Numerical investigation of heat transfer enhancement on a porous vortex-generator applied to a block-heated channel

The numerical simulation is used to obtain the unsteady laminar flow and convective heat transfer in the block-heated channel with the porous vortex-generator. The general Darcy–Brinkman–Forchheimer model is adopted for the porous vortex-generator. The parameters studies including porosity, Darcy number, width-to-height ratio of porous vortex-generator and Reynolds number have been explored on heat transfer enhancement and vortex-induced vibration in detail. The results indicate that heat transfer enhancement and vortex-induced vibration increase with increasing Reynolds number and width-to-height ratio. However, the porosity has slight influence on heat transfer enhancement and vortex-induced vibration. When Darcy number is 10^?3 or 10^?4, installing a porous vortex-generator with B/h = 1.0 improves overall heat transfer the best along heated blocks, and has a strong reduction of vortex-induced vibration.     

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.     

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.     

Heat transfer of rectangular narrow channel with two opposite scale-roughened walls

An experimental study of heat transfer and pressure drop in a rectangular channel roughened by scaled surfaces on two opposite walls with flows directed in the forward and downward directions for Reynolds numbers (Re) in the range of 1500 ⩽ Re ⩽ 15,000 was performed. Nusselt number ratios between the scale-roughened and smooth-walled ducted flows (Nu/Nu_∞) were in the range of 7.4–9.2 and 6.2–7.4 for laminar forward and downward flows respectively. The Nu/Nu_∞ values for turbulent developed flows in the scale-roughened channel with forward and downward flows were about 4.5 and 3 respectively. A comparison of present data with reported results using different types of surface roughness demonstrated the better thermal performances of present scale-roughened channel with forward flow at conditions of Re > 10,000. Experimental correlations of heat transfer and friction coefficient were derived for the present scale-roughened rectangular channel.     

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.     

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.     

Bénard convection from a circular cylinder in a packed bed

Bénard convection around a circular heated cylinder embedded in a packed bed of spheres is studied numerically. The Forchheimer–Brinkman–extended Darcy momentum model with the Local Thermal Non-Equilibrium energy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the Rayleigh number (10³ ≤ Ra ≤ 5 × 10⁷) and the thermal conductivity ratio (0.1 ≤ k_r ≤ 10,000). The structural properties of the packed bed are kept constant as: cylinder-to-particle diameter ratio D/d = 20 and porosity ε = 0.5, while the Prandtl number is fixed at Pr = 0.71. It is found that the presence of the porous medium suppresses significantly the strong free convection produced in the empty enclosure, and reduces considerably the high intensity of the pair of vortices generated behind the cylinder. Also, the results show that the porous medium can play the role of insulator or enhancer of heat transfer from the heat source, depending mainly on their thermal conductivities regardless of the Rayleigh number.     

Rotation effects on non-Darcy convection in an enclosure filled with porous medium

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper taking into consideration the Forchheimer–Brinkman-extended Darcy model. The enclosure is filled with a fluid-saturated porous medium and executes a steady counterclockwise angular velocity about its longitudinal axis. The staggered grid arrangement together with the Marker and Cell (MAC) method was employed to solve the governing equations. The governing parameters considered are the porosity, 0.4 ≤ ϵ ≤ 0.99, the Darcy number, 0.005 ≤ Da ≤ 0.01 and the Taylor number, 8.9 × 10⁴ ≤ Ta ≤ 3.8 × 10⁵, and the centrifugal force is assumed weaker than the Coriolis force. It is found that higher porosities have weaker flow circulation when the Coriolis effect is smaller than the buoyancy effect. The global quantity of the heat transfer rate increases by increasing the porosity and the Darcy number and decreases by increasing the Taylor 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.     

Numerical simulation of turbulent fluid flow and heat transfer characteristics in heat exchangers fitted with porous media

Numerical simulations have been carried out to investigate the turbulent heat transfer enhancement in the pipe filled with porous media. Two-dimensional axisymmetric numerical simulations using the k–? turbulent model is used to calculate the fluid flow and heat transfer characteristics in a pipe filled with porous media. The parameters studied include the Reynolds number (Re = 5000–15,000), the Darcy number (Da = 10^?1–10^?6), and the porous radius ratio (e = 0.0–1.0). The numerical results show that the flow field can be adjusted and the thickness of boundary layer can be decreased by the inserted porous medium so that the heat transfer can be enhanced in the pipe. The local distributions of the Nusselt number along the flow direction increase with the increase of the Reynolds number and thickness of the porous layer, but increase with the decreasing Darcy number. For a porous radius ratio less than about 0.6, the effect of the Darcy number on the pressure drop is not that significant. The optimum porous radius ratio is around 0.8 for the range of the parameters investigated, which can be used to enhance heat transfer in heat exchangers.     

Unsteady conjugate natural convection in a square enclosure filled with a porous medium

Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy–Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 10⁴, 10⁵, 10⁶, of Darcy number effect Da = 10^?5, 10^?4, 10^?3, ∞, of the transient factor effect 0 < τ < 1000 and of the heat conductivity ratio k_2,1 = 3.7 × 10^?2, 5.7 × 10^?4, 6.8 × 10^?5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.     

Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel

In this paper, we report the influence of different terms appearing in the momentum equation on the stability of buoyancy-assisted mixed convection in a vertical channel filled with a porous medium. Four different models: (i) Darcy–Brinkman (DB), (ii) Darcy–Brinkman–Forchheimer (DBF), (iii) Darcy–Brinkman–Wooding (DBW), and (iv) Darcy–Brinkman–Forchheimer–Wooding (DBFW) are considered and a comparative study is made based on a linear stability analysis. We consider a Prandtl number range of Pr = 0.1–10, which corresponds to water and gases. Judged from the instability boundary curves, it is found that with reduction of Darcy number there exists an equivalence of DB with DBF model from one side, and an equivalence of DBW with DBFW model from the other side. When the medium is a gas, a significant difference between DB and DBW (or DBF and DBFW) is visible, which is not the case for water. Furthermore, it is found that in case of a gas, inertia force destabilizes the flow, whereas, form drag stabilizes it. In contrast to a fluid-filled channel (where inertia term always destabilizes the buoyancy-assisted flow), here this destabilizing property might turn into a stabilizing one when fluid viscosity and permeability of the medium are changed. In the case of water, for Da = 10^?2, the inertia term stabilizes the flow beyond Re = 25. When Da is reduced by one order of magnitude, the destabilizing effect continued up to Re = 220. The combined effect of form drag (Forchheimer term) and inertia (Wooding term) on the stability of the flow is more intensive than their individual effects provided the medium is highly permeable. In most cases studied here, the disturbance flow patterns are similar for DB and DBF from one side, and DBW and DBFW from the other side.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Steady natural convection flow in a square cavity filled with a porous medium for linearly heated side wall(s)

In this paper natural convection flows in a square cavity filled with a porous matrix has been investigated numerically when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Darcy–Forchheimer model without the inertia term is used to simulate the momentum transfer in the porous medium. Penalty finite element method with bi-quadratic rectangular elements is used to solve the non-dimensional governing equations. Numerical results are presented for a range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.2 ⩽ Pr ⩽ 100) in terms of stream functions and isotherm contours, and local and average Nusselt numbers.     

Jet impingement cooling of a constant heat flux horizontal surface in a confined porous medium: Mixed convection regime

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions with the limitation of the Darcy model. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Péclet number (1 ? Pe ? 1000), Rayleigh number (10 ? Ra ? 100), half jet width (0.1 ? D ? 1.0), and the distance between the jet and the heated portion (0.1 ? H ? 1.0). It is found that the average Nusselt number increases with increase in either Rayleigh number or jet width for high values of Péclet number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The correlation for Nu_avg in the forced convection regime is suggested. It is shown that mixed convection mode can cause minimum average Nusselt number unfavorably due to counteraction of jet flow against buoyancy driven flow. Hence, careful consideration must be given while designing a system of jet impingement cooling through porous medium.     

Numerical analysis of natural convection heat transfer in a horizontal annulus partially filled with a fluid-saturated porous substrate

The current study centers around a numerical investigation of natural convection heat transfer within a two-dimensional, horizontal annulus that is partially filled with a fluid-saturated porous medium. In addition, the porous sleeve is considered to be press fitted to the inner surface of the outer cylinder. Both cylinders are maintained at constant and uniform temperatures with the inner cylinder being subjected to a relatively higher temperature than the outer one. Moreover, the Forchheimer and Brinkman effects are taken into consideration when simulating the fluid motion inside the porous sleeve. Furthermore, the local thermal equilibrium condition is assumed to be applicable for the current investigation. The working fluid is air while copper is used to represent the solid phase. The porosity is considered to be uniform and constant with ε = 0.9. The main objective of this study is to examine the effect of the porous sleeve on the buoyancy induced flow motion under steady-state condition. Such an effect is studied using the following dimensionless parameters: Pr = 0.05–50, Ra = 10²–10⁶ and Da = 10^?4–10^?6. Also, the study highlights the effect of the dimensionless porous sleeve thickness (b) and thermal conductivity ratio (k_s/k_f) in the range between 1.1–1.9 and 1–150, 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.     

Numerical study of heat transfer enhancement for a novel flat-plate solar water collector using metal-foam blocks

This paper reports a numerical study of enhanced forced convection in a channel of solar water collector using multiple metal-foam blocks. Both Darcy–Brinkman–Forchheimer flow model and two-equation energy model based on local thermal non-equilibrium are used to characterize the thermo-flow fields inside the porous regions. Solution of the coupled governing equations for the porous/fluid composite system is obtained using a stream function-vorticity analysis. The results show that the recirculation caused by metal-foam block will significantly augment the heat transfer rate on heated surface. Besides, a useful correlated equation to predict Nu_m is proposed and the validity of the LTE condition is examined.     

Experimental study of natural convection in PV roof solar collector

The aim of this paper is to propose the PV roof solar collector (PV-RSC) to investigate the natural convection heat transfer and estimated the convective heat transfer coefficient in the channel. The experimental set-up was composed of a PV panel on the upper layer and the lower layer is aluminum plate of the channel. The inclination angle and air gap of channel were fixed at 30° and 15 cm, respectively. The channel width is 0.7 m, and length is 1.2 m. The data analysis were confirmed the effect of radiative exchange influent to natural convection within the channel. On the basis of the experimental results, an empirical formula is found; the Nu as a function of Ra_s sin30, that is Nu_s = 0.3282 (Ra_s sin30)^0.2249. The correlation obtained to range 3 × 10⁸ < Ra_s sin30 < 7 × 10⁸. A comparison between PV-RSC and normal PV panel, it was confirmed that the PV-RSC could be generated electric power than that normal PV panel by about 30 W; and also the percentage of power generation increase was rising about 25% throughout the day.     

Transpiration cooling of a nose cone by various foreign gases

The transpiration cooling mechanisms used for thermal protection of a nose cone was investigated experimentally and numerically for various cooling gases. The effects of injection rates, model geometry, inlet temperature and Reynolds number of the main stream were studied for air, nitrogen, argon, carbon dioxide and helium. The experiments used a hot gas wind tunnel with T_∞ = 375 K and 425 K and Re_∞ = 4630–10,000. The experimental results indicated that even a small amount of coolant injection drastically reduced the heat transfer from the hot gases with the cooling effectiveness increasing with increasing injection rate, although the increases became smaller as the gas injection rate was further increased. The temperature and cooling effectiveness distribution along the transpiration surface of the nose cone model exhibited similar tendencies for all the coolants employed in present experimental research. The temperature decreased from the stagnation point towards the downstream region, then increased because of the non-uniform mass flow distribution of the coolant and thermal conduction from the metal backplane, whereas the cooling effectiveness variation was the reverse. The local cooling effectivenesses and thermal capacities were found to depend on the coolant thermophysical properties. Two-dimensional numerical simulations using the RNG κ?ε turbulence model for the main stream flow and the Darcy–Brinkman–Forchheimer momentum equations and thermal equilibrium model for the porous zone compared well with the general features in the experiments.