Investigation of transient coupled conduction and radiation heat transfer in the linearly anisotropic scattering cylindrical medium by spectral collocation method

2022 ◽  
Vol 172 ◽  
pp. 107308
Author(s):  
Yasong Sun ◽  
Xinyu Li ◽  
Jiazi Zhao ◽  
Yang Hu ◽  
Xin Jing ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Collocation Method ◽  
Radiation Heat Transfer ◽  
Anisotropic Scattering ◽  
Spectral Collocation Method ◽  
Radiation Heat ◽  
Spectral Collocation

Spectral Collocation Method for Transient Combined Radiation and Conduction in an Anisotropic Scattering Slab With Graded Index

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Ya-Song Sun ◽  
Ben-Wen Li
Keyword(s):  
Heat Transfer ◽  
Collocation Method ◽  
Transfer Problem ◽  
Anisotropic Scattering ◽  
Spectral Collocation Method ◽  
Discrete Ordinates ◽  
Spectral Collocation ◽  
Discrete Ordinates Method ◽  
Conduction Heat Transfer ◽  
Graded Index

The spectral collocation method for transient combined radiation and conduction heat transfer in a planar participating medium with spatially variable refractive index is introduced and formulated. The angular dependence of the problem is discretized by discrete ordinates method and the space dependence is expressed by Chebyshev polynomial and discretized by spectral collocation method. Due to the exponential convergence of spectral methods, very high accuracy can be obtained even using a small resolution for present problem. Numerical results in one-dimensional planar slab by Chebyshev collocation spectral-discrete ordinates method (SP-DOM) are compared with those available data in references. Effects of various parameters such as the variable thermal conductivity, the scattering albedo, the emissivity of boundary, the conduction-radiation parameter, the optical thickness, and the graded index are studied for absorbing, emitting, and anisotropic scattering medium. The SP-DOM has been found to successfully and efficiently deal with transient combined radiation and conduction heat transfer problem in graded index medium.

scholarly journals Numerical study of heat transfer of a micropolar fluid through a porous medium with radiation

2018 ◽  
Vol 22 (1 Part B) ◽  
pp. 557-565 ◽  
Author(s):  
Fakhrodin Mohammadi ◽  
Mohammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Collocation Method ◽  
Micropolar Fluid ◽  
Legendre Polynomials ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Shifted Legendre Polynomials ◽  
Non Linear

An efficient Spectral Collocation method based on the shifted Legendre polynomials was applied to get solution of heat transfer of a micropolar fluid through a porous medium with radiation. A similarity transformation is applied to convert the governing equations to a system of non-linear ordinary differential equations. Then, the shifted Legendre polynomials and their operational matrix of derivative are used for producing an approximate solution for this system of non-linear differential equations. The main advantage of the proposed method is that the need for guessing and correcting the initial values during the solution procedure is eliminated and a stable solution with good accuracy can be obtained by using the given boundary conditions in the problem. A very good agreement is observed between the obtained results by the proposed Spectral Collocation method and those of previously published ones.

Scaling Anisotropic Scattering in Radiation Heat Transfer for a Planar Medium

1982 ◽  
Vol 104 (1) ◽  
pp. 68-75 ◽  
Author(s):  
H. Lee ◽  
R. O. Buckius
Keyword(s):  
Heat Transfer ◽  
Radiation Heat Transfer ◽  
Anisotropic Scattering ◽  
Isotropic Scattering ◽  
Scattering Medium ◽  
Radiation Heat ◽  
Scattering Problems ◽  
Solution Methods ◽  
The One ◽  
Planar Medium

Radiation heat transfer in a planar participating medium which scatters anisotropically is scaled to an isotropically scattering medium. Only isotropic scattering problems need to be solved with a scaled optical depth and albedo. The scaling is derived from approximate solution methods to the equation of transfer. From the P-1 approximation, the two-flux method, and the modified linear anisotropic scattering model, three scalings are derived. The scaling that gives the best results when comparing the scaled solutions to exact solutions is the one derived from the P-1 approximation.

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