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

Abstract A meshless local Petrov–Galerkin approach is employed for solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media. The meshless local Petrov–Galerkin approach with upwind scheme for radiative transfer is based on the discrete ordinate equations. The moving least square approximation is used to construct the shape function. Three particular test cases for coupled radiative and conductive heat transfer are examined to verify this new approximate method. The dimensionless temperatures and the dimensionless heat fluxes are obtained. The results are compared with the other benchmark approximate solutions. By comparison, the results show that the meshless local Petrov–Galerkin approach has a good accuracy in solving the coupled radiative and conductive heat transfer in absorbing, emitting and scattering media.

[1]  R. C. Birkebak,et al.  POLYNOMIAL APPROXIMATION SOLUTION OF HEAT TRANSFER BY CONDUCTION AND RADIATION IN A ONE-DIMENSIONAL ABSORBING, EMITTING, AND SCATTERING MEDIUM , 1982 .

[2]  Walter W. Yuen,et al.  Heat Transfer by Conduction and Radiation in a One-Dimensional Absorbing, Emitting and Anisotropically-Scattering Medium , 1980 .

[3]  S. Baek,et al.  Analysis of combined conductive and radiative heat transfer in a two-dimensional rectangular enclosure using the discrete ordinates method , 1991 .

[4]  J. Howell,et al.  Empirical evaluation of an important approximation for combined-mode heat transfer in a participating medium using the finite-element method , 1995 .

[5]  Walter W. Yuen,et al.  Analysis of combined conductive-radiative heat transfer in a two-dimensional rectangular enclosure with a gray medium , 1986 .

[6]  L. H. Liu.  Meshless Local Petrov-Galerkin Method for Solving Radiative Transfer Equation , 2006 .

[7]  Liwu Liu.  Meshless method for radiation heat transfer in graded index medium , 2006 .

[8]  M. Modest.  Radiative heat transfer , 1993 .

[9]  J. Reddy,et al.  The Finite Element Method in Heat Transfer and Fluid Dynamics , 1994 .

[10]  S. Atluri,et al.  A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics , 1998 .

[11]  Satya N. Atluri,et al.  MESHLESS LOCAL PETROV-GALERKIN (MLPG) METHOD FOR CONVECTION DIFFUSION PROBLEMS , 2000 .

[12]  M. Pinar Mengüç,et al.  Thermal Radiation Heat Transfer , 2020 .

[13]  Suhas V. Patankar,et al.  Improved Treatment of Scattering Using the Discrete Ordinates Method , 1994 .

[14]  Ephraim M Sparrow,et al.  Advances in Numerical Heat Transfer , 1996 .

[15]  H. Sadat.  On the use of a meshless method for solving radiative transfer with the discrete ordinates formulations , 2006 .

[16]  S. Atluri,et al.  The meshless local Petrov-Galerkin (MLPG) method , 2002 .

[17]  R. J. Grosh,et al.  Effect of surface emissivity on heat transfer by simultaneous conduction and radiation , 1962 .

[18]  Tiffany Shih,et al.  Numerical properties and methodologies in heat transfer , 1983 .

[19]  M. M. Razzaque,et al.  Coupled Radiative and Conductive Heat Transfer in a Two-Dimensional Rectangular Enclosure With Gray Participating Media Using Finite Elements , 1984 .

[20]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[21]  S. Patankar,et al.  Finite volume method for radiation heat transfer , 1994 .

[22]  I. Singh,et al.  HEAT TRANSFER ANALYSIS OF TWO-DIMENSIONAL FINS USING MESHLESS ELEMENT FREE GALERKIN METHOD , 2003 .

[23]  Jianyu Tan,et al.  Meshless approach for coupled radiative and conductive heat transfer in one-dimensional graded index medium , 2006 .

[24]  R. J. Grosh,et al.  Heat Transfer by Simultaneous Conduction and Radiation in an Absorbing Medium , 1962 .