Steady State Heat Conduction in Exchanger Tubes by Using the Meshfree Boundary Integral Equation Method: Conduction Shape Factor and Degenerate Scale

Regarding the steady state heat conduction problem in exchanger tubes, the meshfree boundary integral equation method (BIEM) is employed to determine the shape factor in this paper. Different from the conventional boundary element method (BEM), the present method is free of mesh generation. After using the parametric function to represent the boundary contour and adopting the Gaussian quadrature, only collocating points on the boundary is required to obtain the linear algebraic equations. By introducing the local exact solution, the singular integral in the sense of the Cauchy principal value can be novelly determined. In addition, the boundary layer effect due to the nearly singular integral in the BIE can be dealt with. Two cases of different boundary conditions are considered. One is the isothermal condition on both the inner and outer surfaces. The other is the isothermal condition on the inner surface and the convection condition on the outer surface. Besides, numerical instability is found and the non-uniqueness solution due to the degenerate scale is examined through calculating the conduction shape factor and the temperature on the outer surface.