Numerical quadrature and twodimensional radiative heat transfer
Abstract
The paper discusses four methods for the numerical integration of a twovariable integral equation for the radiative flux in a diffuse grey cavity represented by a semiinfinite congruent parallel strip geometry. Method 1 involves only the application of GaussLegendre quadrature to the nondimensional finite xsegment and GaussLaguerre quadrature to the nondimensional infinite ysegment. In Method 2, the infinite segment is inverted onto a finite segment, and GaussLegendre quadrature is used in each direction. Method 3 is similar to Method 2 except that the infinite segment is divided into at least one finite segment and an infinite segment that is inverted. Method 4 is similar to Method 3 except that physical reasoning rather than inversion is used, thus eliminating a numerical integration in the finite segment. It is shown that Method 4 is the only technique which can be used to bring about a convergence to an acceptable solution as the order of quadrature increases. The flexibility of Method 4 is discussed for different parameters.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 1976
 DOI:
 10.1002/nme.1620100302
 Bibcode:
 1976IJNME..10..491L
 Keywords:

 Convergence;
 Error Analysis;
 Integral Equations;
 Numerical Integration;
 Quadratures;
 Radiative Heat Transfer;
 Computer Techniques;
 Diffuse Radiation;
 Parallel Plates;
 Transformations (Mathematics);
 Fluid Mechanics and Heat Transfer