Time-dependent natural convection fluid flow of stably stratified fluid in an asymmetrically heated vertical channel filled with an anisotropic porous material

This paper presents a theoretical analysis of the combined effects of anisotropic porous material and thermal stratification on the transient natural convection fluid flow in an asymmetrically heated vertical parallel channel. The solutions of the governing equations for the temperature and velocity fields are obtained using Laplace transform technique, Riemann sum approximation, and the D'Alembert method. The choice of the D'Alembert method is to provide a simple decoupling procedure for the coupled governing equations while still retaining their original orders. The research established that owing to the layering effect induced by the thermal stratification $(S)$, the temperature and the velocity distributions of the fluid are found to be attenuated with an increase in thermal stratification. It is also observed that the inclusion of anisotropic parameters in the transport equations aids in regulating the fluid velocity, temperature, Nusselt number, skin friction, and mass flow rate. In addition, by neglecting the anisotropic parameter and taking into account the adiabatic stratification of the fluid, the numerical values for the mass flow rate of the present research favorably compared with the numerical results obtained by Singh et al.     

Transient behavior of fluid flow and heat transfer with phase change in vertical porous channels

The transient behavior of flow boiling in vertical porous channels is numerically studied in this paper. The velocity and temperature fields under different parameters for both aiding and opposing flows are investigated. Distinctly different flow and heat transfer features are observed in the comparison of aiding and opposing flows. An analysis of liquid saturation along the heated wall indicates that the minimum liquid saturation for aiding flow is located at the tail of the heated section, whereas for opposing flow, it is within the heated section and shifts upstream with the increase of Rayleigh number and decrease of Peclet number.     

Numerical simulation of turbulent fluid flow and heat transfer characteristics of heated blocks in the channel with an oscillating cylinder

In this study, numerical simulations have been carried out to investigate the influence of transient flow field structures, and the heat transfer characteristics of heated blocks in the channel with a transversely oscillating cylinder. To solve the interaction problems between liquid and solid interface in the simulations, a Galerkin finite element formulation with Arbitrary Lagrangian–Eulerian method (ALE) is adopted.The main parameters in the study are Reynolds numbers (Re = 800–8000), dimensionless oscillating frequencies (F = 0.1–0.4), dimensionless amplitudes (L = 0.05–0.4). The results of numerical simulations show that the oscillating cylinder induces the flow vibration. This phenomenon disturbs the flow and thermal fields in the channel flow, and the heat transfer rate in the channel would be enhanced. Furthermore, the resonance effect of channel flow and oscillating cylinder can be observed as the oscillating frequency of the cylinder approach to the vortex shedding frequency. Due to the phenomenon of resonance in the channel flow, the heat transfer rate is enhanced more remarkably. In the studied ranges, the results show that the optimum dimensionless cylinder oscillating frequency and dimensionless amplitude value are 0.21 and 0.1 and that the heat transfer from heated blocks is enhanced as the oscillating frequency of the cylinder is in a lock-in region.     

Laminar heat transfer in an asymmetrically heated rectangular duct

This paper presents a numerical study concerning the effects of non-uniform heating on the heat transfer of a thermally undeveloped gas flow in a horizontal rectangular duct; a vertical side wall is uniformly heated, and the other walls are insulated. As an initial step of the study, the duct flow is assumed to be laminar, and buoyancy effects are considered. The heat transfer rate and drag increase with the secondary flow due to buoyancy; the effects of the buoyancy force on the heat transfer and friction coefficient of the thermally undeveloped region are found to depend only upon modified Grashof numbers of the duct entrance.     

Three-dimensional numerical simulation of heat and fluid flow in noncircular microchannel heat sinks

A three-dimensional model of heat transfer and fluid flow in noncircular microchannel heat sinks is developed and analyzed numerically. It is found that Nusselt number has a much higher value at the inlet region, but quickly approaches the constant fully developed value. The temperature in both solid and fluid increases along the flow direction. In addition, the comparison of thermal efficiencies is conducted among triangular, rectangular and trapezoidal microchannels. The result indicates that the triangular microchannel has the highest thermal efficiency.     

Local and average heat transfer in the thermally developing region of an asymmetrically heated channel

Forced convection heat transfer between parallel plates kept at unequal wall temperatures has been studied assuming laminar, incompressible, steady flow of a Newtonian fluid of constant thermophysical properties. Unequal wall temperatures have been characterized by an asymmetry parameter. It has been shown that the heat transferred from the walls monotonically varies with the axial distance even though the Nusselt number (at one of the walls) does not vary continuously due to asymmetry. It has been found that a modified Nusselt number varies continuously with the asymmetry parameter. Plots to obtain heat transferred from each wall have been presented which serve the purpose of mean Nusselt number. Non-dimensional heat transferred from the two walls is independent of the asymmetry parameter. The down stream boundary condition applicable for the thermal field when the walls are kept at unequal temperatures has been brought out which becomes necessary when solving elliptic form of conservation of thermal energy equation, say, when axial conduction is included.     

Direct numerical simulation of wall-normal rotating turbulent channel flow with heat transfer

Direct numerical simulation of wall-normal rotating channel flow with heat transfer has been performed for the rotation number N_τ from 0 to 0.1, the Reynolds number 194 based on the friction velocity of non-rotating case and the half-height of the channel, and the Prandtl number 1. The objective of this study is to reveal the effects of rotation on the characteristics of turbulence and heat transfer. Some statistical turbulence and heat transfer quantities, including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and turbulence structures, are investigated. Based on the present calculated results, two typical rotation regimes are identified. When 0 < N_τ < 0.06, the turbulence statistics correlated with the spanwise velocity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. When N_τ > 0.06, all the turbulence statistics are suppressed significantly. To elucidate the effects of rotation on the turbulent heat transfer, the budget terms in the transport equation of turbulent heat fluxes are analyzed. Remarkable change of the direction of near-wall streak structures of the velocity and temperature fluctuations, nearly in alignment with the absolute mean flow direction, is revealed. An attempt to evaluate the mean spacing and the direction of streaky structures near the wall has been examined based on the two-point correlations of the velocity and temperature fluctuations.     

开缝型翅片流动与传热三维数值模拟

通过数值模拟,研究空调系统使用的开缝型翅片的传热与阻力特性。对三种型式的开缝型翅片进行模拟,得出了流场和温度场。通过对比分析发现,双边交替开缝的slit-2型翅片,换热性能最好,X型双向开缝片的性能次之,单边开缝的slit-1型翅片换热效果低于前两种。数值模拟还得出,空气流过slit-x型翅片的阻力最大,流过slit-1型翅片的阻力最小。     

Analysis of fluid flow and heat transfer in a channel with staggered porous blocks

Fluid flow and heat transfer characteristics in a channel with staggered porous blocks were numerically studied in this paper. The Navier–Stokes and Brinkman–Forchheimer equations were used to model the fluid flow in the open and porous regions, respectively. Coupling of the pressure and velocity fields was resolved using the SIMPLER algorithm. The local thermal equilibrium model was adopted in the energy equation to evaluate the solid and fluid temperatures. The effect of Darcy number, Reynolds number, porous block height and width on the velocity field were studied. In addition, the effects of the above parameters as well as the thermal conductivity ratio between the porous blocks and the fluid on the local heat transfer were analyzed. The pressure drops across the channel for different cases were discussed. The results show that the flow behavior and its associated local heat transfer are sensitive to the variation of the above parameters. It is predicted by the present study that an increase in the thermal conductivity ratio between the porous blocks and the fluid results in significant enhancement of heat transfer at the locations of the porous blocks.     

Developing fluid flow and heat transfer in a channel partially filled with porous medium

A three-dimensional computational model is developed to analyze fluid flow in a channel partially filled with porous medium. In order to understand the developing fluid flow and heat transfer mechanisms inside the channel partially filled with porous medium, the conventional Navier–Stokes equations for gas channel, and volume-averaged Navier–Stokes equations for porous medium layer are adopted individually in this study. Conservation of mass, momentum and energy equations are solved numerically in a coupled gas and porous media domain along a channel using the vorticity–velocity method with power law scheme. Detailed development of axial velocity, secondary flow and temperature field at various axial positions in the entrance region are presented. The friction factor and Nusselt number are presented as a function of axial position, and the effects of the size of porous media inside the channel partially filled with porous medium are also analyzed in the present study.     

Entropy generation of convection heat transfer in an asymmetrically heated packed duct

An expression for the volumetric rate of entropy generation has been derived and displayed graphically to analyze the convection heat transfer for a fully established flow in a rectangular packed duct with L/H=16 and H/W=0.125. The top and bottom walls of the duct are heated by constant, asymmetric heat fluxes, while the other walls are insulated that is the L2 thermal boundary conditions. Entropy generation maps reveal the regions where excessive entropy generation occurs due to physical and geometric parameters for a specified task within the system.     

Features of convective heat transfer in heated helium channel flow

The aim of the present work is to choose an optimal method for thermohydraulic calculation of the gas flow in channels with intense heating at the flow Reynolds number below 10,000. These conditions are typical of the cooling channels of the High-Flux-Test Module of the International-Fusion-Materials-Irradiation-Facility (IFMIF/HFTM). A low Reynolds number and a high heating rate can result in partial relaminarization of the initially turbulent flow, and hence in a decrease in the heat transfer. A number of turbulence models offered by the commercial STAR-CD code were tested on the basis of the comparison of the numerical predictions with experimental data. This comparison showed that the low-Reynolds-number k-ε turbulence models predict the heat transfer characteristics close to the experimental data. The k-ε linear low Reynolds number turbulence model of Lien was applied as more appropriate for the thermohydraulic analysis of the IFMIF high flux test module.     

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.     

Laminar fully developed forced-convection flow within an asymmetrically heated horizontal double-passage channel

The present analytical study is concerned with the thermal characteristics of hydrodynamically and thermally fully developed flow in an asymmetrically heated horizontal channel, which is divided into two passages (by means of a baffe) for two separate flow streams. Each stream will have its own pressure gradient and hence its own individual velocity profile. Based upon bulk mean temperature of the whole flow in the channel, Nusselt numbers and the generalized temperature profiles in the fully developed regions are determined by means of integration of the momentum and energy equations. Three possible combinations of the thermal boundary conditions on the two wall plates of the channel are considered: isothermal-isothermal, isothermal-isoflux, and isoflux-isoflux. Results show that the thermal characteristics of the fully developed flow could be significantly affected by the position of the baffle, the pressure-gradient ratio by the two separate streams, and thermal boundary conditions on the channel walls.     

Three－Dimensional Numerical Simulation of Natural Convection Heat Transfer in an Inclined Cylindrical Annulus

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Experimental study of heat transfer enhancement in an asymmetrically heated rectangular duct with perforated baffles

The paper presents results of an experimental study of heat transfer and friction in rectangular ducts with baffles (solid or perforated) attached to one of the broad walls. The duct has width-to-height ratio of 7.77; the baffle pitch-to-height ratio is 29; the baffle height-to-duct height ratio is 0.495. The Reynolds number of the study ranges from 2850 to 11500. The baffled wall of the duct is uniformly heated while the remaining three walls are insulated. These boundary conditions correspond closely to those found in solar air heaters. Over the range of the study, the Nusselt number for the solid baffles is 73.7–82.7% higher than that for the smooth duct, while for the perforated baffles, it ranges from 60.6–62.9% to 45.0–49.7%; decreasing with the increase in the open area ratio of these baffles from 18.4% to 46.8%. The friction factor for the solid baffles is found to be 9.6–11.1 times of the smooth duct, which decreased significantly for the perforated baffles with the increase in the open area ratio; it is only 2.3–3.0 times for the perforated baffles with open area ratio of 46.8%. Performance comparison with the smooth duct at equal pumping power shows that the baffles with the highest open area ratio give the best performance.     

Analysis of heat transfer with liquid-vapor phase change in a forced-flow fluid moving through porous media

This study focuses on the experimental analysis of transient-regime heat transfer with liquidvapor phase change in a fluid as it flows through a porous media composed of small bronze spheres. Three distinct zones can be observed: liquid, two-phase and superheated vapor. The boundaries between these zones are determined using temperature and pressure fields. An N-shaped profile is observed for the temperature values along the main flow axis. The first local maximum value on the temperature curve corresponds to the boundary between the liquid zone and the two-phase zone. When a local minimum temperature exists, it corresponds to the boundary between the two-phase and the vapor zones. A finite element numerical simulation is used to predict the saturation field, which is numerically determined from the boundaries of the two-phase zone and of the experimental temperature field. The liquid and vapor pressure fields are then deduced for all three phase zones of the porous medium.     

Convective heat transfer over a heated square porous cylinder in a channel

A numerical study is made of the unsteady flow and convection heat transfer for a heated square porous cylinder in a channel. The general Darcy–Brinkman–Forchheimer model is adopted for the porous region. The parameters studies including porosity, Darcy number, and Reynolds number on heat transfer performance have been explored in detail. The results indicate that the average local Nusselt number is augmented as the Darcy number increases. The average local Nusselt number increases as Reynolds number increases; in particular, the increase is more obvious at a higher Darcy number. In contrast, the porosity has slight influence on heat transfer.     

Numerical simulation of fluid flow and convection heat transfer in sintered porous plate channels

Fluid flow and convective heat transfer of water in sintered bronze porous plate channels was investigated numerically. The numerical simulations assumed a simple cubic structure formed by uniformly sized particles with small contact areas and a finite-thickness wall subject to a constant heat flux at the surface which mirrors the experimental setup. The permeability and inertia coefficient were calculated numerically according to the modified Darcy’s model. The numerical calculation results are in agreement with well-known correlation results. The calculated local heat transfer coefficients on the plate channel surface, which agreed well with the experimental data, increased with mass flow rate and decreased slightly along the axial direction. The convection heat transfer coefficients between the solid particles and the fluid and the volumetric heat transfer coefficients in the porous media predicted by the numerical results increase with mass flow rate and decrease with increasing particle diameter. The numerical results also illustrate the temperature difference between the solid particles and the fluid which indicates the local thermal non-equilibrium in porous media.     

Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder

A numerical investigation was conducted to analyze the unsteady flow field and heat transfer characteristics in a horizontal channel with a built-in heated square cylinder. Hydrodynamic behavior and heat transfer results are obtained by the solution of the complete Navier–Stokes and energy equations using a control volume finite element method (CVFEM) adapted to the staggered grid. The Computation was made for two channel blockage ratios (β=1/4 and 1/8), different Reynolds and Richardson numbers ranging from 62 to 200 and from 0 to 0.1 respectively at Pr=0.71. The flow is found to be unstable when the Richardson number crosses the critical value of 0.13. The results are presented to show the effects of the blockage ratio, the Reynolds and the Richardson numbers on the flow pattern and the heat transfer from the square cylinder. Heat transfer correlation are obtained through forced and mixed convection.