enthalpies of the radiant systems, respectively. The fuel thermal energy that should be supplied to the gas water heater is as follows: ˙ F ¼ ηWH Q ˙ HL Q

ð19Þ

The differential governing equations of airflow was solved using ANSYS version 14. These equations were discretized and converted into algebraic equations using the finite volume method. The coupled velocity and pressure equations were solved using the SIMPLE algorithm. The air flow in both the systems was laminar, that is, Ra < 109 . The Rayleigh numbers were obtained from Lch ¼ 1 m (the floor heating) and Lch ¼ 0.15 m (the skirting board) as well as Pr ¼ 0.7, T ¼ 301 K, and T 0 ¼ 293 K. It should be mentioned that the laminar flow condition might not be held in a real room owing to obstructions (i.e., furniture) and ventilation inlets/outlets. However, the focus was on the performance comparison of the floor heating and the skirting board heating systems in same flow conditions. Finer meshes adjacent to the walls were implemented to resolve the effect of the boundary layer. Based on the geometry characteristic, structured meshes were used. All the flow governing equations were solved simultaneously and the computation was stopped when the residual of flow properties approached 10−5 . The process mentioned was repeated several times for different mesh sizes. To find the optimum mesh size, the room mean temperature and the friction coefficient on Wall 3 were calculated based on different numbers of cells. The results are shown in Figs. 5(a and b). As shown in these figures, 920,000 cells guarantee that the results of the flow field are independent of the mesh size with a reasonable computation time. The exergy equations were solved using an inhouse computer code written in FORTRAN version 6.1. This code

Fig. 5. Mesh dependency checking with two parameters: (a) mean temperature; (b) skin friction versus cell numbers © ASCE

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was later linked with ANSYS FLUENT 14 in order to use the predicted room temperature value in the exergy calculations.

Results and Discussion


Validation To verify the CFD results of the present study, the room air temperatures of the skirting board system and floor heating system in Case 2 were compared with the available measured data for these two systems in the literature [Olesen et al. 1980; Fig. 6(a)]. The conditions in the present simulation and the experimental study for the validation were: T out ¼ −5°C, T room ¼ 21°C, T floor;floor heating ¼ 27°C, T skirt ¼ 47°C, room height ¼ 2.7 m, and air changes rate ¼ 0. Note, the comparisons were performed under the same boundary conditions, same room dimensions (i.e., 4 × 4 × 2.7 m), and same flow pattern (i.e., laminar flow) of the Olesen et al. study. Fig. 6(a) shows that the maximum error between the results of the present study and the measured data is less than 2% [Fig. 6(b)] and this states that the present simulation predicts the room temperature with reasonable accuracy compared to the experimental data. Energy Analysis The temperature distributions adjacent to the floor in Cases 1 and 2 for the floor heating system are shown in Figs. 7(a and b). As shown in these figures, when there is no door and window in the room, the maximum temperature occurs in the middle line of the floor surface, and it is approximately 28°C. In the case of including a door and window, this maximum temperature reaches 25.3°C and happens at the very right corner of the room. The floor temperature distributions of Cases 1 and 2 in the skirting board heating system are shown in Figs. 7(c and d), respectively. As shown in these figures, when there was no door and window, the maximum temperature occurred close to the walls and it was approximately 25.3°C. However, this temperature was not the maximum temperature in the room because the maximum temperature was above the skirting board, that is, 15 cm above the floor, and was 33°C. Fig. 7(d) shows the floor temperature distribution in Case 2. As shown in this figure, the temperature distribution changed compared to that in Case 1. This figure also shows that

the uniformity of temperature far from the walls was no longer held. Fig. 8 shows the temperature distribution above the skirting board on Wall 4. As shown in this figure, the maximum temperature was approximately 33°C and was at the bottom of Wall 4 far from the window. Fig. 8(b) shows the variation of the room temperature on Line 1 (i.e., adjacent to Wall 4). As shown in this figure, by getting close to the ceiling, the temperature on this line decreased to 25°C. Fig. 8(c) shows the variation of the room temperature on Line 2 (i.e., adjacent to Wall 4 passed across the window height). As shown in this figure, the temperature decreased below the bottom side of the window, and owing to high heat loss of the window to the outdoors, this trend reversed above the bottom side of the window. Fig. 9(a) shows a comparison between the temperature distributions of skirting board and floor heating systems across Line 2 on Wall 4. As shown in this figure, the floor heating system had the same trend of temperature variation compared to the thermal skirt system. However, it had a lower temperature at the bottom of the wall and higher temperature far from the bottom as well as less temperature variation across the room height compared to the skirting board system. This fact showed that the floor heating system had a better thermal performance than the skirting board system adjacent to the window. Fig. 9(b) shows the temperature distributions on Line 1 shown in Wall 4, at different distances from the wall in the skirting board system. As shown in this figure, a low temperature variation was seen far from Wall 4 and this yielded a better thermal performance of the skirt boarding system in the middle of the room. Fig. 10 shows the room temperature variations versus the distance from Wall 4 at different heights of the room in the two heating systems. As shown in this figure, the room temperature adjacent to Wall 4 across the room height in the floor heating system was higher than the skirting board system. This figure also shows that a sudden decrease close to Wall 4 was seen in the room temperature at low height of the room in Case 1. This decrease occurred in the middle of the room in Case 2 [Fig. 11(a)] because there was no window in this case. It was also seen that there was a sudden increase in the low heights of the room far away from Wall 4 in Case 1 in the floor system and this increase occurred in the middle of the room in Case 2 [Fig. 11(a)]. This increase is due to the high heat loss of Wall 4 in Case 1. Fig. 10(a) also shows that the mean temperatures of the floor heating system all over the distances were higher than that of the skirting board system. This means that the thermal skirt system was not able to provide good thermal

Fig. 6. (a) Verification of the room air temperature obtained in the present study with the measured temperatures (Olesen et al. 1980); (b) the error created between the measured and simulated results in the floor and thermal skirt heating systems, T out ¼ −5°C, T room ¼ 21°C, T floor;floor heating ¼ 27°C, T skirt ¼ 47°C, room height ¼ 2.7 m, air changes rate ¼ 0 © ASCE

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Fig. 7. Temperature distributions (K) adjacent to the floor in skirt boarding and floor heating systems: (a) Case 1—floor heating; (b) Case 2—floor heating; (c) Case 1—skirt boarding; (d) Case 2—skirt boarding

conditions in the room. However, this condition was affordable by increasing the supplied heat into the room. Fig. 11(a) shows the temperature distributions of both the heating systems at different distances from the walls in Case 1. As shown in this figure, the maximum temperature was seen in the middle of the room in the floor heating system whereas this place had the minimum temperature in the skirting board system. Fig. 11(b) shows the comparison of room temperatures in Cases 1 and 2 in the two heating systems. The temperature adjacent to Wall 4 in Case 1 was higher than that in Case 2 because the window increased the wall heat loss. The room temperature difference between Cases 1 and 2 in the skirting board system was higher than the floor heating system. The process was held in the steady-state condition of the heating systems. However, as the system started up, it first needed to bring the temperature of water (≈ 15°C) inside the piping system as well as the tank water to the steady-state inlet temperature of the water heater given in Table 2. It meant that extra heat was required to warm up water at the beginning of the system startup. The corresponding required equations for calculating the unsteady parameters are given in Appendix [Eqs. (20)–(23)]. Fig. 12(a) shows the rate of energy efficiency of the floor heating and skirting © ASCE

board systems during the system initial operating time. As shown in this figure, at the early time of startup, the total thermal efficiencies of both heating systems were low. It should be mentioned that it took between 6 and 8 min for the water inside the heating systems to reach the steady-state temperature of inlet hot water in the both cases. As shown in this figure, it took approximately 9 h in both the heating systems to reach the steady-state efficiency. It is also shown that from the beginning time, t ≥ ti , the energy efficiency of the thermal skirt system was 8% higher than the floor heating system. Fig. 12(a) shows the initial energy efficiency of the two systems for two cases, namely t ≤ ti and t → ∞. As shown in this figure, the thermal efficiencies of the thermal skirt and floor heating systems were 16 and 24%, respectively, for t ≤ ti. It also indicated that the thermal efficiency of the thermal skirt system was less than that of the floor heating system only in t ≤ ti of the system operating time. This was due to the higher temperature of hot water inside the thermal skirt system compared to the floor heating. Fig. 12(b) also shows the steady-state thermal efficiencies of the heating systems, that is, ηt → ∞. As shown in this figure, in this case the thermal efficiency of the thermal skirt system was approximately 8% higher than that of the floor heating system.

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Fig. 8. Room temperature distribution on Wall 4: (a) 2D temperature; (b) 1D temperature on Line 1; (c) 1D temperature on Line 2

Fig. 9. Comparison of the temperature distributions: (a) between skirt boarding and floor heating systems across Line 2 on Wall 4; (b) different distances from Line 2 on Wall 4 © ASCE

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Fig. 10. Room temperature variations versus the distance from Wall 4 at different heights of the room in (a) a floor heating system; (b) a skirt boarding system

Fig. 11. Air temperature distributions adjacent to Wall 4 in Cases 1 and 2 in the two heating systems: (a) comparison of the two systems in Case 1; (b) comparison of Cases1 and 2

Fig. 12. (a) Energy efficiencies variations during the initial time of system startup; (b) initial and steady energy efficiencies in the floor heating and thermal skirt heating systems © ASCE

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Exergy Analysis


Fig. 13 shows the exergy efficiencies of the floor and skirting board systems during the initial operating times. As shown in this figure, at these times the exergies in both the heating systems were low till they approached the steady-state condition. It is also shown that from the beginning time, t ≥ ti , the exergy efficiency of the thermal skirt system was 4% higher than the floor heating system. Figs. 13 and 14(a) shows the exergy destruction between the supplied hot water and the radiant surface and also the exergy destruction

between the radiant surface and the room air. As shown in this figure, the exergy destruction between the supplied hot water and the radiant surface in the skirting board system was lower than the floor heating system because this system had a lower temperature difference between the temperatures of supplied hot water and the radiant surface compared to the floor heating system. The exergy destruction between the radiant surface and the room in the floor heating system was lower than the skirting board system because this system had a lower temperature difference between the radiant surface and the room temperatures. Fig. 14(b) shows the total exergies in the two systems. As shown in this figure, despite the high exergy destruction of the skirting board system, this system still had a higher total exergy than the floor heating system. This was due to the higher temperature of supplying hot water in the skirting board heating system compared to the floor heating system.

Conclusions

Fig. 13. Exergy variations during the initial time of system startup

In the present research, the energy and exergy analyses of the floor and skirting board heating systems were carried out in a common used room. The energy analysis showed that in the case of the same supplied heat fluxes given to the room in the two systems, the floor heating system had a better thermal performance adjacent to the wall having a window compared to the skirting board system. This is a very significant characteristic of the floor heating system and a drawback of the thermal skirt system. This means that despite the higher thermal energy of the skirt boarding system (i.e., 8%) compared to the floor heating system, the skirting board system could not provide good thermal conditions in the room. Although the exergy destruction between the supplied hot water and the room in the skirting board system was higher (i.e., 40%) compared to the floor heating system, these two systems had almost the same second law efficiency. This fact also shows that the skirting board heating system is not as efficient as the floor heating system. Furthermore, this study clearly showed that the floor heating systems were very effective in terms of both energy end exergy performances compared to the skirting board system in the room having a window on its walls and this should not be ignored by the building designers. Generally, this study indicated that the skirting board heating system is more suitable to use in rooms with no windows on their walls. In this case, good thermal conditions are provided all over the room. Note that the purpose of this study was to compare the floor heating systems in terms of energy and average thermal conditions. Although laminar flows were assumed, however, in real offices (with furniture, openings, and other flows), higher Ra numbers are expected, therefore the flow might be turbulent and the results might differ. More research is required for a further detailed analysis in such conditions or something similar.

Appendix. Transient Condition To study the transient condition of the systems, it is first needed to find the volumes of water in the piping system as well as in the water heater tank. For doing this, the following equation was used: mw;tankþpipe ¼ ρw ðLpipe × Apipe þ V tank Þ

ð20Þ

where Lpipe = piping length; Apipe = pipe area; and V tank = volume of water heater tank. The extra heat to warm this volume of water is Fig. 14. (a) Exergy destructions between the supplied hot water and the radiant surface (1) and the radiant surface and the room (2); (b) comparison of the total exergies in floor and thermal skirt heating systems © ASCE

Qextra ¼ mw;tank

pipe CðT in;s

− 15°CÞ

ð21Þ

where T in;s = water inlet temperature at the steady-state condition. It should be pointed out that this extra heat should be provided by the

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gas heater and this means that a high amount of fuel is consumed when approaching the steady-state condition. The time required to reach the steady-state inlet temperature is ti ¼

˙ pipe m ˙ w;pipe m

ð22Þ

The total thermal efficiency of the system since the beginning (i.e., unsteady state to steady state) is calculated as follows:


ηth;total ¼

QHL × ðti þ ts Þ 0 ðt ≤ ti Þ ≤ ts ≤ ∞ Qextra × ti þ QF × ηWH × ts

ð23Þ

where ts = time of heating after reaching the steady-state temperature.

Notation The following symbols are used in this paper: A = area (m2 ); B = thermal expansion coefficient (1=K); Cp = specific heat capacity (J=kg · K); E˙ = energy rate (W); ˙ = exergy rate (W); Ex K = thermal conductivity coefficient (W=m · K); ˙ = flow rate (kg=s); m L = length (m); H = enthalpy (J=kg); P = pressure(pa); ˙ = heat transfer rate (W); Q S = entropy (J=kg · K); T = temperature (K); U = heat transfer coefficient; V = volume (m3 ); u, v, w = air flow velocity components (m=s); η = efficiency; and ρ = density (kg=m3 ). Subscripts Des F gen HL I In L out S St surr Th W Wh μ

= = = = = = = = = = = = = = =

destruction; fuel; generation; heat loss; initial; inlet; loss; outlet; steady; storage; surrounding; thermal; water; water heater; and viscosity (kg=m · s).

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© ASCE

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