A NUMERICAL STUDY OF THE PERTURBATION OF A GRADIENT TEMPERATURE FIELD FOR ARBITRARY PROXIMITY BETWEEN TWO SPHERES USING LEGENDRE SPECTRAL METHOD

作者：Chowdhury A^*

来源：Romanian Journal of Physics, 2015, 60(3-4): 401-414.

• Legendre spectral method
• Touching-spheres
• Bi-spherical coordinates
• Pure perturbation

The temperature distribution around two spheres is considered when the main field has a constant gradient at infinity. The beneficial effects of introducing an approach involving bi-spherical coordinates over other well-known method's in the literature are interrogated thoroughly. Together with a transformation of the dependent variable which leads to separation of variables, this method allows the solution to be sought in Legendre series. The method is validated to have an exponential convergence and proved to be highly efficient in obtaining any desirable level of accuracy with a reasonable number of terms, even for a difficult case of two almost-touching spheres. Solutions with both longitudinal and transverse gradients at infinity are obtained, and the contour lines of the temperature field are presented graphically. The pattern of the temperature field is thoroughly investigated in the region between the spheres when the distance between them is much smaller than their radii.

• 出版日期2015