Numerical study of natural convection in a vertical porous annulus with discrete heating

In this paper natural convection flows in a vertical annulus filled with a fluid-saturated porous medium has been investigated when the inner wall is subject to discrete heating. The outer wall is maintained isothermally at a lower temperature, while the top and bottom walls, and the unheated portions of the inner wall are kept adiabatic. Through the Brinkman-extended Darcy equation, the relative importance of discrete heating on natural convection in the porous annulus is examined. An implicit finite difference method has been used to solve the governing equations of the flow system. The analysis is carried out for a wide range of modified Rayleigh and Darcy numbers for different heat source lengths and locations. It is observed that placing of the heater in lower half of the inner wall rather than placing the heater near the top and bottom portions of the inner wall produces maximum heat transfer. The numerical results reveal that an increase in the radius ratio, modified Rayleigh number and Darcy number increases the heat transfer, while the heat transfer decreases with an increase in the length of the heater. The maximum temperature at the heater surface increases with an increase in the heater length, while it decreases when the modified Rayleigh number and Darcy number increases. Further, we find that the size and location of the heater effects the flow intensity and heat transfer rate in the annular cavity.     

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.     

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.     

Thermosolutal convection from a discrete heat and solute source in a vertical porous annulus

Double-diffusive convection in a vertical annulus filled with a fluid-saturated porous medium is numerically investigated with the aim to understand the effects of a discrete source of heat and solute on the fluid flow and heat and mass transfer rates. The porous annulus is subject to heat and mass fluxes from a portion of the inner wall, while the outer wall is maintained at uniform temperature and concentration. In the formulation of the problem, the Darcy–Brinkman model is adopted to the fluid flow in the porous annulus. The influence of the main controlling parameters, such as thermal Rayleigh number, Darcy number, Lewis number, buoyancy ratio and radius ratio are investigated on the flow patterns, and heat and mass transfer rates for different locations of the heat and solute source. The numerical results show that the flow structure and the rates of heat and mass transfer strongly depend on the location of the heat and solute source. Further, the buoyancy ratio at which flow transition and flow reversal occur is significantly influenced by the thermal Rayleigh number, Darcy number, Lewis number and the segment location. The average Nusselt and Sherwood numbers increase with an increase in radius ratio, Darcy and thermal Rayleigh numbers. It is found that the location for stronger flow circulation is not associated with higher heat and mass transfer rates in the porous annular cavity.     

Thermal transport analysis for natural convection in a porous corrugated rhombic enclosure

A numerical study of fluid flow and heat transfer, applying natural convection is carried out in a porous corrugated rhombic enclosure. A uniform heating source is applied from the bottom boundary wall while the inclined side walls are maintained to a constant cold temperature and the top corrugated wall is retained at insulated condition inside the enclosure. The heat transfer and flow features are presented for a wide spectrum of Rayleigh numbers (Ra), 10⁴ ≤ Ra ≤ 10⁶, and Darcy numbers (Da), 10^?3 ≤ Da ≤ 10^?2. The number of undulations (n) for the top and bottom walls have been varied from 1 to 13 keeping the amplitude of undulation fixed. It is revealed that the characteristics of heat transfer are conceivably modulated by changing the parameter of the undulation number on the enclosure walls, specifically at the bottom and top. The influencing control of n in altering the heat transfer rate is felt maximum on the left wall and minimum for the right wall, and there is a strong interplay between Ra and Da together with n on dictating the heat transfer characteristics. The critical value, where heat transfer rate is observed as maximum is at n = 11 and thereafter the values decrease.     

About enhancement of heat transfer over a circular cylinder embedded in a porous medium

Studies of the steady viscous flow and heat transfer past a circular cylinder are presented for some fluid saturated fibrous porous media. Numerical results have been obtained according to the Darcy-Brinkman model by means of the finite element method. Forced convection is analyzed by assuming a solid matrix of constant porosity and permeability in a Péclet number range without any effect of thermal dispersion. Analysis of the influence of the Darcy number on isotherms, streamlines, and velocity contours shows the conditions of the enhancement of heat transfer from the cylinder to the surrounding porous medium.     

管内填充多孔介质强化换热的数值研究

管内填充多孔介质强化换热的基本原理是构造热边界层,增大壁面附近流体的温度梯度,并且流动阻力增幅不大。本文运用数值模拟的方法,模拟填充多孔介质管内的流场和温度场,探讨填充比例φ、渗透率Da以及空隙率ε对管内对流换热的影响规律。研究表明,提高填充比例φ和减小渗透率Da都能明显提高换热效果,但也增加了管内流动阻力。空隙率ε对强化换热作用不大,但高空隙率可以明显降低管内流动阻力,在实际中应选用空隙率较大的多孔介质。     

Effect of Darcy,fluid rayleigh and heat generation parameters on natural convection in a porous square enclosure: A Brinkman-extended Darcy model

A Pressure-velocity solution for natural convection for fluid saturated heat generating porous medium in a square enclosure is analysed by finite element method. The numerical solutions obtained for wide range of fluid Rayleigh number, Ra_f, Darcy number, Da, and heat generating number, Q_d. The justification for taking these non-dimensional parameters independently is to establish the effect of individual parameters on flow patterns. It has been observed that peak temperature occurs at the top central part and weaker velocity prevails near the vertical walls of the enclosure due to the heat generation parameter alone. On comparison, the modified Rayleigh number used by the earlier investigators[4,6], can not explain explicitly the effect of heat generation parameter on natural convection within an enclosure having differentially heated vertical walls. At higher Darcy number, the peak temperature and peak velocity are comparatively more, resulting in better enhancement of heat transfer rate.     

Fully developed natural convection heat and mass transfer in a vertical annular porous medium with asymmetric wall temperatures and concentrations

This work examines the effects of the modified Darcy number, the buoyancy ratio and the inner radius-gap ratio on the fully developed natural convection heat and mass transfer in a vertical annular non-Darcy porous medium with asymmetric wall temperatures and concentrations. The exact solutions for the important characteristics of fluid flow, heat transfer, and mass transfer are derived by using a non-Darcy flow model. The modified Darcy number is related to the flow resistance of the porous matrix. For the free convection heat and mass transfer in an annular duct filled with porous media, increasing the modified Darcy number tends to increase the volume flow rate, total heat rate added to the fluid, and the total species rate added to the fluid. Moreover, an increase in the buoyancy ratio or in the inner radius-gap ratio leads to an increase in the volume flow rate, the total heat rate added to the fluid, and the total species rate added to the fluid.     

Non-darcy natural convection from a heated vertical plate in saturated porous media with mass transfer

The nonsimilar and self-similar flows for the steady natural convection over a vertical heated surface in a saturated porous medium with mass transfer using non-Darcy model have been studied under boundary layer approximations. The differential equations governing both the nonsimilar and self-similar flows have been solved numerically using an implicit finite-difference scheme developed by Keller. The results indicate that both heat transfer and velocity field are appreciably affected by the modified Grashof number and mass transfer except that the effect of the modified Grashof number on the heat transfer for large suction is very small. It is found that the maximum velocity occurs at the wall and it increases as the modified Grashof number or injection increases.     

Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure

A numerical investigation is carried out to analyze natural convection heat transfer inside a cavity with a sinusoidal vertical wavy wall and filled with a porous medium. The vertical walls are isothermal while the top and bottom horizontal straight walls are kept adiabatic. The transport equations are solved using the finite element formulation based on the Galerkin method of weighted residuals. The validity of the numerical code used is ascertained by comparing our results with previously published results. The importance of non-Darcian effects on convection in a wavy porous cavity is analyzed in this work. Different flow models for porous media such, as Brinkman-extended Darcy, Forchheimer-extended Darcy, and the generalized flow models, are considered. Results are presented in terms of streamlines, isotherms, and local heat transfer. The implications of Rayleigh number, number of wavy surface undulation and amplitude of the wavy surface on the flow structure and heat transfer characteristics are investigated in detail while the Prandtl number is considered equal to unity.     

Natural convection heat transfer and entropy generation inside porous quadrantal enclosure with nonisothermal heating at the bottom wall

In this work, we study numerically the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bottom wall. The effect of Darcy number is significant in dictating the Nusselt number only for higher values of Rayleigh number and the variation is more profound for larger values of Darcy number. The variation of entropy generation rate is significant with the Darcy number only for higher values of Rayleigh number. The entropy generation due to heat transfer is the significant contributor of irreversibility at low values of Darcy number, while for larger values of Darcy number and Rayleigh number entropy generation due to fluid friction becomes dominant.     

Mixed convection in a square vented enclosure filled with a porous medium

Steady mixed convection flow in a vented enclosure with an isothermal vertical wall and filled with a fluid-saturated porous medium is investigated numerically. The forced flow conditions are imposed by providing an inlet at the bottom surface, and a vent at the top, facing the inlet. The nature and the basic characteristics of the mixed aiding as well as mixed opposing flows that arise are investigated using the Darcy law model. The governing parameters are the Rayleigh number, Péclet number, and the width of the inlet as a fraction of the height of the square enclosure. These parameters are varied over wide ranges and their effect on the heat transfer characteristics is studied in detail.     

Unsteady natural convection from a horizontal annulus filled with a porous medium

The unsteady natural convection flow from a horizontal cylindrical annulus filled with a non-Darcy porous medium has been studied. The unsteadiness in the problem arises due to the impulsive change in the wall temperature of the outer cylinder. The Navier–Stokes equations along with the energy equation governing the unsteady natural convection flow have been solved by the finite-volume method. The effect of time variation on the heat transfer is more pronounced only in a small time interval immediately after the start of the impulsive motion and the steady state is reached after certain time. The results show that the annulus completely filled with a porous medium has the best insulating effectiveness. Convection in the horizontal annulus is confined mostly at top and bottom regions. Hence, only these regions should be insulated. In case of annulus partially filled with a porous material, insulating the region near the outer cylinder is more effective than insulating the region near the inner cylinder. The effect of Darcy number on the heat transfer is more pronounced than that of the Grashof number.     

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.     

Forced convection in horizontal porous channels with hydrodynamic anisotropy

This paper presents an exact solution for fully developing forced convective flow in parallel-plate horizontal porous channels with an anisotropic permeability whose principal axes are oriented in a direction that is oblique to the gravity vector. A constant heat flux is applied on the channel side walls. Basing this analysis on the generalized Brinkman-extended Darcy model which allows the satisfaction of the no-slip boundary condition on solid wall, it is found that anisotropic parameters K^* and ? have a strong influence on the flow fields and heat transfer rate, in the limiting case of low porosity media (Da→0). The results indicate that a maximum (minimum) heat transfer rate is reached when the orientation of the principal axis with higher permeability of the anisotropic porous matrix is parallel (perpendicular) to the vertical direction.     

Transient forced convection heat transfer from a circular cylinder embedded in a porous medium

Studies of the transient heat transfer past a circular cylinder in a steady-state viscous flow are presented for some fluid saturated fibrous porous media. Numerical results have been obtained according to the Darcy-Brinkman model by means of the finite element method. Analysis of the influence of the Darcy and Peclet numbers on the mean Nusselt number exhibits the successive conduction, transition and convection regimes. The duration necessary to reach the steady-state convection heat transfer appears as a function of the Peclet and Darcy numbers.     

Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall

Double — diffusive natural convection in fluid saturated porous medium has been investigated using a generalised porous medium model. One of the vertical walls of the porous cavity considered is subjected to convective heat and mass transfer conditions. The results show that the flow, heat and mass transfer become sensitive to applied mass transfer coefficient in both the Darcy and non-Darcy flow regimes. It is also observed that the Sherwood number approaches a constant value as the solutal Biot number increases.     

Numerical analysis of convective heat transport in a porous semi‐trapezoidal enclosure with radiation effect

A theoretical and numerical study of natural convection of two‐dimensional laminar incompressible flow in a semi‐trapezoidal porous enclosure in the presence of thermal radiation is conducted. The semi‐trapezoidal enclosure has an inclined left wall that in addition to the right vertical wall is maintained at a constant temperature, whereas the remaining (horizontal) walls are adiabatic. The Darcy‐Brinkman isotropic model is utilized. The governing partial differential equations are transformed using a vorticity stream function and nondimensional quantities and the resulting governing nonlinear dimensionless equations are solved using the finite difference method with incremental steps. The impacts of the different model parameters (Rayleigh number [Ra], Darcy number [Da], and radiation parameter [Rd]) on the thermofluid characteristics are studied in detail. The computations show that convective heat transfer is enhanced with the greater Darcy parameter (permeability). The flow is accelerated with the increasing buoyancy effect (Rayleigh number) and heat transfer is also increased with a greater radiative flux. The present numerical simulations are more relevant to hybrid porous media solar collectors.     

Enhancement of Heat Transfer with Porous/Solid Insert for Laminar Flow of a Participating Gas in a 3-D Square Duct

In recent years, porous or solid insert has been used in a duct for enhancing heat transfer in high temperature thermal equipment, where both convective and radiative heat transfer play a major role. In the present work, the study of heat transfer enhancement is carried out for flow through a square duct with a porous or a solid insert. Most of the analyses are carried out for a porous insert. The hydrodynamically developing flow field is solved using the Navier–Stokes equation and the Darcy–Brinkman model is considered for solving the flow in the porous region. The radiative heat transfer is included in the analysis by coupling the radiative transfer equation to the energy equation. The fluid considered is CO₂ with temperature dependent thermophysical properties. Both the fluid and the porous medium are considered as gray participating medium. The increase in heat transfer is analyzed by comparing the bulk mean temperature, Nusselt number, and radiative heat flux for different porous size and orientation, Reyonlds number, and Darcy number.