EFFECTS OF HETEROGENEITY IN FORCED CONVECTION IN A POROUS MEDIUM: TRIPLE LAYER OR CONJUGATE PROBLEM

The effects of variation (in the transverse direction) of permeability and thermal conductivity, on fully developed forced convection in a parallel plate channel or circular duct filled with a saturated porous medium, is investigated analytically on the basis of a Darcy model, for the cases of isoflux and isothermal boundaries. Previous work is extended to the case of a medium composed of three layers, or two layers with an adjacent solid layer. For the parallel plate channel with isoflux boundaries, some general multilayer results are given.     

NON-DARCIAN FORCED CONVECTION ANALYSIS IN AN ANNULUS PARTIALLY FILLED WITH A POROUS MATERIAL

Numerical solutions are presented for fully developed forced convection in concentric annuli partially filled with a porous medium. The porous medium is attached at the inner cylinder, which is maintained at uniform heat flux or at uniform wall temperature while the outer cylinder is adiabatic. The Brinkman-Forchheimer-extended Darcy model was used to model the flow inside the porous medium. The dependence of the fluid flow and heat transfer on several parameters of the problem is thoroughly documented. The inertia coefficient at which the inertial effects reduce the flow rate by 5% is determined as a function of the Darcy number for various thicknesses of the porous substrate. It is also shown that a critical thickness at which the value of the Nusselt number reaches a minimum does not exist if the effective thermal conductivity of the fluid-saturated porous medium is much higher than the fluid conductivity.     

A NUMERICAL STUDY OF THE HEAT TRANSFER TO FLUID FLOW THROUGH CIRCULAR POROUS PASSAGES

A detailed numerical study of heat transfer to a fluid passing through a saturated porous medium is the subject of this study. The Green's function solution method is selected in order to accomplish this task. The interesting features of this methodology are the focus of this article. As a test case, primary consideration is given to the computation of heat transfer to a fluid flowing through a circular passage with impermeable walls filled with porous materials. The analysis includes the heating/cooling effects due to a temperature change at the wall of the passage. In addition, the contributions of frictional heating are examined.     

FLUID FLOW ANALYSIS IN AN AXIALLY ROTATING POROUS PIPE WITH MASS INJECTION AT THE WALL

The laminar flow of an incompressible fluid in the developing region of an axially rotating porous pipe is numerically analyzed using the two-dimensional axisymmetric model in cylindrical coordinates. The numerical results from the present model are compared with existing results in the archival literature, and the agreement between the present results and the corresponding experimental data is very good. Once the model is validated, a parametric study is conducted for the case of the rotating porous pipe with radial blowing along its length and a uniform inlet axial velocity at the entrance. The pressure, velocity, and wall friction distributions are obtained and discussed. It is found that the rotation rate and blowing velocity significantly affect the velocity distribution in the pipe and the shear stresses at the wall.     

太阳能集热组合墙系统的耦合传热与流动分析

针对太阳能集热组合墙系统，分析了太阳辐射及环境温度变化时，组合墙内传热与流动变化。太阳能集热组合墙系统中，多孔介质起半透明隔热体和蓄热体的作用。多孔介质的空隙率、粒径大小对系统的采暖效果影响较大。     

NUMERICAL PREDICTION OF LAMINAR FORCED CONVECTION IN TRIANGULAR DUCTS WITH UNSTRUCTURED TRIANGULAR GRID METHOD

The flow and heat transfer characteristics of smooth triangular ducts with different apex angles of 15, 30, 60, and 90 under the fully developed laminar flow condition were predicted numerically using a finite volume method. The SIMPLE-like algorithm was employed together with an unstructured triangular grid method, where the grid was generated by a Delaunay method. The triangular grid was adopted instead of the traditional rectangular grid to fit better into the triangular cross section of the duct. Two kinds of boundary condition (uniform wall temperature and uniform wall heat flux) were considered. Comparison of the predictions with previous computational results indicated a very good agreement. Both the friction factor and Nusselt number (Nu) showed a strong dependence on apex angle of the triangular duct. When the apex angle was 60, the duct provided the highest steady-state forced convection from its inner surface to the airflow under the laminar flow condition.     

WALL HEAT CONDUCTION EFFECT ON NATURAL CONVECTION IN AN ENCLOSURE FILLED WITH A NON-DARCIAN POROUS MEDIUM

ABSTRACT

A numerical analysis has been made of the conjugate natural convection in a rectangular enclosure filled with a fluid-saturated porous medium and surrounded with four solid walls. The conductance of the walls is assumed to be much greater than that of the cavity filled with a porous medium. The main objective was to investigate the influences of the ratio of thermal conductivity of the wall to that of the fluid-porous matrix composite, the Darcy-modified Rayleigh number, the Prandtl number, and the aspect ratio. The streamlines and isotherms are presented; also, the local and average Nusselt numbers are presented along the interface between walls and cavity. A non-Darcian model was employed and the numerical method was SIMPLE-C. The numerical results indicate that the wall heat conduction effects decrease the heat transfer rate. When the wall heat conduction is considered, the greater the conductance of the solid walls surrounding the cavity, the greater is the rate of heat transfer.     

NUMERICAL ERRORS OF THE GALERKIN FINITE-ELEMENT METHOD FOR NATURAL CONVECTION OF A FLUID LAYER OR A FLUID-SATURATED POROUS LAYER

This paper describes the effects of element size and formula used for the calculation of temperature gradients on the local and average Nusselt numbers of natural convection for the widely used Galerlan finite-element method. Two cases of laminar two-dimensional natural convection are examined, namely, a fluid layer and a porous layer. The numerical error in the Nusselt numbers decreases with decreasing element size. The maximum error occurs at the position of a maximum of the local Nusselt number. In addition to the effect of element size, the Nusselt numbers are shown to vary with the formula used for calculating temperature gradients. The Nusselt numbers extrapolated to zero element size for different formulas are found, in both cases, to be virtually identical and also to agree well with the experimental data and the results computed by finite-difference methods     

NUMERICAL SOLUTION OF FORCED CONVECTION HEAT TRANSFER IN He II

A theoretical investigation of one-dimensional forced convection heat transfer in He II is conducted. The problem of interest involves a flow tube containing He II, which is heated at its midpoint along its length. Two modes of heating are analyzed: step function and square pulse. The one-dimensional He II energy equation is used to find the temperature distribution along the tube for both steady-state and transient situations. For the steady-state case, a numerical integration routine is used to obtain a solution, whereas for the solution of the transient case, a finite-difference scheme is developed. The numerical temperature profiles are then shown to compare well with the results of an experiment.     

NUMERICAL STUDY OF CONVECTION HEAT TRANSFER DURING THE MELTING OF ICE IN A POROUS LAYER

A numerical study is made of the melting of ice in a rectangular porous cavity heated from above. The Landau transformation is used to immobilize the ice-water interface, and the Darcy-Boussinesq equations are solved by a finite-difference technique. Results are analyzed in terms of the heating temperature and the aspect ratio of the cavity. A comparison is made with the case of melting from below. It was found that melting from above is more effective than melting from below when the heating temperature is between 0 and 8°C: convection arises earlier, the melting process is faster, and the total melt at steady state is thicker. The critical time for onset of convection is minimum when the upper boundary is heated at 6°C. At this heating temperature, one also obtains a maximum heat transfer rate (Nusselt number).     

TURBULENCE MODELING EXPERIENCE IN DUCTS WITH FORCED CONVECTION FLOW

This study presents a general computational method for calculating turbulent quantities in arbitrary three-dimensional ducts. Four different turbulence models for the turbulent Reynolds stresses are compared, namely, a standard K-epsilon model, a nonlinear K- epsilon model, an explicit algebraic stress model (EASM), and a full Reynolds stress model (RSM). The turbulent heat fluxes are modeled by the simple eddy diffusivity concept, the generalized gradient diffusion hypothesis, and the wealth alpha earnings time methods. A finite volume technique for nonstaggered grids combined with the SIMPLEC algorithm is applied. A modified strongly implicit procedure is implemented for solving the equations. The van Leer scheme is applied for the convective terms except for the K and epsilon equations, where the hybrid scheme is used.     

DOUBLE-DIFFUSIVE CONVECTION IN A POROUS ENCLOSURE WITH COOPERATING TEMPERATURE AND CONCENTRATION GRADIENTS AND HEAT GENERATION OR ABSORPTION EFFECTS

The problem of unsteady, laminar double-diffusive convective flow of a binary gas mixture in a rectangular enclosure filled with a uniform porous medium is considered. A temperature-dependent heat source or sink is assumed to exist within the enclosure boundaries. Transverse cooperating gradients of heat and mass are applied on the two opposing vertical walls of the enclosure while the other two horizontal walls are adiabatic and impermeable to mass transfer. A numerical solution based on the finite-difference methodology is obtained. Representative results illustrating the effects of the inverse Darcy number, the heat generation or absorption coefficient, and the buoyancy ratio on the contour maps of the streamline, temperature, and concentration as well as the profiles of velocity, temperature, and concentration at the midsection of the enclosure are reported. In addition, results for the average Nusselt and Sherwood numbers are presented in tabulated form and discussed for various parametric conditions.     

APPLICATION OF A FINITE VOLUME BASED METHOD OF LINES TO TURBULENT FORCED CONVECTION IN CIRCULAR TUBES

Abstract

A stmianafytic analysis of in-tube turbulent forced convection is performed whose special computational feature is the combination of the method of lines, the finite volume technique, and a radial coordinate transformation. First, a numerical solution of the momentum equation was obtained by a simple Runge-Kutta integration scheme. Second, the energy equation was reformulated into a system of ordinary differential equations of first order. Each equation in the system controls the temperature along a line in a mesh consisting of concentric lines. Reliable analytic solutions for the temperature distribution of fluids in the region of thermal development can be determined for combinations of Reynolds and Prandil numbers. Predicted results for the distributions of mean bulk temperature and local Nusselt numbers for air, water, and oils compare satisfactorily with the available experimental data.     

BUOYANT CONVECTION IN A CAVITY WITH A BAFFLE UNDER TIME-PERIODIC WALL TEMPERATURE

A numerical study is made of buoyant convection at high Rayleigh number in a square cavity that contains a horizontal baffle at midheight. The horizontal walls of the cavity are insulated. At the cold left vertical wall, the nondimensional temperature is constant θ = 0, and at the hot right vertical wall, the wall temperature is time periodic, θ     

BUOYANT CONVECTION IN A SQUARE CAVITY PARTIALLY FILLED WITH A HEAT-GENERATING POROUS MEDIUM

Steady-state buoyant convection in a rectangular cavity, partially filled with a fluid-saturated porous medium with spatially uniform internal heat generation, is considered. The Brinkman-extended Darcy model in the porous region is adopted. The overall Rayleigh number is large to render a boundary-layer-type global flow pattern. Scale analysis is performed to obtain a rudimentary understanding of the flow characteristics. In parallel with the theoretical endeavors, numerical solutions are secured over broad ranges of nondimensional parameters. The results indicate that there exists an asymptotic convection regime where the flow is nearly independent of the permeability and conductivity of the porous medium. The effect of the thermal conductivity of porous material is appreciable in the intermediate regime. In the conduction-dominant regime, the porous region acts like a heat-generating solid block. The numerical study gives credence to the reliability of the theoretical arguments.     

MIXED CONVECTION IN A CHANNEL WITH POROUS MULTIBLOCKS UNDER IMPOSED THERMAL MODULATION

This study is made of an enhancement of a mixed-convection heat transfer in a channel containing multiple porous blocks heated from below. The heat flux from the most upstream heater varies in a sinusoidal form, while other heaters have a constant heat flux. The Brinkman-Forchheimer-extended Darcy model and two-equation energy model are adopted to characterize the flow and temperature fields inside porous regions. The explicit effect of thermal modulation at the upstream heater is examined by acquiring comprehensive numerical solutions. The heat transfer enhancement is pronounced at the far downstream heaters when resonance is realized. The resonance frequency is close to the characteristic frequency of the system, which scales with the time for the main stream to travel from a heater to a neighboring heater. The evolutions of flow and temperature fields are exemplified to provide physical interpretations. The effects of pore density and of porous block height are reported. The benefit of heat transfer augmentation, as opposed to the increased friction factor, is assessed to justify the use of thermal modulation in the upstream heater.     

FREE CONVECTION IN OPEN-TOP ENCLOSURES FILLED WITH A POROUS MEDIUM HEATED FROM BELOW

Free convection is studied for porous medium-filled enclosures that are open for fluid flow at the top. For such setups a mixed boundary condition for the transport variable at the top is examined, which is different from the classical approach (Lapwood problem) in systems where flow is governed by Darcy's law. While the latter led to open and to closed paths within each convection cell, the mixed boundary condition induces open convection cells only. By numerical means, the onset of convection, total heat and mass transfer, and the transition from the first to the second mode are examined. At 16.5, the critical Rayleigh number for the onset of convection in the system with mixed boundary condition is much lower than the classical value.