Jet impingement interaction with cross flow in horizontal porous layer under thermal non-equilibrium conditions

In the present article the jet impingement cooling of heated portion of a horizontal surface immersed in a thermally non-equilibrium porous layer is considered for investigation numerically with the presence of a cross flow. The mathematical model is derived for steady, two-dimensional laminar flow based on Darcy model and two-energy equation for fluid and solid phases. A parametric study is carried out by varying the following parameters: cross flow to jet flow velocity ratio parameter (0 ⩽ M ⩽ 1); porosity scaled thermal conductivity ratio parameter (0.1 ⩽ K_r ⩽ 1000); heat transfer coefficient parameter (0.1 ⩽ H ⩽ 1000); Péclet number (1 ⩽ Pe ⩽ 1000) and Rayleigh number (10 ⩽ Ra ⩽ 100). The total average Nusselt number is defined based on the overall thermal conductivity, which is assumed to be the arithmetic mean of the porosity scaled thermal conductivity of the fluid and solid phases. The total average Nusselt number as well as the average Nusselt number for both fluid and solid phases is presented for different governing parameters. It is found that the presence of a weak cross flow in a jet impinging jet may degrade the heat transfer. The results show that the average Nusselt number calculated from the thermal equilibrium model are the maximum possible values and these values can be reproduced by large values of H × K_r.     

Heat transfer in enclosures having a fixed amount of solid material simulated with heterogeneous and homogeneous models

This work compares two different approaches for obtaining numerical solutions for laminar and turbulent natural convection within a cavity filled by a fixed amount of a solid conducting material. In the first model, a porous-continuum, homogeneous or macroscopic approach is considered based on the assumption that the solid and the fluid phases are observed as a single medium, over which volume-averaged transport equations apply. Secondly, a continuum, heterogeneous or microscopic model is considered to solve the momentum equations for the fluid phase resulting in a conjugate heat transfer problem in both the solid and the void space. In the continuum model, the solid phase is composed of square obstacles, equally spaced within the cavity. In both models, governing equations are numerically solved using the finite volume method. The average Nusselt number at the hot wall, obtained from the porous-continuum, homogeneous or macroscopic model, for several Darcy numbers, are compared with those obtained with the second approach, namely the continuum model, with different number of obstacles. When comparing the two methodologies, this study shows that the average Nusselt number calculated for each approach for the same Ra_m differs from each other and that this discrepancy increases as the Darcy number decreases, in the porous-continuum model, or the number of blocks increases, in the continuum model. Inclusion of turbulent transfer raises Nusselt for both the continuum and the porous-continuum models. A correlation is suggested to modify the macroscopic Rayleigh number in order to match the average Nusselt numbers calculated by the two models for Ra_m = const = 10⁴ and Da ranging from 1.2060 × 10⁻⁴ to 1.     

Numerical study of turbulent slot jet impingement cooling on a semi-circular concave surface

An investigation of the flow field and heat transfer characteristics of a slot turbulent jet impinging on a semi-circular concave surface with uniform heat flux has been carried out numerically in this study. The turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known k–ε turbulence model and its associate wall function to describe the turbulent structure. In addition, a body-fitted curvilinear coordinate system is employed to transform the physical domain into a computational domain.Numerical computations have been conducted with variations of jet exit Reynolds number Re_2B (5920 ? Re_2B ? 23,700), dimensionless jet-to-surface distance H/B (0.5 ? H/B ? 12), dimensionless jet width B/D (0.033 ? B/D ? 0.05) and the heat flux q″ (1663 W/m² ? q″ ? 5663 W/m²). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. The variations of local Nusselt numbers along the semi-circular concave surface decrease monotonically from its maximum value at the stagnation point. The numerical results show that the local Nusselt numbers are reasonably predicted with a maximum discrepancy within 15%. As the Reynolds number fixes, the effect of the impingement distance (H/B) on the average Nusselt (Nu_avg) is not significant except at low H/B = 0.5. This study provides fundamental insight into turbulent slot jet impingement cooling on the semi-circular concave surface.     

Natural convection in a rectangular enclosure containing an oval-shaped heat source and filled with Fe3O4/water nanofluid

This work concerns with the study of natural convection heat transfer in rectangular cavities with an inside oval-shaped heat source filled with Fe₃O₄/water nanofluid. The finite element method is employed to solve the governing equations for this problem. Average Nusselt numbers are presented for a wide range of Rayleigh number (10³ ≤ Ra ≤ 10⁵), volume fraction of nanoparticles (0 ≤ ϕ ≤ 14%), and four different size and shapes of the heat source. Depending on concentration of the nanoparticle, geometry of the heat source, and the value of Rayleigh number different behaviors are monitored for average Nusselt numbers. Configuration of the heat source dictates a significant change on the behavior of the average Nusselt number, while addition of the nanoparticles has a negative effect on the magnitude of Nusselt number for this problem.     

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.     

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.     

Numerical thermal analysis and optimization of a water jet impingement cooling with VOF two-phase approach

The fluid flow and heat transfer characteristics of a free-surface liquid jet impingement cooling have been investigated numerically. The slot jet with water impinging normally on a flat plate is employed. To describe the turbulent structure, the turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known turbulence model, which are associated with wall function. Numerical computations have been conducted with variations of jet exit Reynolds number (11,000 ≤ Re_d ≤ 17,000), dimensionless jet-to-surface distance (3 ≤ H/d₀ ≤ 12), dimensionless jet width (1 ≤ B/d₀ ≤ 2), and the heat flux (140 kW/m² ≤ q″ ≤ 280 kW/m²). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. Under the studied ranges, the variations of local Nusselt numbers by hydraulic diameter Nu_d of the dimensionless jet-to-surface distance 3 ≤ H/d₀ ≤ 12 along the flat plate decrease monotonically from its maximum value at the stagnation point. In addition, the shape of the inlet area and jet-to-surface distance are optimized by using the response surface methodology (RSM) and the genetic algorithm (GA) method after solutions are carefully validated with available experimental results in the literature. Based on the optimal results, the optimum condition is in H/d₀ = 7.86 and B/d₀ = 2 for this physical model.     

Steady forced convection heat transfer from a heated circular cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated circular cylinder in the steady cross-flow regime has been investigated numerically by solving the momentum and thermal energy equations using a finite volume method and the QUICK scheme on a non-uniform Cartesian grid. The dependence of the average Nusselt number on the Reynolds number (5 ⩽ Re ⩽ 40), power-law index (0.6 ⩽ n ⩽ 2) and Prandtl number (1 ⩽ Pr ⩽ 1000) has been studied in detail. The numerical results are used to develop simple correlations as functions of the pertinent dimensionless variables. In addition to the average Nusselt number, the effects of Re, Pr and n on the local Nusselt number distribution have also been studied to provide further physical insights. The role of the two types of thermal boundary conditions, namely, constant temperature and uniform heat flux on the surface of the cylinder has also been presented.     

Numerical simulation of natural convection heat transfer in a porous cavity heated from below using a non-Darcian and thermal non-equilibrium model

The present paper investigates the numerical simulation of steady laminar incompressible natural convection heat transfer in an enclosed cavity that is filled with a fluid-saturated porous medium. The bottom wall is subjected to a relatively higher temperature than the top wall while the vertical walls are considered to be insulated. The flow field is modeled upon incorporating different non-Darcian effects, such as the convective term, Brinkman effect and Forchhiemer quadratic inertial effect. Moreover the two-equation model is used to separately account for the local fluid and solid temperatures. The numerical solution is obtained through the application of the finite volume method. The appraisals of the sought objectives are performed upon identifying key dimensionless groups of parameters. These dimensionless groups along with their operating domains are: Rayleigh number 1 ⩽ Ra ⩽ 400, Darcy number 10⁻⁴ ⩽ Da ⩽ 10⁻³, effective fluid-to-solid thermal conductivity ratio 0.1 ⩽ κ ⩽ 1.0, and the modified Biot number 1 ⩽ χ ⩽ 100. The non-Darcian effects are first examined over a broad range of Rayleigh number. Next, the implications of the group of parameters on the flow circulation intensity, local thermal non-equilibrium (LTNE) and average Nusselt number are highlighted and pertinent observations are documented.     

Jet impingement cooling of a horizontal surface in an unconfined porous medium: Mixed convection regime

Two-dimensional slot jet impingement cooling of an isothermal horizontal surface immersed in an unconfined porous medium is simulated numerically to gain insight into thermal characteristics under mixed convection conditions with the limitation of the Darcy model. The jet direction is considered to be perpendicular from the top to the horizontal heated element; therefore, the jet flow and the buoyancy driven flow are in opposite directions. 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 ? 0.5), 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. It is shown that mixed convection mode can cause minimum average Nusselt number at two values of Péclet number and a maximum average Nusselt number occurs in between theses two Péclet numbers at higher Rayleigh number 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.     

The effect of inclination on impinging jets at small nozzle-to-plate spacing

The effect of inclination on heat transfer characteristics of an impinging slot air jet is experimentally investigated. The effects of inclination angle (0° ? θ ? 40°) and dimensionless pumping power on the Nusselt number are considered. The focus is on cases where the nozzle-to-plate spacing is equal to or less than one nozzle diameter (H/d_h ? 1.0). The results show that the heat transfer characteristics of small nozzle-to-plate spacings are significantly different from those of large nozzle-to-plate spacings. In the cases of fixed flow rate conditions, the impingement point and average Nusselt numbers at small nozzle-to-plate spacing (H/d_h ? 1.0) increase as the inclination angle increases due to an increase in the pumping power, while the impingement point and average Nusselt numbers at large nozzle-to-plate spacing (H/d_h > 1.0) decrease as the inclination angle increases due to momentum loss of the wall jet. In the cases of fixed pumping power conditions, the impingement point and average Nusselt numbers at both of small and large nozzle-to-plate spacings are independent of the inclination angle. Based on the experimental results, correlations for the impingement point and average Nusselt numbers of the impinging jet are suggested as a function of the pumping power alone.     

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.     

Heat transfer enhancement by flow bifurcations in asymmetric wavy wall channels

The enhancement characteristics of heat transfer, through a transition scenario of flow bifurcations, in asymmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element method. The heat transfer characteristics, flow bifurcation and transition scenarios are determined by increasing the Reynolds numbers for three geometrical aspect ratios r = 0.25, 0.375, and 0.5, and Prandtl numbers 1.0 and 9.4. The transition scenarios to transitional flow regimes depend on the aspect ratio. For the aspect ratios r = 0.25 and 0.5, the transition scenario is characterized by one Hopf flow bifurcation. For the aspect ratio r = 0.375, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a periodic flow, and a second Hopf flow bifurcation from a periodic to quasi-periodic flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω₁, and ω₁ and ω₂, respectively. For all the aspect ratios and Prandtl numbers, the time-average mean Nusselt number and heat transfer enhancement increases with the Reynolds number as the flow evolves from a laminar to a transitional regime. For both Prandtl numbers, the highest increase in the Nusselt number occurs for the aspect ratio r = 0.5; whereas, the lowest increases happen to r = 0.25. The increase of the Nusselt number occurs at the expense of a higher pumping power, which, for both Prandtl numbers, grows as the aspect ratio increases from r = 0.25 to r = 0.5 for reaching a specific Nusselt number. This enhancement is obtained without the necessity of high volumetric flow rates associated with turbulent flow regimes, which demand much higher pumping powers. Significant heat transfer enhancements are obtained when the asymmetric wavy channel is operated in the appropriate transitional Reynolds number range.     

CFD modeling (comparing single and two-phase approaches) on thermal performance of Al2o3/water nanofluid in mini-channel heat sink

CFD modeling of laminar forced convection on Al₂O₃ nanofluid with size particles equal to 33 nm and particle concentrations of 0.5, 1 and 6 wt.% within 130 < Re < 1600 in mini-channel heat sink is executed by four individual models (single phase, VOF, mixture, Eulerian). Three-dimensional steady-state governing partial differential equations was discretized using finite volume method.Influences of some important parameters such as nanoparticle concentration and Reynolds number on the enhancement of nanofluid heat transfer have been investigated. The difference between the two-phase models results was marginal, and they were more precise by comparison with experimental reference data than single phase model. Besides with regard to the most precise and less CPU usage and run time, mixture model was chosen to obtain a correlation based on dimensionless numbers for the Nusselt number and friction factor estimation.     

Estimation of heat transfer coefficients in oscillating flows: The thermoacoustic case

The classical linear thermoacoustic theory is integrated through a numerical calculus with a simple energy conservation model to allow estimates of the optimal length of thermoacoustic heat exchangers and of the magnitude of the related heat transfer coefficients between gas and solid walls. This information results from the analysis of the temperature and heat flux density distributions inside a thermally isolated thermoacoustic stack. The effects of acoustic amplitude, plate spacing, plate thickness and Reynolds number on the heat transfer characteristics are examined. The results indicate that a net heat exchange between the acoustically oscillating gas and the solid boundary takes place only within a limited distance from the stack edges. This distance is found to be an increasing function of the plate spacing in the range (0 ⩽ y₀/δ_κ ⩽ 2), becoming constant for y₀/δ_κ ⩾ 2. The calculated dimensionless convective heat transfer coefficients, the Nusselt numbers, between gas and solid wall are comparable to those evaluated from classical correlations for steady laminar flow revised under the “Time-Average Steady-Flow Equivalent” (TASFE) and “root-mean-square Reynolds number” (RMSRe) models. Numerical results agree with measurements of the heat transfer coefficient found in literature to within 20%.     

Conjugate heat transfer in open cavities with a discrete heater at its optimized position

In this article, we determined optimum position of a discrete heater by maximizing the conductance and then studied heat transfer and volume flow rate with the discrete heater at its optimum position in open cavities. Continuity, Navier–Stokes and energy equations are solved by finite difference-control volume numerical method. The relevant governing parameters were: the Rayleigh numbers from 10⁶ to 10¹², the Prandtl number, Pr = 0.7, the cavity aspect ratio, A = H/L from 0.5 to 2, the wall thickness l/L from 0.05 to 0.15, the heater size h/L from 0.15 to 0.6, and the conductivity ratio k_r from 1 to 50. We found that the global conductance is an increasing function of the Rayleigh number, the conductivity ratio, and a decreasing function of the wall thickness. Best thermal performance is obtained by positioning the discrete heater at off center and slightly closer to the bottom. The Nusselt number and the volume flow rate in and out the open cavity are an increasing function of the Rayleigh number and the wall thickness, and a decreasing function of the conductivity ratio. The Nusselt number is a decreasing function of the cavity aspect ratio and the volume flow rate is an increasing function of it.     

Comparative evaluation of the performance of sinuous symmetrically-heated natural convection channels

Buoyancy-driven flows established in vertical channels are investigated numerically. Two different sinuous morphologies for a vertical channel are proposed as alternatives to a typical (straight) vertical channel; one is a sinus-shaped channel, and the other is a three-segment channel. The objective is to carry out a comparative evaluation of the thermal and dynamic performance of the proposed configurations, comparing their performance with that corresponding to a typical vertical channel. The low-Reynolds k − ω turbulence model is employed to simulate the transitional or fully turbulent flow. The average Nusselt number and the dimensionless mass flow rate are obtained for Rayleigh numbers ranging 10² ≤ Ra_H ≤ 10¹⁵, with an aspect ratio of the channel equal to 0.1. Sizeable increases in the Nusselt number and the mass flow rate are found for the sinuous configurations, under given conditions.     

Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium

The heat and mass transfer characteristics of free convection about a permeable horizontal cylinder embedded in porous media under the coupled effects of thermal and mass diffusion are numerically analyzed. The surface of the horizontal cylinder is maintained at a uniform wall temperature and uniform wall concentration. The transformed governing equations are obtained and solved by Keller box method. Numerical results for the dimensionless temperature profiles, the dimensionless concentration profiles, the Nusselt number and the Sherwood number are presented. Increasing the buoyancy ratio N and the transpiration parameter f_w increases the Nusselt number and the Sherwood number. For thermally assisting flow, when Lewis number Le increases, the Nusselt (Sherwood) number decreases (increases). Whereas, for thermally opposing flow, both the Nusselt number and the Sherwood number increase with increasing the Lewis number.     

Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in unconfined flowing Newtonian fluids have been investigated numerically. The governing equations, namely, continuity, Navier–Stokes and energy, have been solved in the steady flow regime over wide ranges of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr ? 100). Prior to the investigation of drag and heat transfer phenomena, the critical values of the Reynolds number for wake formation (0.55 < Re^c < 0.6) and for the onset of vortex shedding (39.5 < Re_c < 40) have been identified. The corresponding values of the lift coefficient, drag coefficient, and Strouhal number are also presented. After establishing the limit of the steady flow regime, the influence of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr = 0.72, 1, 10, 50 and 100) on the global flow and heat transfer characteristics have been elucidated. Detailed kinematics of the flow is investigated in terms of the streamline and vorticity profiles and the variation of pressure coefficient in the vicinity of the cylinder. The functional dependence of the individual and total drag coefficients on the Reynolds number is explored. The Nusselt number shows an additional dependence on the Prandtl number. In addition, the isotherm profiles, local Nusselt number (Nu_L) and average Nusselt number (Nu) are also presented to analyze the heat transfer characteristic of a semi-circular cylinder in Newtonian media.     

Momentum and heat transfer phenomena of spheroid particles at moderate Reynolds and Prandtl numbers

The momentum and heat transfer phenomena of spheroid particles in an unbounded Newtonian fluid have been numerically investigated by solving governing conservation equations of the mass, the momentum and the energy. The numerical solution methodology has been benchmarked by performing comparisons between present results with those reported in the literature. Further, extensive new results have been obtained to elucidate effects of pertinent dimensionless parameters such as the Reynolds number (Re), the Prandtl number (Pr) and the aspect ratio (e) on the flow and heat transfer behaviour of spheroid particles in the range of parameters: 1 ? Re ? 200; 1 ? Pr ? 1000 and 0.25 ? e ? 2.5. Regardless of the value of the Reynolds number, the total and individual drag coefficients of oblate spheroids (e < 1) are smaller than those of spheres (e = 1) and opposite trend has been observed for prolate spheroids (e > 1). Irrespective of values of Reynolds and Peclet numbers, the average Nusselt number is large for prolate particles as compared to spheres and opposite trend has been observed for the case of oblate particles. Major contribution of this work is the development of simple correlations for the total drag coefficient and the average Nusselt number of unconfined isolated spheroid particles based on present numerical results which can be used in new applications.