Influence of channel aspect ratio on heat transfer in rotating rectangular ducts with skewed ribs at high rotation numbers

Centerline heat transfer measurements along two opposite ribbed walls in three rotating rectangular ducts roughened by 45° staggered ribs with channel aspect ratios (AR) of 1:1, 2:1 and 4:1 are performed at Reynolds (Re), rotation (Ro) and buoyancy (Bu) numbers in the ranges of 5000–30,000, 0–2, and 0.005–8.879, respectively. These channel geometries are in common use as the internal cooling passages of a gas turbine rotor blade and the tested Ro and Bu ranges are considerably extended from the previous experiences. This study focuses on the heat transfer characteristics in response to the change of AR under the parameter ranges examined. With zero-rotation (Ro = 0), the local Nusselt numbers (Nu₀) along the centerlines of two opposite ribbed walls increase as AR increases due to the increased rib-height to channel-height ratio. The Bu impact on heat transfer appears to be AR dependent, i.e. the increase of Bu elevates Nusselt number ratios Nu/Nu₀ in the square channel but impairs heat transfer in the rectangular channels of AR = 2 and 4. Acting by the Coriolis effect alone, all the leading edge Nu values in the present Ro range are lower than the zero-rotation references but started to recover as Ro increases from 0.1 in the channels of AR = 1, 2 and from 0.3 in the channel of AR = 4. The trailing edge Nu/Nu₀ ratios increase consistently from unity as Ro increases but their responses toward the increase of AR are less systematic than those found along the leading edge. The above findings, with the aids of extended Ro and Bu ranges achieved by this study, serve as the original contributions for this technical community. The Nu/Nu₀ ratios in the rotating channels of AR = 1, 2, and 4 fall in the ranges of 0.6–2.2, 0.5–2.7, and 0.5–2.1, respectively. A set of heat transfer correlations is derived to represent all the heat transfer data in the periodically developed flow regions of three rotating ducts.     

Development of correlations for Nusselt number and friction factor for solar air heater with roughened duct having multi v-shaped with gap rib as artificial roughness

This paper presents the results of an experimental investigation of heat transfer and friction in the flow of air in rectangular ducts having multi v-shaped rib with gap roughness on one broad wall. The investigation encompassed Reynolds number (Re) from 2000 to 20,000, relative gap distance (G_d/L_v) values of 0.24–0.80, relative gap width (g/e) values of 0.5–1.5, relative roughness height (e/D) values of 0.022–0.043, relative roughness pitch (P/e) values of 6–12, relative roughness width ratio (W/w) values of 1–10, angle of attack (α) range of 30°–75°. The optimum values of geometrical parameters of roughness have been obtained and discussed. For Nusselt number (Nu), the maximum enhancement of the order of 6.74 times of the corresponding value of the smooth duct has been obtained, however the friction factor (f) has also been seen to increase by 6.37 times of that of the smooth duct. The rib parameters corresponding to maximum increase in Nu and f were G_d/L_v = 0.69, g/e = 1.0, e/D = 0.043, P/e = 8, W/w = 6 and α = 60°. Based on the experimental data, correlations for Nu and f have been developed as function of roughness parameters of multi v-shaped with gap rib and flow Reynolds number.     

Flow visualizations and heat transfer measurements for a rotating pin-fin heat sink with a circular impinging jet

This work experimentally investigated the fluid flow and heat transfer behaviors of jet impingement onto the rotating heat sink. Air was used as impinging coolant, while the square heat sinks with uniformly in-line arranged 5 × 5 and 9 × 9 pin-fins were employed. The side length (L) of the heat sink equaled 60 mm and was fixed. Variable parameters were the relative length of the heat sink (L/d = 2.222 and 4.615), the relative distance of nozzle-to-fin tip (C/d = 0–11), the jet Reynolds number (Re = 5019–25,096) and the rotational Reynolds number (Re_r = 0–8114). Both flow characteristics of stationary and rotating systems were illustrated by the smoke visualization. Besides, the results of heat transfer indicate that, for a stationary system with a given air flow rate, there was a larger average Nusselt number (Nu₀) for the 9 × 9 pin-fin heat sink with L/d = 4.615 and C/d = 11. For a rotating system, a bigger Re_r meant a more obvious heat transfer enhancement (Nu_Ω/Nu₀) in the case of smaller Re, but Nu_Ω/Nu₀ decreased with increasing Re. In this work, Nu_Ω/Nu₀ in L/d = 2.222 is higher than in L/d = 4.615; among the systems in L/d = 2.222, bigger Nu_Ω/Nu₀ exists in the case of C/d = 9–11, but among the systems in L/d = 4.615, bigger Nu_Ω/Nu₀ exists in the case of C/d = 1–3. Finally, according to the base of Nu_Ω/Nu₀ ? 1.1, the criterion of the substantial rotation was suggested to be Re_r/Re ? 1.154.     

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.     

New approach relevant to total heat transfer coefficient including the effect of radiation and convection at the ceiling in a cooled ceiling room

In this study, radiative and convective heat transfer coefficients at the ceiling are determined for a cooled ceiling room. Firstly, convective heat transfer is simulated numerically neglecting the radiative heat transfer at the surfaces (ε_f = ε_w = ε_c = 0), then, radiative heat transfer is calculated theoretically for different surface emissivities (ε_f = ε_w = ε_c = 0.5, 0.6, 0.7, 0.8 and 0.9) for different room dimensions (3 × 3 × 3, 4 × 3 × 4 and 6 × 3 × 4 m) and thermal conditions (T_f = 25 °C, T_w = 28–36 °C and T_c = 0–25 °C). Numerical data is compared with the results of correlations based on experimental data given in literature. New equations related to convective and total (including the effect of convection and radiation) heat transfer coefficients for ceiling are found in the current study.     

Heat transfer and pressure drop in furrowed channels with transverse and skewed sinusoidal wavy walls

This comparative study examines the detailed Nusselt number (Nu) distributions, pressure drop coefficients (f) and thermal performance factors (η) for two furrowed rectangular channels with transverse and skewed sinusoidal wavy walls. Detailed heat transfer measurements over these transverse and skewed sinusoidal wavy walls at the Reynolds numbers (Re) = 1000, 1500, 2000, 5000, 10,000, 15,000, 20,000, 25,000 and 30,000 are performed using the steady-state infrared thermo-graphic method. Impacts of Re on Nu and f for two tested furrowed channels with transverse and skewed waviness are individually examined. In addition to the macroscopic mixing between the near-wall recirculations and core flows due to the shear layer instabilities in each wavy channel, the secondary flows tripped by the skewed wall-waves further elevate heat transfer performances and distinguish their Nu distributions from those over the transverse wavy wall. The area-averaged Nusselt numbers ($\overline{\mathit{Nu}}$) for two tested furrowed channels with transverse and skewed waviness with 5000 < Re < 30000 fall, respectively, in the ranges of 3.45–3.71 and 3.98–4.2 times of the Dittus–Boelter levels. A set of $\overline{\mathit{Nu}}$ and f correlations for each tested furrowed channel is individually derived using Re as the controlling parameter. By way of comparing the thermal performance factors (η) with a selection of rib-roughened channels, the η factors for the present skewed wavy channel are compatible with those in the channel roughened by the compound V-ribs and deepened scales due to the relative low pressure drop penalties with the equivalent heat transfer augmentations to those offered by V-ribs.     

Steam jet ejector cooling powered by waste or solar heat

A small scale steam jet ejector experimental setup was designed and manufactured. This ejector setup consists of an open loop configuration and the boiler operate in the temperature range of T_b = 85–140 °C. The typical evaporator liquid temperatures range from T_e = 5 °C to 10 °C while the typical water-cooled condenser pressure ranges from P_c = 1.70 kPa to 5.63 kPa (T_c = 15–35 °C). The boiler is powered by two 4 kW electric elements while a 3 kW electric element simulates the cooling load in the evaporator. The electric elements are controlled by means of variacs.Primary nozzles with throat diameters of 2.5 mm, 3.0 mm and 3.5 mm are tested while the secondary ejector throat diameter remains unchanged at 18 mm. These primary nozzles allow the boiler to operate in the temperature range of T_b = 85–110 °C. When the nozzle throat diameter is increased, the minimum boiler temperature decreases. A primary nozzle with a 3.5 mm throat diameter was tested at a boiler temperature of T_b = 95 °C, an evaporator temperature of T_e = 10 °C and a critical condenser pressure of P_crit = 2.67 kPa (22.6 °C). The system's COP is 0.253.In a case study the experimental data of a solar powered steam jet ejector air conditioner is investigated. Solar powered steam ejector air conditioning systems are technical and economical viable when compared to conventional vapour compression air conditioners. Such a system can either utilise flat plate or evacuated tube solar thermal collectors depending on the type of solar energy available.     

Three-dimensional numerical study on fin-and-oval-tube heat exchanger with longitudinal vortex generators

Three-dimensional numerical study was performed for heat transfer characteristics and fluid flow structure of fin-and-oval-tube heat exchangers with longitudinal vortex generators (LVGs). For Re (based on the hydraulic diameter) ranges from 500 to 2500, it was found that the average Nu for the three-row fin-and-oval-tube heat exchanger with longitudinal vortex generators increased by 13.6–32.9% over the baseline case and the corresponding pressure loss increased by 29.2–40.6%. The results were analyzed on the basis of the field synergy principle to provide fundamental understanding of the relation between local flow structure and heat transfer augmentation. It was confirmed that the reduction of the intersection angle θ between the velocity field and the temperature field was one of the essential factors influencing heat transfer enhancement. Three geometrical parameters – placement of LVGs (upstream and downstream), angles of attack (α = 15°, 30°, 45° and 60°) and tube-row number (n = 2, 3, 4 and 5) – were also investigated for parameter optimization. The LVGs with placement of downstream, angles of attack α = 30° and minimum tube-row number provide the best heat transfer performance. The effects of the three geometrical parameters on heat transfer enhancement were also analyzed from the view point of the field synergy principle and it was found that the results can be well explained by the field synergy principle.     

Air-side thermal hydraulic performance of offset strip fin aluminum heat exchangers

Experimental studies on the air-side heat transfer and pressure drop characteristics for 16 types offset strip fins and flat tube heat exchangers were performed. Parameters including fin space s, fin height h, fin thickness t, fin length l and flow length d, a series of tests were conducted in region of air-side Reynolds number 500–7500, at a constant tube-side water flow rate of 2.5 m³/h. The air-side thermal performance data were analyzed using the effectiveness-NTU method. The heat transfer coefficients and pressure drop data with different fin space s, fin height h, and fin length l were reported in terms of frontal air velocity. The general correlations for Colburn j-factor and Fanning fraction f-factor were derived by regression analysis and F significance test. The correlations for j and f factors can predict 95% and 90% of the experimental data within  ± 10%. And the average deviations of predictive data for the j and f factors are 0.2% and 1.2%, mean deviations are 4.2% and 5.3%.     

Heat transfer behavior in a rotating aluminum foam heat sink with a circular impinging jet

This work experimentally studied heat transfer associated with an impinging jet onto a rotating heat sink. Air was used as the impinging coolant, and a square Al-foam heat sink was adopted. The variable parameters were the jet Reynolds number (Re), the relative nozzle-to-foam tip distance (C/d), the rotational Reynolds number (Re_r) and the relative side length of the square heat sink (L/d). The effects of Re, C/d, Re_r and L/d on the dimensionless temperature distributions and the average Nusselt number were considered. For a stationary system, the results reveal that the average Nusselt number (Nu₀) with Al-foam was two to three times that without Al-foam. Nu₀ increased with Re. A larger L/d responded to a larger Nu₀ based on the same jet flow rate. The effect of C/d on Nu₀ was negligible herein. For a rotating system, when Re and L/d were small and C/d was large, the average Nusselt number (Nu_Ω) increased considerably with Re_r. Additionally, for Nu_Ω/Nu₀ ? 1.1, the results suggest that rotation was substantial at Re_r/Re ? 1.13 when L/d = 4.615 with C/d = 0–5 and at Re_r/Re ? 1.07 when L/d = 3.0 with C/d = 0–5. For L/d = 2.222, rotation was substantial at Re_r/Re ? 1.44 when C/d = 0 and was always substantial when C/d ? 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.     

Combined convection heat transfer for thermally developing aiding flow in an inclined circular cylinder with constant heat flux

Experiments have been conducted to study the local and average heat transfer by mixed convection for hydrodynamically fully developed, thermally developing and thermally fully developed laminar air flow in an inclined circular cylinder. The experimental setup consists of aluminum cylinder as test section with 30 mm inside diameter and 900 mm heated length (L/D = 30), is subjected to a constant wall heat flux boundary condition. The investigation covers Reynolds number range from 400 to 1600, heat flux is varied from 70 W/m² to 400 W/m² and cylinder angles of inclination including 30°, 45° and 60°. The hydrodynamically fully developed condition has been achieved by using aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths. The entrance sections included two long calming sections, one with length of 180 cm (L/D = 60), another one with length of 240 cm (L/D = 80) and two short calming sections with lengths of 60 cm (L/D = 20), 120 cm (L/D = 40). The results present the surface temperature distribution along the cylinder length, the local and average Nusselt number distribution with the dimensionless axial distance Z⁺. For all entrance sections, the results showed an increase in the Nusselt number values as the heat flux increases and as the angle of cylinder inclination moves from θ = 60° inclined cylinder to θ = 0° horizontal cylinder. The mixed convection regime has been bounded by the convenient selection of Re number range and the heat flux range, so that the obtained Richardson numbers (Ri) is varied approximately from 0.13 to 7.125. The average Nusselt numbers have been correlated with the (Rayleigh numbers/Reynolds numbers) in empirical correlations.     

Effect of fin thickness on the air-side performance of wavy fin-and-tube heat exchangers under dehumidifying conditions

This study investigated the effect of fin thickness on the air-side performance of wavy fin-and-tube heat exchangers under dehumidifying conditions. A total of 10 samples were tested with associated fin thickness (δ_f) of 0.115 mm and 0.25 mm, respectively. For a heat exchanger with two rows (N = 2) and fin pitch F_p of 1.41 mm, the effect of fin thickness on the heat transfer coefficient is more pronounced. The heat transfer coefficients for δ_f = 0.25 mm is about 5–50% higher than those for δ_f = 0.115 mm whereas the pressure drop for δ_f = 0.25 mm is about 5–20% higher. The unexpected difference in heat transfer coefficient subject to fin thickness is attributable to better interactions between the directed main flow and the swirled flow caused by the condensate droplet for δ_f = 0.25 mm. The maximum difference in heat transfer coefficients for N = 2 and F_p = 2.54 mm subject to the influence of fin thickness is reduced to about 20%, and there is no difference in heat transfer coefficient when the frontal velocity is above 3 m/s. For N ⩾ 4 and F_p = 2.54 mm, the influence of fin thickness on the heat transfer coefficients diminishes considerably. This is because of the presence of tube row, and the unsteady/vortex shedding feature at the down stream of wavy channel. Based on the present test results, a correlation is proposed to describe the air-side performance for wavy fin configurations, the mean deviations of the proposed heat transfer and friction correlations are 7.9% and 7.7%, respectively.     

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.     

Heat transfer by free convection from the inside surface of the vertical and inclined elliptic tube

Free convection from the inside surface of vertical and inclined elliptic tubes of axis ratio (a:b) 2:1 with a uniformly heated surface (constant heat flux) is investigated experimentally. The effects of orientation angle (α) and inclination angle (ϕ) on the heat transfer coefficient were studied. The orientation angle (α) is varied from 0° (when the major axis is horizontal) to 90° (when the major axis is vertical) with steps of 15°. The inclination angle (ϕ) is measured from the horizontal and varied from 15° to 75° with steps of 15°. The vertical position is considered as a special case of the inclined case when ϕ = 90. The experiments covered a range of Rayleigh number, Ra from 2.6 × 10⁶ to 3.6 × 10⁷. The local and average Nusselt numbers are estimated for different orientation angles and inclination angles at different Rayleigh numbers. The results obtained showed that the local Nu increased with the increase of axial distance from the lower end of the elliptic tube until a maximum value near the upper end, and then, it gradually decreased. The average Nu increases with the increase of α or ϕ at the same Ra. The results obtained are correlated by dimensionless groups and with the available data of the inclined and vertical elliptic tubes.     

Effect of flow geometry parameters on transient heat transfer for turbulent flow in a circular tube with baffle inserts

The effect of the flow geometry parameters on transient forced convection heat transfer for turbulent flow in a circular tube with baffle inserts has been investigated. The characteristic parameters of the tubes are pitch to tube inlet diameter ratio H/D = 1, 2 and 3, baffle orientation angle β = 45°, 90° and 180°. Air, Prandtl number of which is 0.71, was used as working fluid, while stainless steel was considered as pipe and baffle material. During the experiments, different geometrical parameters such as the baffle spacing H and the baffle orientation angle β were varied. Totally, nine types of baffle inserted tube were used. The general empirical equations of time averaged Nusselt number and time averaged pressure drop were derived as a function of Reynolds number corresponding to the baffle geometry parameters of pitch to diameter ratio H/D, baffle orientation angle β, ratio of smooth to baffled cross-section area S_o/S_a and ratio of tube length to baffle spacing L/H were derived for transient flow conditions. The proposed empirical correlations were considered to be applicable within the range of Reynolds number 3000 ⩽ Re ⩽ 20,000 for the case of constant heat flux.     

Asymptotic analysis of heat transfer in turbulent Rayleigh–Bénard convection

Based on asymptotic considerations a heat transfer law for turbulent Rayleigh–Bénard convection is found that differs from existing correlations which often are of a power law type with respect to their Rayleigh number dependence. From the asymptotic temperature profile, derived by matching temperature gradients in the overlap region of the wall layer and the core layer, a Nusselt number follows which includes a logarithmic term. This correlation is in good agreement with data from highly accurate Rayleigh–Bénard experiments for Rayleigh numbers between 10⁵ and 10¹⁵ and Prandtl numbers larger than 0.5. It is an alternative to existing power laws or more complicated correlations for Nu = Nu(Ra,Pr).     

Estimation of temperature dependent heat transfer coefficient in a vertical rectangular fin using liquid crystal thermography

This paper presents a methodology for the estimation of temperature dependent heat transfer coefficient for a vertical rectangular fin by using the inverse heat transfer method with Liquid crystal thermography (LCT) data. Steady state, laminar natural convection experiments have been done on a vertical rectangular fin of size 150 × 250 × 4, (L × w × t, all dimensions are in mm). The variation of heat transfer coefficient is considered as a power law function of temperature excess (h = a_oθ^b) and is derived from the basic Nusselt number equation used for laminar natural convection, Nu = aRa^b. With this functional form, the one dimensional fin equation in finite difference form is repeatedly solved using the Gauss–Seidel iterative method. Treating this as a one parameter estimation in ‘a’ the sum of the squares of the difference between the simulated and Thermochromic Liquid Crystal (TLC) measured temperatures is minimized with the Golden section search algorithm to retrieve ‘a’. Estimate of ‘a’ and the accompanying uncertainties are first reported for synthetically generated temperature distribution for assumed values of ‘a’. The effect of noise on the estimate of ‘a’ is discussed. This is followed by retrievals with experimentally obtained TLC temperature distribution for a range of heat inputs to the fin base. The required temperature distributions for accomplishing the retrievals over the surface are obtained using calibrated R40C5W Thermochromic Liquid Crystal (TLC) sheets. As an additional proof of the accuracy of the method, the retrieved value of ‘a’ is used to simulate the temperature distribution in the fin which is then compared with the actual TLC measured temperature distribution.     

Numerical study of heat-transfer enhancement by punched winglet-type vortex generator arrays in fin-and-tube heat exchangers

The potential of punched winglet type vortex generator (VG) arrays used to enhance air-side heat-transfer performance of finned tube heat exchanger is numerically investigated. The arrays are composed of two delta-winglet pairs with two layout modes of continuous and discontinuous winglets. The heat transfer performance of two array arrangements are compared to a conventional large winglet configuration for the Reynolds number ranging from 600 to 2600 based on the tube collar diameter, with the corresponding frontal air velocity ranging from 0.54 to 2.3 m/s. The effects of different geometry parameters that include attack angle of delta winglets (β = 10 deg, β = 20 deg, β = 30 deg) and the layout locations are examined. The numerical results show that for the punched VG cases, the effectiveness of the main vortex to the heat transfer enhancement is not fully dominant while the “corner vortex” also shows significant effect on the heat transfer performance. Both heat transfer coefficient and pressure drop increase with the increase of attack angle β for the side arrangements; the arrays with discontinuous winglets show the best heat transfer enhancement, and a significant augmentation of up to 33.8–70.6% in heat transfer coefficient is achieved accompanied by a pressure drop penalty of 43.4–97.2% for the 30 deg case compared to the plain fin. For the front arrangements of VGs higher heat transfer enhancement and pressure drop penalty can be obtained compared to that of the side arrangement cases; the case with front continuous winglet arrays has the maximum value of j/f, a corresponding heat transfer improvement of 36.7–81.2% and a pressure drop penalty of 60.7–135.6%.     

Multi-parameters optimization for microchannel heat sink using inverse problem method

This work describes an inverse problem method to optimize the geometric design for microchannel heat sinks using a novel multi-parameter optimization approach, which integrates the simplified conjugate-gradient scheme and a fully developing three-dimensional heat transfer and flow model. Overall thermal resistance is the objective function to be minimized with number of channels, N, channel aspect ratio, α, and the ratio of channel width to pitch, β, as search variables. With a constant bottom area (10 mm × 10 mm), constant heat flux applied to the heat sink bottom surface (100 W cm^?2), and constant pumping power (0.05 W), the optimal design values are N = 71, α = 8.24, and β = 0.6, with a minimum overall thermal resistance of 0.144 K W^?1. Increasing pumping power reduces overall thermal resistance of the optimal design; however, the design’s effectiveness declines significantly under high pumping power. The N and α values in the optimal design increase and β decreases as pumping power increases.