Thermal-fluid characteristics of plate-fin heat sinks cooled by impingement jet

This work experimentally and numerically studies the thermal-fluid characteristics of plate-fin heat sinks under impingement cooling by adjusting the impinging Reynolds number, the impingement distance, and the fin dimensions. The parameters and the ranges under consideration are the impinging Reynolds number (Re = 5000–25,000), the impingement distance (Y/D = 4–28), the fin width (W/L = 0.08125–0.15625) and the fin height (H/L = 0.375–0.625). The results show that the heat transferred by the heat sink increases with the impinging Reynolds number. The thermal performance can be improved significantly even at low impinging Reynolds number. However, the improvement becomes indistinct as the impinging Reynolds number increases. The thermal resistance declines as the impingement distance increases, and is minimal at Y/D = 20 for various impinging Reynolds numbers. Additionally, the thermal resistance increases as the impingement distance increases further. Increasing the fin width can effectively reduce the thermal resistance. However, as the fin width increases beyond a particular value, the thermal resistance increases dramatically. Reducing the thermal resistance by increasing the fin height depends on a suitable impinging Reynolds number and fin width. Therefore, the effect of the fin height is weaker than that of the impinging Reynolds number or the fin width.     

Numerical study of the heat sink with un-uniform fin width designs

The thermal performances of the heat sink with un-uniform fin width designs with an impingement cooling were investigated numerically. The governing equations are discretized by using a control-volume-based finite-difference method with a power-law scheme on an orthogonal non-uniform staggered grid. The coupling of the velocity and the pressure terms of momentum equations are solved by the SIMPLEC algorithm. The well-known k ? ε two-equations turbulence model is employed to describe the turbulent structure and behavior. The parameters include the five Reynolds number (Re = 5000–25000), three fin heights (H = 35, 40, 45 mm), and five fin width designs (Type-1–Type-5). The objective of this study is to examine the effects of the fin shape of the heat sink on the thermal performance. The results show that the Nusselt number increases with the Reynolds number. The increment of the Nusselt number decreases gradually with the increasing Reynolds number. Furthermore, the effects of fin dimensions on the Nusselt number at high Reynolds numbers are more significant than that at low Reynolds numbers. It is also found that there is potential for optimizing the un-uniform fin width design.     

Numerical study of pin-fin heat sink with un-uniform fin height design

This study presents the numerical simulation of the heat sink with an un-uniform fin height with a confined impingement cooling. The governing equations are discretized by using a control-volume-based finite-difference method with a power-law scheme on an orthogonal non-uniform staggered grid. The coupling of the velocity and the pressure terms of momentum equations are solved by the SIMPLEC algorithm. The well-known k–ε two-equations turbulence model is employed to describe the turbulent structure and behavior. The parameters include the Reynolds number (Re = 15,000 and Re = 25,000) and 12 un-uniform fin height designs (Type-b to Type-m). The objective of this study is to examine the effects of the fin shape of the heat sink on the thermal performance. It is found that the junction temperature can be reduced by increasing the fin height near the center of the heat sink. The results also show that there is a potential for optimizing the un-uniform fin height design.     

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 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.     

Nonlinear flow and heat transfer dynamics of impinging jets onto slightly-curved surfaces

The nonlinear flow and heat transfer characteristics for a slot-jet impinging on slightly-curved surfaces are experimentally studied here. The effects of curved surface geometry and jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. Two different slightly-curved surface geometries of convex and concave are used as target surfaces. The nozzle geometry is a rectangular slot, and the dimensionless nozzle-to-surface distance equals to L¹ = 8. The constant heat fluxes are accordingly applied to the surfaces to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of Re = 8617, Re = 13 350 and Re = 15 415 for both curved surfaces. The velocity distributions of issuing jet from the nozzle exit to the target surface are obtained by a highly sensitive hot-wire anemometer. The T-type thermocouples are used to measure local temperatures of both the air jet and the plates. Two-dimensional velocity measurements show that the surfaces are remained out of the potential core region for all Re tested here. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported. The correlations reveal that the impinging cooling rate is higher with the concave surface and increase with increasing Re.     

Entropy generation in impinging flow confined by planar opposing jets

In this paper, entropy generation in impinging flow confined by planar opposing jets is investigated systematically for the first time. Different from previous works on entropy generation for practical flows, in this study the lattice Boltzmann method, which is more suitable for massive parallel computing, is used to solve the governing equations for flow field as well as the entropy generation equation, instead of traditional numerical methods. The effects of the Reynolds number 10 ≤ Re ≤ 500 and the distance ratio between opposing jets 2/5 ≤ W/L ≤ 4/5 on entropy generation are revealed. It is found that the local entropy generation number is more sensitive to the variation of W/L than Re when Re > 50. The total entropy generation number increases exponentially with Re but decreases as a power function of W/L. In addition, the entropy generation will receive significant influence from the damping traveling pressure wave during the transient state and the maximum emerges when the gas ejected from the top and bottom jets begins meeting and impinging.     

Cooling of two smooth cylinders in row by a slot jet of air with low turbulence

According to the current literature on the cooling of two cylinders in row, by a uniform flow of air, the first cylinder is always a heat transfer promoter versus the second one. The aim of the present paper is to summarize the state of art of the literature on the cooling of two cylinders in row by a slot jet of air. Additional experiments are carried on in order to investigate the possible application of jet cooling to heat transfer apparatuses, including electronics, in order to study the positions of the two cylinders in row which realize the same heat transfer on each cylinder. In the experiments a slot jet of air with low turbulence is employed with a slot height, S, equal to the impinged cylinder diameter, D, i.e. D/S = 1.0. The first cylinder is set at two distances H from the slot exit, H/S = 4 and 6, while the distance of the second cylinder from the first one, L, is variable from L/S = 2–11. The Reynolds number, Re, defined with the cylinder diameter D, spans in the range Re = 11,000–22,200. If the first cylinder is set at the dimensionless distance from the slot exit which realizes the maximum mean heat transfer on the first cylinder, i.e. H/S = 6, the second one has generally a lower mean Nusselt number. The only exception is when the second cylinder is set at the dimensionless distance L/S = 4 and the Reynolds number is at the maximum value experimented, i.e. Re = 22,200. If the first cylinder is set at the dimensionless distance H/S = 4 the mean Nusselt number on the second cylinder is greater if its distance from the first one is in the range L/S = 3.5–7 for Re = 14,300–22,200. The first cylinder acts as a heat transfer promoter, as happens in uniform flow, only for Re = 22,200.     

Conjugated heat transfer on leading edge of a wedge-shaped concave wall internally impinged by hot jets from corrugated orifice plate

An experimental and numerical investigation is conducted to study the conjugated heat transfer performance on the leading edge of a wedge-shaped concave wall subjected to external cold flow and internal hot jets impingement. A corrugated impinging plate with an extended front-extended port inside the concave cavity is proposed for the purpose of heat transfer enhancement. The effects of corrugation length-to-diameter ratio (H_j/d) ranging from 5 to 11 and width-to-diameter ratio (W_j/d) ranging from 2.5 to 6 on the conjugated heat transfer performance are examined under some representative jet Reynolds numbers (Re_j) in the range of 7900–31,700. The results show that the corrugated impinging plate has a significant impact on improving the conjugated heat transfer performance in the vicinity of concave wall leading edge. The presence of corrugation plays two roles by reducing the jet impinging distance on one hand and aggravating the jet confinement on the other hand. Therefore, it produces more complicated jet impinging flow and convective heat transfer behaviors than the baseline case without corrugation. According to the tested results, the specified area-averaged heating effectiveness is increased approximately 6.3%–18.8% under Re_j = 7900 and 2.5%–9.4% Under Re_j = 31,700 respectively by increasing the corrugation length when W_j/d is fixed as 2.5. The specified area-averaged heating effectiveness is increased approximately 16.1%–22.1% under Re_j = 7900 and 7.7%–12.7% under Re_j = 31,700 respectively by increasing the corrugation width when H_j/d is fixed as 9. In general, the corrugation with larger length and width seems to perform the better heating effectiveness over the entire concave surface. The enhancement of heating effectiveness related to the baseline case behaves more significantly under a smaller jet Reynolds number.     

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.     

Measurement of local heat/mass transfer coefficients on a dimple using naphthalene sublimation

Local and average heat/mass transfer characteristics on a single dimple were investigated using a naphthalene sublimation technique. The dimple depth in this study ranged from 20% to 40% of the channel height. The experimental conditions covered the range from laminar to low-velocity turbulent flow regimes, 500 ? Re_H ? 5000. Secondary flows from the dimple were clearly observed in the transient flow regime of Re_H = 2000–3000. The velocity fluctuation in the mixing layer over the dimple increased with the dimple depth and the Reynolds number. The impingement of the mixing layer and the induced secondary flows augmented the Sherwood number around the rear rim of the dimple and in the rear plateau region, respectively. For a Reynolds number of 3000, the Sherwood number increased significantly due to the increased fluctuation in the mixing layer and the intensified secondary flows from the dimple. The heat/mass transfer augmentation factors increased as the Reynolds number increased, reaching 1.5 at a Reynolds number of 5000.     

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.     

Influences of nozzle-plate spacing on boiling heat transfer of confined planar dielectric liquid impinging jet

We have investigated the single-phase and boiling heat transfer of dielectric liquid under the Reynolds numbers (2000, 3000 and 5000) and under nozzle-plate spacing (H/W; 0.5, 1.0 and 4.0) in a submerged impinging jet system. The boiling incipience increases in proportion to the Reynolds number and in inverse proportion to the nozzle-to-surface spacing. The critical heat flux at H/W = 1.0 is lower than those of outer spacings, such as H/W = 0.5 and 4.0, due to the characteristics of the jet impingement heat transfer distribution. We suggest a correlation equation of nozzle-plate spacing (H/W) having the lowest CHF for various jet velocities.     

Heat transfer in a turbulent slot jet flow impinging on concave surfaces

An experimental and numerical study is conducted to investigate turbulent slot jet impingement cooling characteristics on concave plates with varying surface curvature. Air is used as the impingement coolant. In the experimental work, a slot nozzle specially designed with a sixth degree polynomial in order to provide a uniform exit velocity profile was used. The experiments were carried out for the jet Reynolds numbers in the range of 3423 ≤ Re ≤ 9485, the dimensionless nozzle-to-surface distance range of 1 ≤ H/W ≤ 14 for dimensionless values of the curvature of impinging surfaces in the range of R/L = 0.5, 0.725, and 1.3 and a flat impingement surface. Constant heat flux was applied on the plates. Numerical computations were performed using the k-ε turbulence model with enhanced wall functions. For the ranges of the governing parameters studied, the stagnation, and local and average Nusselt numbers have been obtained both experimentally and numerically. The numerical results showed a reasonable agreement with the experimental data.     

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.     

Nonlinear flow and heat transfer dynamics of a slot jet impinging on a slightly curved concave surface

The nonlinear flow and heat transfer characteristics for a slot jet impinging on a slightly curved concave surface are experimentally studied here. The effects of jet Reynolds number on the jet velocity distribution and circumferential Nusselt numbers are examined. The nozzle geometry is a rectangular slot and the dimensionless nozzle-to-surface distance equals to L^⁎ = 8. The constant heat fluxes are accordingly applied to the surface to obtain an impingement cooling by the air jet at ambient temperature. The measurements are made for the jet Reynolds numbers of 8617, 13 350 and 15 415. New correlations for local, stagnation point, and average Nusselt numbers as a function of jet Reynolds number and dimensionless circumferential distance are reported.     

Experiments on impingement heat transfer with film extraction flow on the leading edge of rotating blades

A transient liquid crystal experiment was performed to study the heat transfer characteristic of impingement cooling with outflow film on the leading edge of turbine blades under rotating conditions. In the experiments, the angles between the jet direction and rotating shaft were 0°, 30°, and 45°, respectively. The impinging jet Reynolds number, based on the diameter of the impingement hole, ranged from 2000 to 12,000. The rotation number Ro (Ωd/u) ranged from 0 to 0.278. The relative impingement distance was fixed at 2. The results showed that, due to the effect of rotation, the spreading rate of the jet flow was enhanced and the heat transfer was weakened for all Reynolds numbers. For the condition of Re = 4000 and Ro = 0.139 with corresponding angles θ = 0°, 30°, 45°, the Nusselt number of the stagnation point decreased by 33%, 30%, and 35%, respectively, compared to the stationary results. Furthermore, for the corresponding angles θ = 30° and 45°, the location of the stagnation point is offset 0.6d (jet impingement hole diameter) and 0.9d down, respectively, when Ro = 0.139. The average Nusselt numbers on the suction surface and the pressure surface both decreased with increased rotating speed. Moreover, the reduction of the average Nusselt number on the pressure surface was larger than that on the suction surface. At Ro = 0.139, the average Nusselt number on the suction surface decreased less than 10% for all three angles, while on the pressure surface, the decrease was almost 20% compared to the result for Ro = 0.     

The investigation of groove geometry effect on heat transfer for internally grooved tubes

An experimental study of surface heat transfer and friction characteristics of a fully developed turbulent air flow in different grooved tubes is reported. Tests were performed for Reynolds number range 10,000–38,000 and for different geometric groove shapes (circular, trapezoidal and rectangular). The ratio of tube length-to-diameter is 33. Among the grooved tubes, heat transfer enhancement is obtained up to 63% for circular groove, 58% for trapezoidal groove and 47% for rectangular groove, in comparison with the smooth tube at the highest Reynolds number (Re = 38,000). Correlations of heat transfer and friction coefficient were obtained for different grooved tubes. In evaluation of thermal performance, it is seen that the grooved tubes are thermodynamically advantageous (Ns, a < 1) up to Re = 30,000 for circular and trapezoidal grooves and up to Re = 28,000 for rectangular grooves. It is observed that there is an optimum value of the entropy generation number at about Re = 17,000 for all investigated grooves.     

Experimental investigation of mixed convection heat transfer for thermally developing flow in a horizontal circular cylinder

An experimental investigation is presented on mixed (free and forced) convection to study the local and average heat transfer for hydrodynamically fully developed, thermally developing and thermally fully developed laminar air flow in a horizontal 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, the heat flux varied from 60 W/m² to 400 W/m² and with cylinder inclination angle of θ = 0° (horizontal). The hydrodynamically fully developed condition is achieved by using an 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 60 cm (L/D = 20), 120 cm (L/D = 40). The surface temperature variation along the cylinder surface, the local and average Nusselt number variation with the dimensionless axial distance Z⁺ were presented. For all entrance sections, it was found an increase in the Nusselt number values as the heat flux increases. It was concluded that the free convection effects tended to decrease the heat transfer results at low Re while to increase the heat transfer results for high Re. The combined convection regime could be bounded by a suitable selection of Re number ranges and the heat flux ranges. The obtained Richardson numbers (Ri) range varied approximately from 0.13 to 7.125. The average Nusselt numbers were correlated with the (Rayleigh numbers/Reynolds numbers). The proposed correlation has been compared with available literature and showed satisfactory agreement.