Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 127 (2015) 95 – 101
International Conference on Computational Heat and Mass Transfer-2015
Numerical Simulation of Heat Transfer Enhancement in Periodic Converging-Diverging Microchannel Abhishek Kumar Chandraa, Kaushal Kishora, P. K. Mishrab, Md. Siraj Alama* b
a Department of Chemical Engineering, Motilal Nehru National Institute of Technology, Allahabad-211 004, India Department of Mechanical Engineering, Motilal Nehru National Institute of Technology, Allahabad-211 004, India
Abstract Heat transfer performance and fluid flow in three-dimensional converging–diverging microchannel of circular cross-section are studied numerically. Three different types of microchannel, diameter 100 µm and length 6.125 mm each are used for simulation for the Reynolds number range of 50 to 1000. The effect of Reynolds Number, converging/diverging angle and convergingdiverging cross-section length on pressure drop and heat transfer in proposed microchannels are investigated and discussed. The result indicated that the flow in the converging-diverging cross-section induces stronger recirculation and flow separation, which decreases with decreasing the converging and diverging angle and increases with increasing aspect ratio. However, the local and global heat transfer performances in the channels are improved by the converging-diverging cross-section at the expense of higher pressure drop compared to the straight channel with the same cross-section. Conversely, special attentions are given to analyze the thermal performance of microchannels through variation of thermal resistance with pumping power. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review underresponsibility responsibility organizing committee of ICCHMT – 2015. Peer-review under of of thethe organizing committee of ICCHMT – 2015 Keywords: converging-diverging flow; heat transfer; non-uniform microchannel; thermal performance
1. Introduction In the year 2009, International Technology Roadmap for Semiconductors (ITRS) has published a report, which makes clear that thermal management of new generation’s high performance chip packages is most important since dimensions decreases continually. Additionally highlighted, the operating performance and long term reliability of
* Corresponding author. Tel.: +91-532-227-1584; fax: +91-532-244-5101. E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of ICCHMT – 2015
doi:10.1016/j.proeng.2015.11.431
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these devices are also affected. For example, a high speed digital circuits containing 10 5 gates would dissipate 100 W. Therefore, heat removal demand makes thermal management so important and requires more effective cooling options. The most attractive and efficient solution for this problem is microchannel based circuits with liquid cooling media. Microchannel based cooling systems are very promising due to material and process compatibility with electronic system. However, their performance is still far from being quite satisfactory and lot of research efforts have to be done to solve the existing problem and develop an advanced microchannel cooling system which accommodate the high heat dissipation rates and associated fluxes. Although the need of enhancement in microchannel was first discussed by [1, 2] to meet high heat flux cooling needs. However, they recommended that enhancement techniques must be carefully evaluated with the increased pressure drop penalties in a given system. These techniques have acknowledged for enhancement of heat transfer in single phase flow in microchannels and minichannels [3]. The results implied that increase in heat transfer performance from these techniques placed a single-phase liquid system in competition with a two phase system. The cooling limits of single phase cooling media have been evaluated in plain channels [4] and investigated the use of variety of microstructures into the channels for heat transfer enhancement. Further, they investigated the pressure drop and heat transfer in an off-set strip fins enhanced microchannel for single phase fluid flow [5]. Experimental result shows that excellent improvement in heat transfer over plain or traditional microchannel with pressure drop penalty. On the other hand, polymeric microchannels with corrugated walls were analyzed for flow control and mixing [6]. The surface roughness effect on heat transfer was experimentally investigated in a rectangular microchannel [7]. The result shows that the local and average Nusselt numbers significantly departed from conventional theories for relative roughness 0.04 to 0.06. Some of the previous works are listed in Table 1. Table 1. Previous works on varying-cross section channels. Authors
Heat Transfer Enhancement technique
Results
Naphon (2007)
Flow disruption
Δp and Nu in the higher wavy angle channel are significant higher.
(40 Wavy channel) Colgan et al. (2007)
Flow disruption (staggered and continuous fins)
Able to cool chips with average power densities of 400 W/cm2 or more.
Brackbill & Kandlikar (2007)
Surface roughness (triangular element)
The roughness elements cause an early transition to turbulent flow.
Meis et al. (2010)
Flow obstacle (triangular, rectangular, and circular/elliptical)
The triangle obstacle is consistently better than the other configurations Next one is the circle and then, rectangle.
Sui et al. (2010)
Flow disruption (wavy channel)
The relative waviness can be increased along the flow direction, which results in higher heat transfer performance.
Zhang et al. (2010)
Surface roughness
Global heat transfer performance is improved by the roughness elements.
(triangle, rectangle and semicircle) Liu et al. (2011)
Surface microstructures
The microstructure shield shape groove has the best heat exchange performance
Dharaiya & Kandilkar (2013)
Surface roughness (Sinusoidal element)
Nu number increases with increase in roughness height. And no effects of roughness pitch.
Kuppusamy et al. (2014)
Secondary flow
Thermal boundary layer re-development and flow mixing affect the overall performance of MCHS.
It is observed that sinusoidal wall shape was the most common shape, studied in past with range of Reynolds numbers that covers both laminar and turbulent flows. It is also observed from the literatures that by the two important means heat transfer can be enhances in microscale; 1) by interrupting the thermal boundary and 2) by inducing the mainstream separation. In the current study the boundary layer separation and thermal boundary layer redeveloping concept in microscale are used to propose a new design of microchannel with periodic convergingdiverging cross-section and examine the local and average, flow and heat characteristics. In addition, numerical
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computations have been conducted to compare the pressure drop and heat transfer in the proposed microchannel to straight microchannel. The flexibility of CFD tools is utilized to examine the proposed microchannel in detail for better design of various microflow devices. 2. Model for periodic converging-diverging microchannel 2.1. Geometry description Typical configuration of microchannel with periodic converging-diverging cross-section is used in the present study is shown in Fig. 1. The hydrodynamic and thermal (convective) performance of newly proposed channels are compared with the baseline microchannel (straight microchannel), which have the same diameter and length. In this numerical study fluid domain are kept under constant heat flux and constant temperature, boundary conditions. In the microchannel cold water enters at a constant temperature of 300 K and gains the heat from the wall. In the current simulation studies, three microchannels of diameter 100 µm are used. Two of them are the newly proposed channel, shown in Fig. 2. The length for all the microchannels is same and it is 6.125 mm. Microchannel of type A & B has 24 numbers of converging–diverging cross-sections. The main objective of the current study is to analyze the effects of converging-diverging cross-section on the overall performance of the microchannel.
Fig. 1. Schematic of microchannel with periodic converging-diverging cross-section. 125 θ
125
62.5
125
125
62.5
r 100 µm
60 µm
100 µm
80 µm
z 62.5
62.5
Fig. 2. Computational domain of one module of converging-diverging cross-section of type A and B channel.
2.2. Mathematical Modeling In this investigation the minimum dimension of microchannel is greater than 10 µm, under such conditions, the continuum assumption is valid. Thus, the classical momentum, continuity and energy equations for laminar flow and heat transfer in microchannel can be presented with following assumption: 1) 3-dimensional, Steady-state, incompressible flow of a Newtonian fluid (2) The effect of body forces (gravity, etc.) are negligible (3) The thermophysical properties of both fluid is set as piecewise linear function and microchannel material are temperature-independent (4) Viscous dissipation is taken into consideration. The governing equations as follows: ͳ ߲ ߲ ͳ ߲ ሺߩݒݎ ሻ ሺߩݒఏ ሻ ሺߩݒ௭ ሻ ൌ Ͳ ߠ߲ ݎ ߲ݖ ݎ߲ ݎ
ߩ ቆݒ
߲ݒ ݒఏ ߲ݒ ݒఏଶ ߲ݒ ߲ ߲ ͳ ߲ ͳ ߲ ଶ ݒ ʹ ߲ݒఏ ߲ ଶ ݒ െ ݒ௭ ቇൌെ ߤ ቈ ൬ ሺݒݎ ൰ ଶ െ ߲ݎ ߠ߲ ݎ ݎ ߲ݖ ߲ ݖଶ ߲ݎ ߲ݎ߲ ݎ ݎ ߠ߲ ݎଶ ݎଶ ߲ߠ
(1)
(2)
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ߩ ൬ݒ
߲ݒ௭ ݒఏ ߲ݒ௭ ߲ݒ௭ ߲ ͳ ߲ ߲ݒ௭ ͳ ߲ ଶ ݒ௭ ߲ ଶ ݒ௭ ݒ௭ ൰ൌെ ߤ ቈ ൬ݎ ൰ ଶ ߲ݎ ߠ߲ ݎ ߲ݖ ߲ݎ ߲ ݖଶ ߲ݖ ݎ߲ ݎ ߠ߲ ݎଶ
ߩܥመ ൬ݒ
(3)
߲ܶ ݒఏ ߲ܶ ߲ܶ ͳ ߲ ߲ܶ ͳ ߲ଶܶ ߲ଶܶ ݒ௭ ൰ ൌ ݇ ቈ ൬ ݎ൰ ଶ ଶ ଶ ߠ߲ ݎ ߲ݎ ߲ݖ ߲ݖ ݎ߲ ݎ߲ ݎ ߠ߲ ݎ ଶ ߲ݒ ଶ ͳ ߲ݒఏ ߲ݒ௭ ଶ ߤ ቊ൬ ൰ ൬ ݒ ൰൨ ൬ ൰ ቋ ߲ݎ ߲ݖ ߠ߲ ݎ ଶ
ଶ
(4) ଶ
߲ݒఏ ͳ ߲ݒ௭ ߲ݒ௭ ߲ݒ ͳ ߲ݒ ߲ ݒఏ ߤ ቐ൬ ൰ ൬ ൰ ൭ ݎቀ ቁ൱൩ ቑ ߲ݖ ߲ݎ ߲ݖ ߠ߲ ݎ ߠ߲ ݎ ߲ݎ ݎ Three boundary conditions are required to close the above mathematical formulation are written as follows: x At the inlet boundary “velocity inlet” boundary condition is imposed. The temperature of the coolant is also specified at the inlet cross-section and the pressure is fixed to 1 bar. x At the surface of the channel no slip and no penetration boundary condition are imposed. i.e., ݒ ሺݎǡ ߠǡ ݖሻ ൌ Ͳǡ ݒఏ ሺݎǡ ߠǡ ݖሻ ൌ Ͳǡ ݒ௭ ሺݎǡ ߠǡ ݖሻ ൌ Ͳ x A uniform heat flux, q or a constant temperature condition is also imposed to the channel wall for two different cases. x At the outer boundary “pressure outlet” boundary condition is applied at the exit boundary and static gauge pressure is set to zero. The simulation is performed for the Reynolds number falls in the range of 50 to 1000. For constant heat flux condition 0.3 MW/m2 heat flux is applied on the wall and for constant wall temperature condition, the constant temperature 350oC is applied. 3. Numerical Scheme The classical continuity, Navier-Stokes and energy equations are solved along with the prescribed boundary condition using the finite volume based solver Fluent (ANSYS 15). The channel geometries are meshed using structured hexahedral cells. A strong refinement near the walls and in the channel inlet, outlet regions are built to better capture the fluid flow and heat transfer in the channel. The grid size is reduced until difference in the key parameters, f and Nu is less than 0.5% for two consecutive grid size Thus, a computational cell with 3.7×10 5 grids is employed throughout the computations. The mass, momentum and temperature governing equations are discretized using the second order upwind scheme. The flow field is solved using the standard SIMPLE (semi-implicit method for pressure-linked equations) algorithm. This is an iterative solution procedure; computation is initialized by guessing the pressure field. Later, momentum equation is solved to determine the velocity components. The pressure is updated using the continuity equation. The iterations are continued until the sum of residuals for all computational cells became negligible (less than 10−7) and velocity components do not change in successive iteration. The energy equation is solved independently to evaluate temperature field using a converged solution of the flow field. The governing equations are solved on the Fluent (ANSYS 15) platform.
4. Result and Discussion 4.1. Pressure drop Fig. 3 gives the numerical calculation results of local pressure drop pz along z direction for Re = 406.2. In the straight microchannel, the pressure is continuously decreases due to a frictional pressure loss along the channel
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length. In the newly proposed channel, the pressure drop consists of not only along the straight part of microchannel, but also in the converging-diverging cross-sections. The sharp change in flow area at the junction causes significant flow separation and recirculation which creates additional pressure drop. Further, in the diverging cross-section, the pressure gradually increases and recover only 70 to 80% of its, and fluctuates wildly due to the stagnation zone develop at the exit of diverging region. Fig. 5 also shows that pressure drop in type A microchannel are much higher than type B for constant heat flux condition. Furthermore, pressure drop in type A microchannel for constant wall temperature condition is 1.5 times higher than the constant heat flux condition.
4.2. Heat transfer Fig. 4 display the average Nusselt number as a function of Reynolds number for the microchannel. It is worth noting in Fig. 4, heat transfer is enhanced remarkably by the periodic converging-diverging cross-sections in newly proposed microchannel. In the range of 192.66< Re < 796.17, the heat transfer coefficient of 100 µm newly proposed channel is 46.8% –160.2% larger than the straight microchannel. The mechanisms which are responsible for this behaviour as follows: x Increment in heat transfer due to increase in fluid mixing and velocity jump in converging section. x Increment in heat transfer due to manipulation of the boundary layer formation. x Increment in heat transfer due to increase in heat transfer surface. Fig. 5 shows the distribution of wall and average fluid temperature along the flow direction in the one of the converging–diverging cross-section for Re = 796.5 for constant heat flux condition. In the straight microchannel, temperature of wall and average fluid temperature increases linearly along the flow direction. In the range of 0.75 < normalized z* < 0.9 corresponding to the converging-diverging region, in the converging region fluid velocity increases rapidly and break the thermal boundary layer, therefore heat transfer rate reaches to the maximum value. In the diverging region fluid velocity decreases and developing thermal boundary layer, heat transfer rate decreases. As a whole, the temperature of wall and fluid behaves the “humpback” shape with apparent negative gradient along z direction, reaches the minimum value at normalized z* = 0.8 and increases swiftly in the range of 0.8 < normalized z* < 0.9. Further, the minimum temperature of wall and fluid of the type A are well below that of the straight microchannel. Further, at constant wall temperature condition average fluid temperature again shows the “humpback” shapes with apparent negative gradient along z direction. Fig. 6 shows the distribution of local Nusselt number along the one of the converging-diverging cross-section for Re = 796.5. The following trends are observed in the constant heat flux condition: (1) The Nusselt numbers at the entrance of microchannel of type A is higher than the straight microchannel due to weak thermal entrance effect. (2) Due to the sudden contraction in the cross-section, a positive gradient of Nusselt number is found in the converging region. (3) Local Nusselt numbers increases in the converging cross-section and decreases in the diverging crosssection, and the amplitude of fluctuation is almost similar to that of local friction factor.
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Fig. 5. The distribution of temperature along the flow direction in the one of the converging–diverging cross-section.
Fig. 6. Local Nusselt number along the flow direction in the one of the converging–diverging cross-section.
4.3. Thermal resistance In order to give a clearer understanding of the thermal performance of the microchannel, two parameters total thermal resistance and pumping power are used to express the performance. The total thermal resistance is defined as the ratio of the temperature difference of the substrate and the inlet of microchannel to the heating power received by water in the microchannel region. Q is calculated by ݉ܥመ ሺܶ௨௧ െ ܶ ሻ. The pumping power to circulate the coolant in the microchannel is multiplication of pressure drop and the volumetric flow rate. The relation between total thermal resistance and pumping power is shown in Fig. 7. The total thermal resistance reduces dramatically at low pumping power with an increase of pumping power. This is reduces continuously through moderate rate at high pumping power. This can be explained as follows: the convective term of thermal resistance decreases due to rapid increase of heat transfer coefficient with an increase of the Reynolds number as shown in Fig. 4. 5. Conclusion These simulations are the first of their kind for microchannel with periodic converging-diverging cross-section. The proposed microchannel of diameter 100 µm have higher pressure drop than the straight microchannel of 100 µm diameter. In addition, the pressure drop in type B microchannel is much less than the type A. Heat transfer in the newly proposed microchannel is enhanced remarkably compare to straight channel. The averaged Nusselt numbers of channels is increases about 2 times for type A channel, 1.5 times for type B channel than the classical value. The flow in the converging-diverging section induces stronger recirculation and flow separation, which contributes to heat transfer enhancement but also increase the pressure drop. The influence of the converging-diverging crosssection on heat transfer of type A microchannel is weaker than that of type B but the overall performance of type A microchannel is better than type B.
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Fig. 7 Total thermal resistance as a function of pumping power
Fig.7. Total thermal resistance as a function of pumping power.
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