Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular enclosures

Publisher Summary This chapter describes the convective and radiative heat transfer in porous media. Convective and radiative heat transfer and multiphase transport processes in porous media, both with or without phase change, have gained extensive attention. Several applications related to porous media require a detailed analysis of convective heat transfer in different geometrical shapes, orientations, and configurations. Based on the specific application, the flow in the porous medium may be internal or external. Forced convection over external boundaries in the presence of a porous medium constitutes a very important subject area. Analysis of convective heat transfer from this type of external boundary embedded in a porous medium has many important applications. It is shown that for the flow field the boundary effect is confined within a thin momentum boundary layer, which often plays an insignificant role in the overall flow consideration. The models developed for simultaneous heat and mass transfer processes in multiphase porous systems may have differences due to the various assumptions made in developing each model. The thermal radiation characteristics of porous beds are also elaborated.

Convective and Radiative Heat Transfer in Porous Media

We examine critically the accuracy of the two-flux, spherical harmonics and discrete ordinates methods for predicting radiative transfer in a planar, highly-forward scattering and absorbing medium. Numerical results for the radiative fluxes show that the two-flux and P3-approximations yield accurate results compared to solutions based on the FN-method. Indeed, these approximate methods are relatively simple and have potential for generalization to predict radiative transfer in multidimensional systems, as long as an appropriate simplification of the phase function is utilized.

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Comparison of radiative transfer approximations for a highly forward scattering planar medium.

A theoretical and numerical investigation of streamwise-oriented Dean vortices in curved channel flow is presented. The principal results are obtained from three-dimensional pseudospectral simulations of the incompressible time-dependent Navier-Stokes equations. With increasing Reynolds number, a sequence of transitions similar to that observed in non-turbulent Taylor-Couette flow is found. The transition from laminar curved channel Poiseuille flow to axisymmetric Dean vortex flow is studied using linear and weakly nonlinear analyses; these results are compared to the full simulations. Using the code, two transitions that cause the axisymmetric vortices to develop waves travelling in the streamwise direction at higher Reynolds numbers are discovered. The linear stability of axisymmetric Dean vortex flow to non-axisymmetric perturbations is examined. Associated with the two transitions are two different non-axisymmetric flows: undulating and twisting Dean vortex flow. Undulating vortices are similar to wavy Taylor vortices. Twisting vortices, with a much shorter streamwise wavelength, are dissimilar; to our knowledge, they have no counterpart in the Taylor-Couette problem. At sufficiently high Reynolds numbers, linear growth rates associated with twisting vortices far exceed those associated with undulating vortices. For the channel curvatures studied, angular speeds of both kinds of travelling waves are only weakly dependent on Reynolds number and wavenumber. A bifurcation limits the vortex spacings that can be examined and suggests an Eckhaus stability boundary. The development of wavy vortex flows from small-amplitude disturbances shows that full development of undulating vortices may require a streamwise distance greater than one circumference, whereas for sufficiently large Reynolds numbers, twisting vortices reach equilibrium amplitude within half this distance and are therefore more likely to be observed experimentally. We suggest twisting vortices are due to a shear instability.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112088003052

Instability and transition in curved channel flow

The occurrence of secondary flow in curved ducts due to the centrifugal forces can often significantly influence the flow rate. In the present work, the secondary flow of an incompressible viscous fluid in a curved duct is studied by using a finite-volume method. It is shown that as the Dean number is increased the secondary flow structure evolves into a double vortex pair for low-aspect-ratio ducts and roll cells for ducts of high aspect ratio. A stability diagram is obtained in the domain of curvature ratio and Reynolds number. It is found that for ducts of high curvature the onset of transition from single vortex pair to double vortex pair or roll cells depends on the Dean number and the curvature ratio, while for ducts of small curvature the onset can be characterized by the Dean number alone. A comparison with the available theoretical and experimental results indicates good agreement. A correlation for the friction factor as a function of the Dean number and aspect ratio is developed and is found to be in good agreement with the available experimental and computational results for a wide range of parameters.

Laminar secondary flows in curved rectangular ducts

Combined radiation and convection in absorbing, emitting and anisotropically scattering gas-particulate tube flow

Evaluation of the Radiative Heat Flux in Absorbing, Emitting and Linear-Anisotropically Scattering Cylindrical Media

The Influence and Treatment of Mie-Anisotropic Scattering in Radiative Heat Transfer

The validity of the well-established differential approximation in radiative transfer is extended to include linear-anisotropic scattering. Sample results demonstrate the accuracy of the method.

F. H. Azad

Papers

Combined radiation and convection in absorbing, emitting and anisotropically scattering gas-particulate tube flow

Evaluation of the Radiative Heat Flux in Absorbing, Emitting and Linear-Anisotropically Scattering Cylindrical Media

The Influence and Treatment of Mie-Anisotropic Scattering in Radiative Heat Transfer

The differential approximation for radiative transfer in an emitting, absorbing and anisotropically scattering medium