Convective‐radiative fins with simultaneous variation of thermal conductivity,heat transfer coefficient,and surface emissivity with temperature

This paper is a numerical study of thermal performance of a convective‐radiative fin with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature. The convective heat transfer is assumed to be a power function of the local temperature between the fin and the ambient which allows simulation of different convection mechanisms such as natural convection (laminar and turbulent), boiling, etc. The thermal conductivity and the surface emissivity are treated as linear functions of the local temperature between the fin and the ambient which provide a satisfactory representation of the thermal property variations of most fin materials. The thermal performance is governed by seven parameters, namely, convection–conduction parameter Nc, radiation–conduction parameter Nr, thermal conductivity parameter A, emissivity parameter B, the exponent n associated with convective heat transfer coefficient, and the two temperature ratios, θ_a and θ_s, that characterize the temperatures of convection and radiation sinks. The effect of these parameters on the temperature distribution and fin heat transfer rate are illustrated and the results interpreted in physical terms. Compared with the constant properties model, the fin heat transfer rate can be underestimated or overestimated considerably depending on the values of the governing parameters. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20408     

Transient heat transfer in a heat‐generating fin with radiation and convection with temperature‐dependent heat transfer coefficient

The transient heat transfer in a heat‐generating fin with simultaneous surface convection and radiation is studied numerically for a step change in base temperature. The convection heat transfer coefficient is assumed to be a power law function of the local temperature difference between the fin and its surrounding fluid. The values of the power exponent n are chosen to include simulation of natural convection (laminar and turbulent) and nucleate boiling among other convective heat transfer modes. The fin is assumed to have uniform internal heat generation. The transient response of the fin depends on the convection‐conduction parameter, radiation‐conduction parameter, heat generation parameter, power exponent, and the dimensionless sink temperature. The instantaneous heat transfer characteristics such as the base heat transfer, surface heat loss, and energy stored are reported for a range of values of these parameters. When the internal heat generation exceeds a threshold the fin acts as a heat sink instead of a heat source. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21012     

Thermal analysis of a moving fin using the radial basis function approximation

In this study, the heat transfer and temperature distribution in a moving fin have been analyzed. The fin velocity was considered constant, and the thermal conductivity coefficient was variable with temperature, and the fin was under the effect of convection, radiation, and conduction heat transfer. The main equation of the problem was solved by the radial basis function method and validated by the numerical 4th-order Runge–Kutta method. Several parameters such as thermal conductivity parameter from 0 to 1, sink temperature parameter from 0.2 to 0.8, and N_r, N_c, Pe number from 1 to 4, were examined. The outcomes illustrate that increasing the thermal conductivity by 51.5% raises the conduction heat transfers as well as the dimensionless temperature by 3.42%. Moreover, increasing the sink temperature leads to a slow rise in ambient temperature by 22.8% in the maximum state. By raising the N_c and N_r parameters, near 33.3%, the temperature distribution profile is declined by 4% and 10.5%, respectively. And increasing the Pe number by 100% results in a rise in the temperature distribution by about 7%.     

Numerical Evaluation of Flow and Heat Transfer in Plate-Pin Fin Heat Sinks with Various Pin Cross-Sections

A numerical investigation of the thermal and hydraulic performance of 20 different plate-pin fin heat sinks with various shapes of pin cross-sections (square, circular, elliptic, NACA profile, and dropform) and different ratios of pin widths to plate fin spacing (0.3, 0.4, 0.5, and 0.6) was performed. Finite volume method-based CFD software, Ansys CFX, was used as the 3-D Reynolds-averaged Navier-Stokes Solver. A k-ω based shear-stress-transport model was used to predict the turbulent flow and heat transfer through the heat sink channels. The present study provides original information about the performance of this new type of compound heat sink.     

Enhancement of Heat Transfer for Plate Fin Heat Exchangers Considering the Effects of Fin Arrangements

In the present study, the potential of rectangular fins with different fin types of inner zigzag-flat-outer zigzag (B-type) and outer zigzag-flat-outer zigzag (C-type) and with different fin angles of 30° and 90° for 2 mm fin height and 10 mm offset from the horizontal direction for heat transfer enhancement with the use of a conjugated heat transfer approach and for pressure drop in a plate fin heat exchanger is numerically evaluated. The rectangular fins are located on a flat plate channel (A-type). The numerical computations are performed by solving a steady, three-dimensional Navier–Stokes equation and an energy equation by using FLUENT software program. Air is taken as working fluid. The study is carried out at Reynolds number of 400 and inlet temperatures, velocities of cold and hot air are fixed as 300 K, 600 K and 1.338 m.s^?1, 0.69 m.s^?1, respectively. This study presents new fin geometries which have not been researched in the literature for plate fin heat exchangers. The results show that while the heat transfer is increased by about 10% at the exit of a channel with the fin type of C, it is increased up to 8% for the fin angle of 90° when compared to a channel with A-type under the counter flow. The heat transfer enhancements for different values of Reynolds number and for varying fin heights, fin intervals and also temperature distributions of fluids are investigated for parallel and counter flow.     

Measurement of performance of plate-fin heat sinks with cross flow cooling

This work assesses the performance of plate-fin heat sinks in a cross flow. The effects of the Reynolds number of the cooling air, the fin height and the fin width on the thermal resistance and the pressure drop of heat sinks are considered. Experimental results indicate that increasing the Reynolds number can reduce the thermal resistance of the heat sink. However, the reduction of the thermal resistance tends to become smaller as the Reynolds number increases. Additionally, enhancement of heat transfer by the heat sink is limited when the Reynolds number reaches a particular value. Therefore, a preferred Reynolds number can be chosen to reduce the pumping power. For a given fin width, the thermal performance of the heat sink with the highest fins exceeds that of the others, because the former has the largest heat transfer area. For a given fin height, the optimal fin width in terms of thermal performance increases with Reynolds number. As the fins become wider, the flow passages in the heat sink become constricted. As the fins become narrower, the heat transfer area of the heat sink declines. Both conditions reduce the heat transfer of the heat sink. Furthermore, different fin widths are required at different Reynolds numbers to minimize the thermal resistance.     

Design and characterization of a cylindrical,water‐cooled heat sink for thermoelectric air‐conditioners

Thermoelectric air‐conditioners (TEACs) are becoming much concerned due to their many advantages, but the low COPs limit their broad applications. The two key factors to raise the COPs of TEACs are both the improvement of thermoelectric materials and the optimum design of hot side heat sinks. This paper provides a thermoelectric air‐conditioning system with a water‐cooled sleeve heat sink in the hot side of the thermoelectric pellets, and compares the overall heat transfer rates q_t, the total heat resistances R_t between the water‐cooled and air‐cooled heat sinks as well as the optimum fin length, the optimum fluid flow velocity and the optimum fin gap distance. The simulation results show that the overall heat transfer rate of water‐cooled heat sink is more than 20 times that of air‐cooled heat sink under the other same circumstances, as a result of the improvement of heat sink, the optimum COP of the thermoelectric air‐conditioning system with the water‐cooled heat sink proximately doubles that with the air‐cooled heat sink. This novel system could be simply installed and applied all the year round for cooling in summer and heating in winter. Copyright © 2005 John Wiley & Sons, Ltd.     

Designing parameter optimization of a Parallel-Plain Fin heat sink using the grey-based fuzzy algorithm with the orthogonal arrays

In this paper, a grey-based fuzzy algorithm with the orthogonal arrays is employed to find the optimal designing parameters' setting for a heat sink with the Parallel-Plain Fin (PPF) on the multiple thermal performance characteristics. The proposed algorithm, coupling the grey relational analysis with the fuzzy logic, obtains a grey–fuzzy reasoning grade to evaluate the multiple performance characteristics according to the grey relational coefficient of each performance characteristic. In the present study, the designing parameters of the heat sink include the height of fin, the width of gap between fins, the width of slot, the number of slot and the air speed. The design of experiment (DOE) adopts the L₁₆(4⁵) orthogonal arrays table which is four levels and five factors type of factorial design. The average convective heat transfer coefficient, the thermal resistance and the pressure drop are considered as the multiple thermal performance characteristics and explored in the experiment. In addition, the response table, response graph and the analysis of variance (ANOVA) are used to find the optimal settings and the influence of designing parameters on the multiple performance characteristics. The results of confirmation tests with the optimal settings of designing parameters have obviously shown that the multiple thermal performance characteristics are effectively improved through these procedures.     

Application of the Haar wavelet method on a continuously moving convective‐radiative fin with variable thermal conductivity

In this paper, we numerically investigate the heat transfer in a continuously moving convective‐radiative fin with variable thermal conductivity by using Haar wavelets. Heat is dissipated to the environment simultaneously through convection and radiation. The effect of various significant parameters—in particular the thermal conductivity parameter a, convection‐sink temperature θ_a, radiation‐sink temperature θ_s, convection‐radiation parameter N_c, radiation‐conduction parameter N_r, and Peclet number Pe—on the temperature profile of the fin are discussed and interpreted physically through illustrative graphs. Computational results obtained by the present method are in good agreement with the standard numerical solutions. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21038     

Study on forced air convection cooling for electronic assemblies

The slotted fin concept was employed to improve the air cooling performance of plate-fin in heat sinks. Numerical simulations of laminar heat transfer and flow pressure drop were conducted for the integral plate fin, discrete plate fin and discrete slotted fin heat sinks. It is found that the performance of the discrete plate fin is better than that of the integral continuum plate fin and the performance of slotted fin is better than that of the discrete plate fin at the same pumping power of the fan. A new type of heat sink characterized by discrete and slotted fin surfaces with thinner fins and smaller spaces between fins is then proposed. Preliminary computation shows that this type of heat sink may be useful for the next generation of higher thermal load CPUs. The limit of cooling capacity for air-cooling techniques was also addressed. __________ Translated from Journal of Xi’an Jiaotong University, 2006, 40(11): 1241–1245 [译自: 西安交通大学学报]     

Multiwalled Carbon Nanotube Nanofluid for Thermal Management of High Heat Generating Computer Processor

Minichannel heat sink geometries with varying fin spacing were tested with de‐ionized water and MWCNT (1 wt %) nanofluid to evaluate their performance with flow components of a liquid cooling kit. Four heat sinks with fin spacing of 0.2 mm, 0.5 mm, 1.0 mm, and 1.5 mm were used in this investigation. Heat sink base temperature was analogous to processor operating temperature which was the prime parameter of interest in this investigation. The base temperature decreased by reducing the fin spacing and using multiwalled carbon nanotube (MWCNT) nanofluid. The lowest value of heat sink base temperature recorded was 49.7 ^°C at a heater power of 255 W by using a heat sink of 0.2 mm fin spacing and MWCNT nanofluid as a coolant. Moreover, as a result of reduced fin spacing and using MWCNT nanofluid as a coolant the value of overall heat transfer coefficient increased from 1200 W/m²K to 1498 W/m²K, translating to about a 15% increase. The value of thermal resistance also dropped by reducing the fin spacing and using MWCNT nanofluid. The most important aspect of the study is that the heat sinks and MWCNT nanofluid proved to be compatible with the pump and radiator of the commercial CPU liquid cooling kit. The pump was capable to handle the pressure drop which resulted by reducing the heat sink fin spacing and by using MWCNT nanofluid. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(7): 653–666, 2014; Published online 11 November 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21107     

Thermal optimization of tapered pin fin exposed to nonuniform surface heat transfer coefficient

In the present work, thermal analysis and design optimization of tapered pin fin subjected to variable surface heat transfer coefficient have been numerically carried out. It is well known that heat is transferred through the fin by conduction along its length and dissipated from the fin surface via natural convection to the ambient. The thermal analysis and the optimum dimension were carried out using finite element (FE) modeling software ANSYS-17.2. The thermal performance of the tapered pin fin has been studied over a wide range of physical dimensions. In addition, the effect of base to tip surface heat transfer coefficient ratio (ε) on the fin performance is evaluated. It was found that the effect of variable heat transfer coefficient has a significant impact on the fin efficiency. The rate of increase of fin efficiency was lower in the low as well as in high range of ε, meanwhile, it was steeper in the intermediate range of ε. It was also observed that the optimal values of the heat dissipation were higher for lower values of ε at the same conditions.     

The Use of Effectiveness Concepts to Calculate the Thermal Resistance of Parallel Plate Heat Sinks

With this study, a new and more adaptable approach to the thermal design of the large heat sinks used in power electronics is proposed. This method, supported by the results from an extensive experimental program, recognizes that (1) the heat sink fins and the airflow adjacent to them form a simple cross-flow heat exchanger, and (2) conventional NTU-effectiveness methods can be adapted for use in the thermal analysis of the heat sink. This adaptation requires the development and evaluation of an equivalent heat capacity to describe the energy conducted along the fin.

This method was initially used to evaluate the convective heat transfer coefficients between the fin and the cooling air. In this geometry, the developing airflow conditions make the prediction of representative values difficult. The correlation found to describe the test results was then used in an inverted analysis to predict and compare the experimental values for the heat sinks thermal resistance. The method is finally used in a design example where the fin spacing is optimized for a particular test duty. It is concluded that this new approach will make the design of large heat sinks more robust and reliable.     

Analysis of microchannel heat sinks for electronics cooling

This paper presents an analytical and numerical study on the heat transfer characteristics of forced convection across a microchannel heat sink. Two analytical approaches are used: the porous medium model and the fin approach. In the porous medium approach, the modified Darcy equation for the fluid and the two-equation model for heat transfer between the solid and fluid phases are employed. Firstly, the effects of channel aspect ratio (α_s) and effective thermal conductivity ratio (k?) on the overall Nusselt number of the heat sink are studied in detail. The predictions from the two approaches both show that the overall Nusselt number (Nu) increases as α_s is increased and decreases with increasing k?. However, the results also reveal that there exists significant difference between the two approaches for both the temperature distributions and overall Nusselt numbers, and the discrepancy becomes larger as either α_s or k? is increased. It is suggested that this discrepancy can be attributed to the indispensable assumption of uniform fluid temperature in the direction normal to the coolant flow invoked in the fin approach. The effect of porosity (ε) on the thermal performance of the microchannel is subsequently examined. It is found that whereas the porous medium model predicts the existence of an optimal porosity for the microchannel heat sink, the fin approach predicts that the heat transfer capability of the heat sink increases monotonically with the porosity. The effect of turbulent heat transfer within the microchannel is next studied, and it is found that turbulent heat transfer results in a decreased optimal porosity in comparison with that for the laminar flow. A new concept of microchannel cooling in combination with microheat pipes is proposed, and the enhancement in heat transfer due to the heat pipes is estimated. Finally, two-dimensional numerical calculations are conducted for both constant heat flux and constant wall temperature conditions to check the accuracy of analytical solutions and to examine the effect of different boundary conditions on the overall heat transfer.     

Optimum design of a radial heat sink under natural convection

We investigated natural convection heat transfer around a radial heat sink adapted for dissipating heat on a circular LED (light emitting diode) light and optimized heat sink. The numerical results were validated with experimental results and it showed a good agreement. To select the optimum reference model, three types of heat sinks (L, LM and LMS model) were compared. Parametric studies were performed to compare the effects of the number of fins, long fin length, middle fin length and heat flux on the thermal resistance and average heat transfer coefficient. Finally, multi-objective optimizations considering thermal performance and mass simultaneously were performed and Pareto front were conducted with various weighting factors. It was found that it was impossible to optimize both thermal performance and heat sink mass at the same time, and there existed an upper limit to the ratio of weighting factors (ω₁/ω₂).     

Single-Phase Cryogenic Flow and Heat Transfer Through Microscale Pin Fin Heat Sinks

Single-phase heat transfer and pressure drop of liquid nitrogen in microscale heat sinks are studied experimentally in this paper. Effects of geometrical variations are characterized on the thermofluidic performance of staggered microscale pin fin heat sinks. Pitch-to-diameter ratio and aspect ratio of the micro pin fins are varied. The pin fins have square shape with 200 or 400 μm width and are oriented at 45 degrees to the flow direction. Thermal performance of the heat sinks is evaluated for Reynolds numbers (based on pin fin hydraulic diameter) from 108 to 570. Results are presented in a nondimensional form in terms of friction factor, Nusselt number, and Reynolds number and are compared with the predictions of existing correlations in the literature for micro pin fin heat sinks. Comparison of flow and heat transfer performance of the micro pin fin heat sinks reveals that at a particular critical Reynolds number of ～250, pin fin heat sinks with the same aspect ratio but larger pitch ratio show a transition in both friction factor and Nusselt number. In order to better characterize this transition, visualization experiments were performed with the Fluorinert PF5060 using an infrared camera. At the critical Reynolds number, for the larger pitch ratio pin fin heat sink, surface thermal intensity profiles suggest periodic flapping of the flow behind the pin fins at a Strouhal number of 0.227.     

Thermal Analysis and Optimum Fin Length of a Heat Sink

A theoretical analysis of the cooling effect of a heat sink is presented in this study. With the input data of Biot number, Bi, and heat transfer coefficient ratios, H and H *, the optimum heat transfer equation can be utilized to obtain the optimum length of fins in a heat sink, which affects the overall thermal effectiveness of the heat sink. This optimum equation is in transcendental form, which involves three dimensionless parameters, $\sqrt{\hbox{Bi}}$ S opt. , $\sqrt{\hbox{Bi}}$ H , and $\sqrt{\hbox{Bi}}$ H *. Finally, the thermal resistance of a heat sink is derived and examples are provided to illustrate the effect on the cooling performance of a heat sink under various design conditions.     

平板和叉排散热器的综合换热性能分析及结构优化

本文引用无量纲品质因数F,分别对平板和叉排散热器的换热性能进行了综合分析。研究了空气流动速度、肋片排列方式以及几何尺寸对散热器综合换热性能的影响,并且以最小化F为目标函数优化了散热器。计算所得的数据有利于散热器结构的设计与改进。     

A three-dimensional heat sink module design problem with experimental verification

A three-dimensional heat sink module design problem is examined in this work to estimate the optimum design variables using the Levenberg–Marquardt Method (LMM) and a general purpose commercial code CFD-ACE+. Three different types of heat sinks are designed based on the original fin arrays with a fixed volume. The objective of this study is to minimize the maximum temperature in the fin array and to determine the best shape of heat sink. Results obtained by using the LMM to solve this 3-D heat sink module design problem are firstly justified based on the numerical experiments and it is concluded that for all three cases, the optimum fin height H tends to become higher and optimum fin thickness W tends to become thinner than the original fin array, as a result both the fin pitch D and heat sink base thickness U are increased. The maximum temperature for the designed fin array can be decreased drastically by utilizing the present fin design algorithm. Finally, temperature distributions for the optimal heat sink modules are measured using thermal camera and compared with the numerical solutions to justify the validity of the present design.     

Fin performance ratios greater than unity: Not just a theoretical aspiration

Previous work using the fin performance ratio has shown that it may not exceed unity. This study proves that this is not the case under certain conditions relating to the heat transfer from the tip of the fin. Equations for longitudinal rectangular fins have been used to demonstrate how this can be achieved and a performance ratio chart is provided showing performance ratios exceeding unity when the ratio of the heat transfer coefficient at the tip to that along the length of the fin exceeds the maximum effectiveness (a parameter of the problem). Under these conditions the maximum performance ratio is given by the ratio of the heat transfer coefficients (α_e/α) divided by the maximum effectiveness. This has relevance for fins used in boiling and condensing systems where different heat transfer coefficients may exist on different parts of the fins due to the existence of different phases.