Transient Radiation Coupled With Conduction Heat Transfer in a One Dimensional Slab

The present research work views over a solution of radiative transport problem along with conduction in one perspective piece and in the existence of participating media. The radiative transfer equations are developed for anisotropically scattering, absorbing, emitting medium and the equation is being discretized using finite volume method. Heat flux and the incident radiation effects have been computed at three different time step. Transient radiation along with transient conduction is solved and the radiative effect has been measured using radiative transfer equation while the conduction term has been measured using conduction equation.

Download Full-text

Numerical Results of an Integral Formulation of Transient Radiative Transfer

10.1115/imece1999-0597 ◽

1999 ◽

Author(s):

Z.-M. Tan ◽

P.-F. Hsu

Keyword(s):

Steady State ◽

Radiative Transfer ◽

Incident Radiation ◽

Integral Formulation ◽

Time Step ◽

Incident Intensity ◽

Participating Media ◽

Upwind Difference Scheme ◽

The One ◽

Reflecting Surface

Abstract Numerical computations are performed for the transient radiative transfer equation within the one-dimensional parallel plate geometry using an integral formulation obtained in a prior work. The medium under consideration is absorbing and isotropically scattering. One boundary is a black emitting surface or a transparent surface subjected to the collimated incident radiation. The incident intensity is applied at the start of the transient. The other boundary is a cold and black or specularly reflecting surface. The spatial and temporal incident radiation and radiative flux distributions are presented for different boundary conditions and for uniform and nonuniform property distribution. The transient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. The solutions of reflecting boundary condition exhibit distinctive behavior from that of the non-reflecting boundary. The integral formulation is extended to handle the transient transfer within the nonhomogeneous participating media. The integral formulation has several advantages over the differential treatment of the hyperbolic wave of the radiative transport; among others: (1) The avoidance of using a high order upwind difference scheme in resolving the wave front; (2) Providing a sound basis for physical interpretation as the radiative transfer is a volumetric process; and (3) Many integral equation numerical methods that have previously been developed for the steady state integral formulation can be re-applied to treat the transient problem.

Download Full-text

An Integral Formulation of Transient Radiative Transfer

Journal of Heat Transfer ◽

10.1115/1.1371230 ◽

2000 ◽

Vol 123 (3) ◽

pp. 466-475 ◽

Cited By ~ 89

Author(s):

Z.-M. Tan ◽

P.-F. Hsu

Keyword(s):

Radiative Transfer ◽

Incident Radiation ◽

Integral Formulation ◽

Time Dependent ◽

Slab Geometry ◽

Time Step ◽

Participating Media ◽

Quadrature Methods ◽

Time Dependent Domain ◽

Large Time Step

A time-dependent integral formulation is developed for modeling transient radiative transfer. The development is based on a rigorous analysis of the wave propagation process inside the participating media. The physical significance of the present integral formulation is the consideration of the time-dependent domain of computation, which is different from the domain disturbed by radiation (i.e., the wave front envelope). Numerical computations are performed for the medium that is an absorbing and isotropically scattering one-dimensional plane slab geometry. The spatial and temporal incident radiation and radiative flux distributions are presented for different boundary conditions and for uniform and nonuniform property distribution. The transient results at large time step are compared with steady-state solutions by the finite volume and quadrature methods and show excellent agreement. The solutions of reflecting boundary condition exhibit distinctive behavior from that of the non-reflecting boundary.

Download Full-text