Optimal design of geometric parameters of double-layered microchannel heat sinks

This work uses an optimization procedure consisting of a simplified conjugate-gradient method and a three-dimensional fluid flow and heat transfer model to investigate the optimal geometric parameters of a double-layered microchannel heat sink (DL-MCHS). The overall thermal resistance R_T is the objective function to be minimized, and the number of channels N, channel width ratio β, lower channel aspect ratio α_l, and upper channel aspect ratio α_u are the search variables. For a given bottom area (10 × 10 mm) and heat flux (100 W/cm²), the optimal (minimum) thermal resistance of the double-layered microchannel heat sink is about R_T = 0.12 °C/m²W. The corresponding optimal geometric parameters are N = 73, β = 0.50, α_l = 3.52, and, α_u = 7.21 under a total pumping power of 0.1 W. These parameters reduce the overall thermal resistance by 52.8% compared to that yielded by an initial guess (N = 112, β = 0.37, α_l = 10.32, and α_u = 10.93). Furthermore, the optimal thermal resistance decreases rapidly with the pumping power and then tends to approach an constant value. As the pumping power increases, the optimal values of N, α_l, and α_u increase, whereas the optimal β value decreases. However, increasing the pumping power further is not always cost-effective for practical heat sink designs.     

Maximum-power-point tracking control of solar heating system

The present study developed a maximum-power point tracking control (MPPT) technology for solar heating system to minimize the pumping power consumption at an optimal heat collection. The net solar energy gain Q_net (=Q_s ? W_p/η_e) was experimentally found to be the cost function for MPPT with maximum point. The feedback tracking control system was developed to track the optimal Q_net (denoted Q_max). A tracking filter which was derived from the thermal analytical model of the solar heating system was used to determine the instantaneous tracking target Q_max(t). The system transfer-function model of solar heating system was also derived experimentally using a step response test and used in the design of tracking feedback control system. The PI controller was designed for a tracking target Q_max(t) with a quadratic time function. The MPPT control system was implemented using a microprocessor-based controller and the test results show good tracking performance with small tracking errors. It is seen that the average mass flow rate for the specific test periods in five different days is between 18.1 and 22.9 kg/min with average pumping power between 77 and 140 W, which is greatly reduced as compared to the standard flow rate at 31 kg/min and pumping power 450 W which is based on the flow rate 0.02 kg/s m² defined in the ANSI/ASHRAE 93-1986 Standard and the total collector area 25.9 m². The average net solar heat collected Q_net is between 8.62 and 14.1 kW depending on weather condition. The MPPT control of solar heating system has been verified to be able to minimize the pumping energy consumption with optimal solar heat collection.     

Thermal performance of plate-fin heat sinks under confined impinging jet conditions

This paper utilizes the infrared thermography technique to investigate the thermal performance of plate-fin heat sinks under confined impinging jet conditions. The parameters in this study include the Reynolds number (Re), the impingement distance (Y/D), the width (W/L) and the height (H/L) of the fins, which cover the range Re = 5000–25,000, Y/D = 4–28, W/L = 0.08125–0.15625 and H/L = 0.375–0.625. The influences of these parameters on the thermal performance of the plate-fin heat sinks are discussed. The experimental results show that the thermal resistance of the heat sink apparently decreases as the Reynolds number increases; however, the decreasing rate of the thermal resistance declines with the increase of the Reynolds number. An appropriate impingement distance can decrease the thermal resistance effectively, and the optimal impingement distance is increased as the Reynolds number increases. Moreover, the influence of the impingement distance on the thermal resistance at high Reynolds numbers becomes less conspicuous because the magnitude of the thermal resistance decreases with the Reynolds number. An increase of the fin width reduces the thermal resistance initially. Nevertheless, the thermal resistance rises sharply when the fin width is larger than a certain value. Increasing the fin height can increase the heat transfer area which lowers the thermal resistance. Moreover, the influence of the fin height on the thermal resistance seems less obvious than that of the fin width. To sum up all experimental results, Reynolds number Re = 20,000, impingement distant Y/D = 16, fin width W/L = 0.1375, and fin height H/L = 0.625 are the suggested parameters in this study.     

Fluid flow and heat transfer characteristics of cross-cut heat sinks

In this study, effects of cross-cuts on the thermal performance of heat sinks under the parallel flow condition are experimentally studied. To find effects of the length, position, and number of cross-cuts, heat sinks with one or several cross-cuts ranging from 0.5 mm to 10 mm were fabricated. The pressure drop and the thermal resistance of the heat sinks are obtained in the range of 0.01 W<P_p < 1 W. Experimental results show that among the many cross-cut design parameters, the cross-cut length has the most significant influence on the thermal performance of heat sinks. The results also show that heat sinks with a cross-cut are superior to heat sinks containing several cross-cuts in the thermal performance. Based on experimental results, the friction factor and Nusselt number correlations for heat sinks with a cross-cut are suggested. Using the proposed correlations, thermal performances of cross-cut heat sinks are compared to those of optimized plate-fin and square pin-fin heat sinks under the constant pumping power condition. This comparison yields a contour map that suggests an optimum type of heat sink under the constraint of the fixed pumping power and fixed heat sink volume. The contour map shows that an optimized cross-cut heat sink outperforms optimized plate-fin and square pin-fin heat sinks when 0.04 < log L1 < 1.     

A porous model for the square pin-fin heat sink situated in a rectangular channel with laminar side-bypass flow

This work illustrates the compact heat sink simulations in forced convection flow with side-bypass effect. Conventionally, the numerical study of the fluid flow and heat transfer in finned heat sinks employs the detailed model that spends a lot of computational time. Therefore, some investigators begin to numerically study such problem by using the compact model (i.e. the porous approach) since the regularly arranged fin array can be set as a porous medium. The computations of the porous approach model will be faster than those of the detailed mode due to the assumption of the volume-averaging technique. This work uses the Brinkman–Forchheimer model for fluid flow and two-equation model for heat transfer. A configuration of in-line square pin-fin heat sink situated in a rectangular channel with fixed height (H = 23.7 mm), various width and two equal-spacing bypass passages beside the heat sink is successfully studied. The pin-fin arrays with various porosities (ε = 0.358–0.750) and numbers of pin-fins (n = 25–81), confined within a square spreader whose side length (L) is 67 mm, are employed. The numerical results suggest that, within the range of present studied parameters (0.358 ? ε ? 0.750, 25 ? n ? 81 and 1 ? W/L ? 5), the pin-fin heat sink with ε = 0.750 and n = 25 is the optimal cooling configuration based on the maximum ratio of Nusselt number to dimensionless pumping power (Nu/(ΔP × Re³)). Besides, based on medium Nu/(ΔP × Re³) value and suitable channel size, W/L = 2–3 is suggested as the better size ratio of channel to heat sink.     

Multi-objective thermal design optimization and comparative analysis of electronics cooling technologies

A multi-objective thermal design optimization and comparative study of electronics cooling technologies is presented. The cooling technologies considered are: continuous parallel micro-channel heat sinks, in-line and staggered circular pin-fin heat sinks, offset strip fin heat sinks, and single and multiple submerged impinging jet(s). Using water and HFE-7000 as coolants, Matlab’s multi-objective genetic algorithm functions were utilized to determine the optimal thermal design of each technology based on the total thermal resistance and pumping power consumption under constant pressure drop and heat source base area of 100 mm². Plots of the Pareto front indicate a trade-off between the total thermal resistance and pumping power consumption. In general, the offset strip fin heat sink outperforms the other cooling technologies.     

Numerical study of confined slot jet impinging on porous metallic foam heat sink

This study numerically investigates the impinging cooling of porous metallic foam heat sink. The analyzed parameters ranges comprise ε = 0.93/10 PPI Aluminum foam, L/W = 20, Pr = 0.7, H/W = 2–8, and Re = 100–40,000. The simulation results exhibit that when the Re is low (such as Re = 100), the Nu_max occurs at the stagnation point (i.e. X = 0). However, when the Reynolds number increases, the Nu_max would move downwards, i.e. the narrowest part between the recirculation zone and the heating surface. Besides, the extent to which the inlet thermal boundary condition influences the prediction accuracy of the Nusselt number increases with a decreasing H/W and forced convective effect. The application ranges of H/W and Re that the effect of the inlet thermal boundary condition can be neglected are proposed. Lastly, comparing our results with those in other studies reveals that the heat transfer performance of the Aluminum foam heat sink is 2–3 times as large as that without it. The thermal resistance is also 30% less than that of the plate fin heat sink for the same volumetric flow rate and the 5.3 mm jet nozzle width. Therefore, the porous Aluminum foam heat sink enhances the heat transfer performance of impinging cooling.     

Effects of inlet geometry on heat transfer and fluid flow of tangential micro-heat sink

The paper presents the geometric optimization of the micro-heat sink with straight circular microchannels with inner diameter of D_i = 900 μm. The inlet cross-section has a rectangular shape and positioned tangentially to the tube axis with the four different geometries. The fluid flow regime is laminar and water with variable fluid properties is used as a working fluid. The heat flux spread through the bottom sink surface is q = 100 W/cm². Thermal and hydrodynamic performances of the heat sink are compared with results obtained for conventional channel configuration with lateral inlet/outlet cross-section. Besides, the results are compared with the tangential micro-heat sink with D_i = 300 μm. For all the cases, the thermal and hydrodynamic results are compared on a fixed pumping power basis.     

Thermal performance of in-line diamond-shaped pin fins in a rectangular duct

This work experimentally studied the pressure drop and heat transfer of an in-line diamond-shaped pin-fin array in a rectangular duct by using the transient single-blow technique. The variable parameters are the relative longitudinal pitch (X_L = 1.060, 1.414, 1.979) and the relative transverse pitch (X_T = 1.060, 1.414, 1.979). The empirical formula for the heat transfer is suggested. Besides, the optimal inter-fin pitches, X_T = 1.414 and X_L = 1.060, are provided based on the largest heat dissipation under the same pumping power.     

Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients

The characteristics of transient double-diffusive convection in a vertical cylinder are numerically simulated using a finite element method. Initially the fluid in the cavity is at uniform temperature and solute concentration, then constant temperature and solute concentration, which are lower than their initial values, are imposed along the sidewall and bottom wall, respectively. The time evolution of the double-diffusive convection is investigated for specific parameters, which are the Prandtl number, Pr = 7, the Lewis number, Le = 5, the thermal Grashof number, Gr_T = 10⁷, and the aspect ratio, A = 2, of the enclosure. The objective of the work is to identify the effect of the buoyancy ratio (the ratio of solutal Grashof to thermal Grashof numbers: N = Gr_S/Gr_T) on the evolution of the flow field, temperature and solute field in the cavity. It is found that initially the fluid near the bottom wall is squeezed by the cold flow from the sidewall, a crest of the solute field forms and then pushed to the symmetry line. In the case of N > 0, a domain with higher temperature and weak flow (dead region) forms on the bottom wall near the symmetry line, and the area of dead region increases when N varies from 0.5 to 1.5. More crests of the solute field are formed and the flow near the bottom wall fluctuates continuously for N < 0. The frequency of the fluctuation increases when N varies from −0.5 to −1.5. Corresponding to the variety of the thermal and solutal boundary layers, the average rates of heat transfer (Nu) at the sidewall remain almost unchanged while the average rates of mass transfer (Sh) at the bottom wall change much in the cases of N = 1, 0, −1.     

Thermal management using the bi-disperse porous medium approach

Thermal management of distributed electronics similar to data centers is studied using a bi-disperse porous medium (BDPM) approach. The BDPM channel comprises heat generating micro-porous square blocks, separated by macro-pores. Laminar forced convection cooling fluid of Pr = 0.7 saturates both the micro- and macro-pores. Bi-dispersion effect is induced by varying the macro-pore volume fraction ?_E, and by changing the number of porous blocks N², both representing re-distribution of the electronics. When 0.2 ? ?_E ? 0.86, the heat transfer Nu is enhanced twice (from ～550 to ～ 1100) while the pressure drop Δp¹ reduces almost eightfold. For ?_E < 0.5, Nu reduces quickly to reach a minimum at the mono-disperse porous medium (MDPM) limit (?_E → 0). Compared to N² = 1 case, Nu for BDPM configuration is high when N² ? 1, i.e., the micro-porous blocks are many and well distributed. The Nu increase with Re changes from non-linear to linear as N² increases from 1 to 81, with corresponding insignificant pumping power increase.     

Laminar forced convection in a heat generating bi-disperse porous medium channel

Thermal management of heat generating electronics using the Bi-Disperse Porous Medium (BDPM) approach is investigated. The BDPM channel comprises heat generating micro-porous square blocks separated by macro-pore gaps. Laminar forced convection cooling fluid of Pr = 0.7 saturates both the micro- and macro-pores. Bi-dispersion effect is induced by varying the porous block permeability Da_I and external permeability Da_E through variation in number of blocks N². For fixed Re, when 10^?5 ? Da_I ? 10^?2, the heat transfer Nu is enhanced four times (from ～200 to ～800) while the pressure drop Δp1 reduces almost eightfold. For Da_I < 10^?5, Nu decreases quickly to reach a minimum at the Mono-Disperse Porous Medium (MDPM) limit (Da_I → 0). Compared to N² = 1 case, Nu for BDPM configuration is high when N² ? 1, i.e., the micro-porous blocks are many and well distributed. The pumping power increase is very small for the entire range of N². Distributing heat generating electronics using the BDPM approach is shown to provide a viable method of thermo-hydraulic performance enhancement χ.     

Experimental study of forced convection heat transfer from a cam shaped tube in cross flows

An experimental investigation has been conducted to clarify forced convection heat transfer characteristic and flow behavior of an isothermal cam shaped tube in cross flow. The range of angle of attack and Reynolds number based on an equivalent circular tube are within 0° < α < 180° and 1.5 × 10⁴ < Re_eq < 2.7 × 10⁴, respectively.The results show that the mean heat transfer coefficient is a maximum at about α = 90° over the whole range of the Reynolds numbers. It is found that thermal hydraulic performance of the cam shaped tube is larger than that of a circular tube with the same surface area except for α = 90° and 120°. Furthermore, the effect of the diameter of the cam shaped tube upon the thermal hydraulic performance is discussed.     

Power and thermal characterization of a lithium-ion battery pack for hybrid-electric vehicles

A 1D electrochemical, lumped thermal model is used to explore pulse power limitations and thermal behavior of a 6 Ah, 72 cell, 276 V nominal Li-ion hybrid-electric vehicle (HEV) battery pack. Depleted/saturated active material Li surface concentrations in the negative/positive electrodes consistently cause end of high-rate (∼25 C) pulse discharge at the 2.7 V cell⁻¹ minimum limit, indicating solid-state diffusion is the limiting mechanism. The 3.9 V cell⁻¹ maximum limit, meant to protect the negative electrode from lithium deposition side reaction during charge, is overly conservative for high-rate (∼15 C) pulse charges initiated from states-of-charge (SOCs) less than 100%. Two-second maximum pulse charge rate from the 50% SOC initial condition can be increased by as much as 50% without risk of lithium deposition. Controlled to minimum/maximum voltage limits, the pack meets partnership for next generation vehicles (PNGV) power assist mode pulse power goals (at operating temperatures >16 °C), but falls short of the available energy goal.In a vehicle simulation, the pack generates heat at a 320 W rate on a US06 driving cycle at 25 °C, with more heat generated at lower temperatures. Less aggressive FUDS and HWFET cycles generate 6–12 times less heat. Contact resistance ohmic heating dominates all other mechanisms, followed by electrolyte phase ohmic heating. Reaction and electronic phase ohmic heats are negligible. A convective heat transfer coefficient of h = 10.1 W m⁻² K⁻¹ maintains cell temperature at or below the 52 °C PNGV operating limit under aggressive US06 driving.     

3-Dimensional numerical optimization of silicon-based high performance parallel microchannel heat sink with liquid flow

A full 3-dimensional (3D) conjugate heat transfer model has been developed to simulate the heat transfer performance of silicon-based, parallel microchannel heat sinks. A semi-normalized 3-dimensional heat transfer model has been developed, validated and used to optimize the geometric structure of these types of microheat sinks. Under a constant pumping power of 0.05 W for a water-cooled microheat sink, the optimized geometric parameters of the structure as determined by the model were a pitch of 100 μm, a channel width of 60 μm and a channel depth of about 700 μm. The thermal resistance of this optimized microheat sink was calculated for different pumping powers based on the full 3D conjugate heat transfer model and compared with the initial experimental results obtained by Tuckerman and Pease in 1981. This comparison indicated that for a given pumping poser, the overall cooling capacity could be enhanced by more than 20% using the optimized spacing and channel dimensions. The overall thermal resistance was 0.068 °C/W for a pumping power of 2 W.     

The particle thermal conductivity influence of nanofluids on thermal performance of the microtubes

The paper presents the numerical analysis on microchannel laminar heat transfer and fluid flow of nanofluids in order to evaluate the suitable thermal conductivity of the nanoparticles that results in superior thermal performances compared to the base fluid. The diameter ratio of the micro-tube was D_i/D_o = 0.3/0.5 mm with a tube length L = 100 mm in order to avoid the heat dissipation effect. The heat transfer rate was fixed to Q = 2 W. The water based Al₂O₃, TiO₂ and Cu nanofluids were considered with various volume concentrations ϕ = 1,3 and 5% and two diameters of the particles d_p = 13 nm and 36 nm. The analysis is based on a fixed Re and pumping power Π, in terms of average heat transfer coefficient and maximum temperature of the substrate. The results reveal that only the nanofluids with particles having very high thermal conductivity (λ_Cu = 401 W/m K) are justified for using in microcooling systems. Moreover, the analysis is sensitive to both the comparison criteria (Re or Π) and heat transfer parameters (h_ave or t_max).     

Effects of jet plate size and plate spacing on the stagnation Nusselt number for a confined circular air jet impinging on a flat surface

This work deals with the effects of jet plate size and plate spacing (jet height) on the heat transfer characteristics for a confined circular air jet vertically impinging on a flat plate. The jet after impingement was restricted to flow in two opposite directions. A constant surface heat flux of 1000 W/m² was arranged. Totally 88 experiments were performed. Jet orifices individually with diameter of 1.5, 3, 6 and 9 mm were adopted. Jet Reynolds number (Re) was in the range 10,000–30,000 and plate spacing-to-jet diameter ratio (H/d) was in the range 1–6. Eleven jet plate width-to-jet diameter ratios (W/d = 4.17–41.7) and seven jet plate length-to-jet diameter ratios (L/d = 5.5–166.7) were individually considered. The measured data were correlated into a simple equation. It was found that the stagnation Nusselt number is proportional to the 0.638 power of the Re and inversely proportional to the 0.3 power of the H/d. The stagnation Nusselt number was also found to be a function of exp[−0.044(W/d) − 0.011(L/d)]. Through comparisons among the present obtained data and documented results, it may infer that, for a jet impingement, the impingement-plate heating condition and flow arrangement of the jet after impingement are two important factors affecting the dependence of the stagnation Nusselt number on H/d.     

Sintered porous heat sink for cooling of high-powered microprocessors for server applications

This paper experimentally investigates the sintered porous heat sink for the cooling of the high-powered compact microprocessors for server applications. Heat sink cold plate consisted of rectangular channel with sintered porous copper insert of 40% porosity and 1.44 × 10^?11 m² permeability. Forced convection heat transfer and pressure drop through the porous structure were studied at Re ? 408 with water as the coolant medium. In the study, heat fluxes of up to 2.9 MW/m² were successfully removed at the source with the coolant pressure drop of 34 kPa across the porous sample while maintaining the heater junction temperature below the permissible limit of 100 ± 5 °C for chipsets. The minimum value of 0.48 °C/W for cold plate thermal resistance (R_cp) was achieved at maximum flow rate of 4.2 cm³/s in the experiment. For the designed heat sink, different components of the cold plate thermal resistance (R_cp) from the thermal footprint of source to the coolant were identified and it was found that contact resistance at the interface of source and cold plate makes up 44% of R_cp and proved to be the main component. Convection resistance from heated channel wall with porous insert to coolant accounts for 37% of the R_cp. With forced convection of water at Re = 408 through porous copper media, maximum values of 20 kW/m² K for heat transfer coefficient and 126 for Nusselt number were recorded. The measured effective thermal conductivity of the water saturated porous copper was as high as 32 W/m K that supported the superior heat augmentation characteristics of the copper–water based sintered porous heat sink. The present investigation helps to classify the sintered porous heat sink as a potential thermal management device for high-end microprocessors.     

Cooling effectiveness of effusion walls with deflection hole angles measured by infrared imaging

Experimental investigations were performed on the overall cooling effectiveness of three effusion cooling test plates. The test plates had different hole-spacing (PS/d² = 32.5 and 72), different deflection angle (β = 45° and 90°), and the same inclination angle (α = 30°). Although effusion cooling has been applied to advanced gas turbine combustors, its fundamental study seen in the open literature is limited. Using the infrared (IR) imaging technique, the current study documented distribution of the overall cooling effectiveness on the surfaces of above specified flat walls. Based on the IR measured cooling effectiveness data, different effusion cooling configurations (different PS/d² and β) were evaluated and the optimum configuration was determined. The current work demonstrated that the infrared imaging technique served as an ideal method to detail cooling characteristics in the combustor heat transfer research.     

Experimental investigation for sequential triangular double-layered microchannel heat sink with nanofluids

This study examined new innovative design of aluminum rectangular and triangular double-layered microchannel heat sink (RDLMCHS) and (TDLMCHS), respectively, using Al₂O₃–H₂O and SiO₂–H₂O nanofluids. A series of experimental runs for different channel dimensions, different nanoparticles concentrations and types and several pumping powers showed excellent hydrothermal performance for DLMCHS over traditional single-layer (SLMCHS). The results showed that the sequential TDLMCHS provided a 27.4% reduction in the wall temperature comparing with RDLMCHS and has better temperature uniformity across the channel length with less than 2 °C. Sequential TDLMCHS provided 16.6% total thermal resistance lesser than the RDLMCHS at low pumping power and the given geometry parameters. Pressure drop observation showed no significant differences between the two designs. In addition, larger number of channels and smaller fin thickness referred less thermal resistance rather than only increasing the pumping power. Higher nanoparticle concentration showed better thermal stability for both nanofluids than pure water. The Al₂O₃–H₂O nanofluid (0.9 vol.%) showed best performance with the temperature difference of 1.6 °C and lowest thermal resistance of 0.13 °C/W·m².