Analytical Investigation of Orthotropic Unsteady Heat Transfer in Composite Pin Fins

In this paper, an analytical solution of transient heat conduction in multi-layer composite pin fins under the general boundary conditions is presented. The 2D unsteady heat conduction equation in cylindrical coordinate system has been achieved for multi-layer orthotropic laminates. Laplace transformation is applied to change the solution’s domain from time into the frequency. An appropriate Fourier transformation has been derived using the Strum-Liouville theorem and a set of equations are obtained based on the boundary conditions of fin and temperature/heat flux continuity at boundaries located between the layers. The Meromorphic function method is utilized to find the complicated complex integration of inverse Laplace. Diagrams of unsteady temperature distribution and cooling rate of pin fin have been depicted and it is shown that the effects of orthotropic conduction are more noticeable in high convection coefficients.