Effect of surface emissivity on heat transfer by simultaneous conduction and radiation

Meshless local Petrov–Galerkin approach for coupled radiative and conductive heat transfer

“…The averaged dimensionless heat fluxes in the case of Θ 0 = 1.0 for different values of τ L , Θ L and N CR are computed by using MLPG approach and given in Table 1. The results are compared with those obtained by Viskanta and Grosh [2] using numerical integration and iteration. From Table 1, it can be seen that the MLPG approach presented in this paper has a good accuracy in solving the dimensionless heat fluxes in one-dimensional non-scattering gray medium.…”

“…The quartic spline functions are often used to construct the weight function for the MLS approximation and test function in the weighted integration for the standard MLPG method. One of the often used quartic spline functions is given as follows [2]:…”

“…51 nodes are uniformly distributed in the problem domain and its boundaries. The monomial basis p T (x) = [1, τ x , τ 2 x ] is used, and the weight function for the MLS approximation and the test function in the weighted integration of the dimensionless energy equation and the dimensionless radiative transfer equation are given as follows:…”

“…Viskanta and Grosh [1,2] analyzed numerically the problem of combined conduction radiation in a onedimensional absorbing and emitting medium bounded by two parallel plates using an iterative method. Yuen and Wong [3] used a successive approximation technique to solve the heat transfer by conduction and radiation in a one-dimensional absorbing, emitting and anisotropically-scattering medium.…”

Solving nonlinear heat transfer problems using variation of parameters

“…These problems are encountered in the analysis of combustion chambers, rocket nozzles, high-temperature heat exchangers, translucent glass or ceramic coatings, porous insulation, heat treatment of glass plates, and the drawing of optical fibers. The combined conduction-radiation problem has been solved using an integral transformation method [10,11], the finite element method [12,13], the finite difference method [14,15], the finite volume method [16,17], the lattice Boltzmann method [18e20], and finite strip theory [21].…”