Heat transfer by combined conduction and radiation in axisymmetric enclosures

Abstract

Combined conductive and radiative heat transfer through a gray, absorbing, emitting, and scattering medium with internal heat generation in a finite cylindrical enclosure is analyzed. The radiative transport equation is solved by the discrete ordinates method using the DOT-IV transport code, which is coupled to a compatible control-volume-based finite-difference code for the temperature field calculations. The coupled radiative transfer and the energy equations are solved by an iterative procedure. The effects of the conduction-radiation parameter, scattering, optical thickness, and wall emissivity on the medium temperatures and surface heat fluxes are discussed. Nomenclature a = aspect (half-height-to-radius) ratio, H/R I = dimensionless radiation intensity, i/4oT 4 w k = thermal conductivity N = conduction-radiation parameter, kp/4dT 3 w Q R = dimensionless radiative heat flux, q R /oT* w Q T = dimensionless total heat flux, q T /oT 4 w r -position vector T w = wall temperature U = dimensionless internal heat generation, up P = extinction coefficient, K 4-o e =wall emissivity 6 = dimensionless temperature, T/T W K = absorption coefficient o = scattering coefficient a = Stefan-Boltzmann constant r = optical distance, PS, s = r or z T R ,T H = optical depths in the r-, ^-direction, PR, PH fl = direction vector co = single scattering albedo, a/P V T = dimensionless gradient operator, P~l V

Application de la méthode des ordonnées discrètes au transfert radiatif dans des géométries bidimensionnelles complexes :

“…Milieux cylindriques. Figure 3.19: Profil radial de la température adimensionnée obtenu par la quadrature S 4 comparé avec les résultats donnés par Yùcel [23] et ceux de y e = l, et oe=0).…”

An axisymmetric bioheat transfer analysis through a unified model

“…[27][28][29][30][31][32][33] In processed meat, Antaki 27 evaluated the values of biological tissue for τ q as 16 s and τ T as 0.06 s, by fitting DPL predictions over the experiments conducted by Mitra et al 18 In the combined radiation and non-Fourier modeling, the energy balance equation comprises of radiative nonlinear term and non-Fourier instability, which makes the equation quite difficult to solve and analyze. [34][35][36][37][38][39] Many numerical schemes are available to solve the RTE while solving the coupled conduction-radiation equation such as the Monte Carlo method (MCM), 40 the spherical harmonic method, 41 the discrete transfer method (DTM), 42 the discrete ordinate method (DOM), 43 the finite volume method (FVM), 44 the lattice Boltzmann method (LBM), 45 the collapsed dimension method (CDM), 46 the integral equation solution, 47 and the radiation element solution. 48 There are a few articles available on coupled conduction-radiation model and bioheat heat transfer equation (with non-Fourier models).…”

“…In the combined radiation and non‐Fourier modeling, the energy balance equation comprises of radiative nonlinear term and non‐Fourier instability, which makes the equation quite difficult to solve and analyze 34–39 . Many numerical schemes are available to solve the RTE while solving the coupled conduction‐radiation equation such as the Monte Carlo method (MCM), 40 the spherical harmonic method, 41 the discrete transfer method (DTM), 42 the discrete ordinate method (DOM), 43 the finite volume method (FVM), 44 the lattice Boltzmann method (LBM), 45 the collapsed dimension method (CDM), 46 the integral equation solution, 47 and the radiation element solution 48 …”

Numerical Model for Combined Conductive and Radiative Heat Transfer in Annular Packed Beds

“…Fernandes and Francis [4], Harris [5], and Yiicel and Widliams [6] have solved the conduction-radiation problems in a gray absorbing, emitting, and scattering medium bounded by diffuse concentric isothermal cylinders using various numerical methods such as the Galerkin finite element method and the spherical harmonic method. Although these studies revealed the effects of major system parameters on heat transfer characteristics of annular scattering media in some detail, they were not directed toward quantitative prediction of heat transfer performance of actual annular packed beds.…”