Heterogeneous anisotropic conductive heat transfer in composite conical shells: An exact analysis

Abstract

In present paper, problem of anisotropic heat conduction in heterogeneous composite conical shells is solved analytically. Arbitrary values for fiber angle (ranging from zero to 90 degrees) cause anisotropy for the heat conduction problem in composite conical shells. In our analysis, heat convection between conical shell and ambient flow is taken into account. In addition, an external source of radiative heat transfer is modeled. Herein, the heat conduction problem is assumed to be heterogeneous which is due to dependence of the conductivity coefficient on temperature. Kirchhoff transformation followed by an integral transform method are used to solve present heterogeneous heat conduction problem. Green’s functions are applied to find the solution of final ordinary differential equations. Verification of the present analytical solution is obtained through comparing the analytical results with those of a second order finite difference method. Good agreement between the analytical and numerical results has been found. In order to evaluate the capability of our analytical solution in solving real industrial problems, the temperature distributions in a typical pressure vessel and a pin fin are calculated.