Mixed convection in a doubly stratified micropolar fluid saturated non‐Darcy porous medium

The effects of thermal and solutal stratification on mixed convection along a vertical plate embedded in a micropolar fluid saturated non‐Darcy porous medium are analysed. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by pseudo‐similarity variables. The resulting system of equations is then solved numerically using the Keller‐box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The velocity, microrotation, temperature and concentration profiles are shown for different values of the coupling number, non‐Darcy parameter, mixed convection parameter, thermal and solutal stratification parameters. The numerical values of the skin friction, wall couple stress, heat and mass transfer rates for different values of governing parameters are also tabulated. © 2011 Canadian Society for Chemical Engineering     

Thermal convection in a saturated porous medium subjected to isothermal heating

A theoretical study of thermal convection in a fluid-saturated horizontal porous layer is reported for the case of isothermal heating from below. The onset time of natural convection and convective heat transport for large Darcy-Rayleigh number systems are analyzed, based on the propagation theory involving temporal dependence of perturbed quantities. Also, an overall feature of heat transport is discussed in connection with the Forchheimer modification of the Darcy flow model.     

MOMENTUM INTEGRAL METHOD FOR FORCED CONVECTION IN THERMAL NONEQUILIBRIUM POWER-LAW FLUID-SATURATED POROUS MEDIA

Forced convection heat transfer for power-law fluid flow in porous media was studied analytically. The analytical solutions were obtained based on the Brinkman-extended Darcy model for fluid flow and the two-equation model for forced convection heat transfer. As a closed-form exact velocity profile is unobtainable for the general power-law index, an approximate velocity profile based on the parabolic model is proposed by subscribing to the momentum boundary layer integral method. Heat transfer analysis is based on the two-equation model by considering local thermal nonequilibrium between fluid and solid phases and constant heat flux boundary conditions. The velocity and temperature distributions obtained based on the parabolic model were verified to be reasonably accurate and improvement is justified compared to the linear model. The expression for the overall Nusselt number was derived based on the proposed parabolic model. The effects of the governing parameters of engineering importance such as Darcy number, power-law index, nondimensional interfacial heat transfer coefficient, and effective thermal conductivity ratio on the convective heat transfer characteristics of non-Newtonian fluids in porous media are analyzed and discussed.     

The Solidification Process of Melt Casting Explosives in Shell

A solidification process of casting explosives in shell is studied in this paper. Heat enthalpy model and Darcy law are used to simulate the process of phase change and mushy zone. SIMPLER algorithm is used to solve the mass, momentum, and energy equations to obtain the temperature and velocity distribution of the field. Both the conduction and free convection effects on solidification are analyzed. Numerical results show that the solidification time is increased and the temperature distribution is more homogeneous if both the conduction and free convection effects are taken into account during solidification.     

Thermal behavior of longitudinal convective–radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4)

In this study, heat transfer and temperature distribution equations for longitudinal convective–radiative porous fins are presented. It is assumed that the thickness of fins varies with length, so four different shapes (rectangular, convex, triangular and exponential) are considered. Temperature-dependent heat generation, convection and radiation are considered and heat transfer through porous media is simulated using passage velocity from Darcy's model. After deriving equation for all geometries, the Least Square Method (LSM) and fourth order Runge–Kutta method (NUM) are applied for predicting the temperature distribution in the porous fins. The selected ceramic porous materials are Al, SiC, and Si₃N₄. Effects of porosity, Darcy number, Rayleigh number, etc. on transferred heat are examined. As a main outcome, exponential section fin with Si₃N₄ material has the most amount of transferred heat among other shapes and materials.     

Natural Convection in Heat Generating Oval Porous Enclosures: A Non‐Darcian Model

This paper presents a series of numerical simulations dealing with the problem of natural convection flows and associated heat transfer in an enclosure filled with a fluid‐saturated porous medium. The analysis is based on the finite element technique and incorporates the Brinkman‐extended Darcy model for an oval enclosure. The numerical results obtained for a modified Rayleigh number, Ra, Darcy number, Da, offset, E, and eccentricity, e, are presented and discussed. The numerical predictions for a square enclosure compared well with published data. It is found that any increase in Da or Ra results in a higher fluid velocity that is responsible for shifting the core of the flow. Moreover, at higher ovality (E = 0.5), asymmetric flow is observed even at the lower range of Rayleigh number (Ra ? 20), which may be attributed to the effect of curved isothermal wall.     

IMPACT OF THERMAL DISPERSION DURING FORCED CONVECTION CONDENSATION IN A THIN POROUS*/FLUID COMPOSITE SYSTEM

The effect of thermal dispersion during laminar forced convection filmwise condensation within a thin porous/fluid composite system is examined numerically. The model simulates two-dimensional condensation within a very permeable and highly conductive thin porous-layer coated surface. The local volume-averaging technique is utilized to establish the energy equation and to account for the thermal dispersion effect. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field in the porous layer while classical boundary layer equations are used in the pure condensate region. The numerical results, which detail the dependence of the heat transfer rate and temperature field on the governing parameters (e.g., Reynolds number, Rayleigh number, Darcy number, Prandtl number, thermal dispersion coefficient, as well as porous coating thickness and thermal conductivity ratio), are calculated using a finite difference scheme. It is found that due to the better mixing of the thermal dispersion effect, the heat transfer rate is greatly increased and the effect becomes more pronounced as the Reynolds number increases. The results of this study provide valuable fundamental predictions of enhanced film condensation that can be used in a number of practical thermal engineering applications.     

高温辐射环境中液滴的沸腾效应

建立了液滴在高温对流和辐射环境中的受热和蒸发模型,结合液滴均质沸腾模型,编制了计算程序。以正十二烷液滴为例,考虑液滴的膨胀效应以及液滴与周围气流的热物性变化,数值模拟了高温辐射与对流加热下的液滴升温和蒸发过程。分析了不同对流和高温辐射条件下,液滴内部是否能够发生沸腾。研究表明,液滴在高温辐射和对流加热下,蒸发伴随热膨胀;高温热辐射加热可导致液滴内部温度高于表面温度,升温到一定程度后可达到液滴内部沸腾状态;影响液滴沸腾的因素有液滴半径、辐射温度、环境气流温度等;同时,随着液滴蒸发,高温环境中液滴的沸腾过热度逐渐增大。     

表面辐射对部分填充吸湿性多孔介质的封闭腔体内热湿耦合传递的影响

根据多孔介质热质传递原理, 基于有限元的方法数值分析了具有表面热辐射的部分填充吸湿性多孔介质的封闭腔体内部自然对流流动及热湿耦合传递过程, 探讨了表面发射率、Rayleigh数和Darcy数等参数对封闭腔体内部自然对流流动及热湿耦合传递过程的影响, 研究结果表明, 壁面热辐射的作用可以提高多孔介质内部的温度, 而且随着表面发射率的增大, 多孔介质内部的水分逐步向其右上角迁移和聚集。另外, Darcy数、多孔介质与空气的热导率比对方腔内部多孔介质的热量传递和水分迁移影响较小。     

ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN A HORIZONTAL BRINKMAN CAVITY

This investigation reports on a linear stability analysis of the quiescent state within a horizontal porous cavity subject to vertical gradients of temperature and solute. The fluid motion is modeled using the Brinkman extension of Darcy's law, coupled with energy and species conservation equations. The horizontal boundaries are considered rigid-rigid, rigid-free, or free-free. Mixed thermal and solutal boundary conditions, of Dirichlet and Neumann types, are considered. The thresholds for monotonic and oscillatory convection instabilities are determined explicitly in terms of the governing parameters of the problem. The results for a viscous fluid and the Darcy porous medium emerge from the present analysis as limiting cases.     

Influence of natural convection on the heat explosion in porous media

The interaction between natural convection and the heat explosion in porous media is studied. The model consists of a nonlinear heat equation coupled with the Darcy equation for the motion of an incompressible fluid in a porous medium. Numerical simulations are performed using the alternate direction finite difference method and the fast Fourier transform method. A complex behavior of solutions is observed, including periodic and aperiodic oscillations and an oscillating heat explosion. It is shown that convection can decrease the risk of the explosion due to additional mixing and heat loss, but it can also facilitate the explosion due to temperature oscillations arising as a result of instability of stationary convective regimes.     

Inverse determination of boundary heat fluxes in a porous enclosure dynamically coupled with thermal transport

The inverse natural convection problem of estimating the heat source profiles in a porous enclosure is proposed in the present work. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. An iterative Fletcher-Reeves conjugate gradient method is applied such that the gradient of the cost function is introduced when the appropriate sensitivity and adjoint problems are defined. Particularly, the pressure-based SIMPLE algorithm is adopted to solve the continuum direct, sensitivity and adjoint problems in unification. Effects of thermal Rayleigh number, Darcy number, heat flux profiles, sensor locations and quantity on the accuracy of inverse solutions are investigated with or without the measurement errors. Additionally, the fluid and heat transport structures in the uniform porous layer are analyzed using the streamlines and heatlines, and the heat transfer potential is also explained by the variation of overall Nusselt number. Noise data solutions are regularized by stopping the iterations with the discrepancy principle of Alifanov, before the high frequency components of the random noises are reproduced. The present method solves inverse strong convection problem satisfactorily without any a priori information about the unknown heat flux to be estimated.     

MATHEMATICAL MODELING OF THERMAL RADIATION EFFECTS ON TRANSIENT GRAVITY-DRIVEN OPTICALLY THICK GRAY CONVECTION FLOW ALONG AN INCLINED PLANE WITH PRESSURE GRADIENT

We study theoretically the unsteady gravity-driven thermal convection flow of a viscous incompressible absorbing-emitting gray gas along an inclined plane in the presence of a pressure gradient and significant thermal radiation effects. The Rosseland diffusion flux model is employed to simulate thermal radiation effects. The momentum and energy conservation equations are nondimensionalized and solved exactly using the Laplace transform technique. Expressions are derived for the frictional shearing stress at the inclined plane surface and also the critical Grashof number. The effects of time (T), Grashof number (Gr), Boltzmann-Rosseland radiation parameter (K₁), and plate inclination (α) on velocity (u) and temperature (θ) distributions are studied. The flow is found to be accelerated with increasing inclination of the plane, increasing free convection effects, and for greater thermal radiation contribution but decelerated with progression of time. Temperature is found to be enhanced with progression of time and with greater thermal radiation contribution. Applications of the model arise in solar energy collector analysis and industrial materials processing.     

Free convective heat and mass transfer in a doubly stratified non-Darcy micropolar fluid

The flow, heat and mass transfer characteristics of the free convection on a vertical plate with uniform and constant heat and mass fluxes in a doubly stratified micropolar fluid saturated non-Darcy porous medium are studied. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by pseudo-similarity variables. The resulting system of equations is then solved numerically using the Keller-box method. The numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. The effects of the micropolar, Darcy, non-Darcy and stratification parameters on the dimensionless velocity, microrotation, wall temperature, wall concentration, local skin-friction coefficient and wall couple stress coefficient are presented graphically.     

Mathematical Modeling of Flow and Heat-Transfer Phenomena in Glass Furnace Channels and Forehearths

A three-dimensional mathematical model was developed to calculate fluid-flow and heat-transfer phenomena in a channel/forehearth system used for delivering glass from the melting end to the forming end of a continuous-glass-fiber furnace. The model allowed for a varying cross section of the delivery system and for the temperature-dependent physical properties of the molten glass. Also, a formulation was presented to calculate heat transfer by radiation at the combustion gas/glass interface. The model was used to investigate the effects of natural convection, throughput, and radiation in the glass on velocity and temperature distribution in a glass delivery system. The results showed that, although the natural convection velocities were much lower than the average velocity due to throughput, the presence of natural convection significantly affected the flow path lines in the system. The results also illustrated the distribution of surface and bottom glass streams entering a channel into different forehearths.     

RADIATIVE DRYING MODEL OF POROUS MATERIALS

A transient one dimensional first principles model is developed for the drying of a porous material (paper) that includes both heat and mass transfer. All three modes of heat transfer are considered; conduction, convection and radiation. The conduction is assumed to be in one dimension, through the porous material. The convection is assumed to exist only at the surface as a boundary condition. The radiation is assumed to be a volumetric phenomenon, so that the material internally absorbs, emits, and scatters energy. The absorption and scattering coefficients are spectrally dependent. Furthermore, the material is considered to have a non-unity refractive index with diffuse surfaces. In the mass transfer it is assumed that water exists in three phases: bound, free and vapor. The results provide profiles within the material for each moisture phase, temperature, and pressure and the effect of radiation on these distributions.     

GENERALIZED FINITE DIFFERENCE SOLUTION FOR HEAT AND MASS TRANSFER FROM A FINITE CYLINDER DURING QUENCH

A generalized nondimensional solution is presented that describes heat or mass transfer from a finite cylinder during quench. The solution is applicable to three important cases:

Conduction with convection heat transfer at the surface during any single step hot or cold quench.

Conduction with radiation heat transfer at the surface during a single step cold quench with negligible background radiation.

Diffusion with surface desorption of a diatomic gas from a metal specimen during a single step quench in a high vacuum with negligible background pressure.

Application of the generalized solution, which utilizes the numerical method of finite differences with forward stepping, is illustrated by determining a cylinder's transient temperature distribution and surface transfer rate (both instantaneous and cumulative) for an example L/D ratio of 2.0. Selected results are graphed and tabulated for the three cases. The results for the conduction/convection case are verified using the familiar analytical product solution as well as the lumped solution. For the conduction/radiation and diffusion/desorption cases, no analytical solutions are available other than the lumped limit which is in agreement.     

INTERACTION OF SURFACE RADIATION WITH CONJUGATE MIXED CONVECTION FROM A VERTICAL PLATE WITH MULTIPLE NONIDENTICAL DISCRETE HEAT SOURCES

Some of the important results of a numerical investigation into interaction of surface radiation with conjugate mixed convection from a discretely heated vertical plate with three nonidentical heat sources are provided here. The heat sources with identical rate of volumetric heat generation are placed flush-mounted along the plate in the descending order of their height from the bottom to the top ends of the plate. The heat sources are positioned at the leading edge, center, and the trailing edge of the plate, while the cooling medium considered is air, which is assumed to be radiatively transparent. The governing equations for fluid flow and heat transfer are initially converted into vorticity-stream function form and are later solved using the finite volume method coupled with Gauss-Seidel iterative solver. A computer code is written for the purpose. The effects of modified Richardson number, surface emissivity, and thermal conductivity on temperature distribution, peak temperature, drag coefficient, and relative contributions of mixed convection and radiation to heat dissipation are studied.     

RADIATIVE DRYING MODEL OF POROUS MATERIALS

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (paper) that includes both heat and mass transfer. All three modes of heat transfer are considered; conduction, convection and radiation. The conduction is assumed to be in one dimension, through the porous material. The convection is assumed to exist only at the surface as a boundary condition. The radiation is assumed to be a volumetric phenomenon, so that the material internally absorbs, emits, and scatters energy. The absorption and scattering coefficients are spectrally dependent. Furthermore, the material is considered to have a non-unity refractive index with diffuse surfaces. In the mass transfer it is assumed that water exists in three phases: bound, free and vapor. The results provide profiles within the material for each moisture phase, temperature, and pressure and the effect of radiation on these distributions.     

水泥窑窑体表面换热系数的计算方法

提出了一种计算水泥窑窑体面换热系数的新方法。这种方法充分考虑了强制对流，自然对流，热辐射和窑体大小对换热系数的影响。推导了窑体表面强制对流与自然对流的换热关系式，通过互相比较得到了可忽略强制对流域自然对流的条件。结果表明，大多数情况下窑体表面的强制流换热数量极相等。因此利用向量总和法建立了混合对流换热关系式。进一步的研究发现，辐射散热所占的比例很大，采用黑度小的材料可显著降低熟料热耗。该方法...