Analytical method on heat conduction performance of anisotropic pin fins

A mathematical model was constructed to describe the heat conduction problem of anisotropic pin fins. Through dimensionless analyses, the dimensionless criterion numbers were obtained, which affected the heat transfer process of the fins. Variable separation method, Taylor expansion, and integral averaging were applied to solve the differential equation. Analytical correlations for fin efficiency and heat transfer rate were derived and numerically verified. Based on the proposed analytical solutions, the influence of the direction of the heat conductivity principal axis on anisotropic pin fins was analyzed. The results showed that within the range of radial Bi was 0.05—10, axial Bi was 0.005—10, cross Bi was 0.2—10, and length to diameter ratio of fin was 2—20, the relative error of fin efficiency from the proposed correlation was less than 1.06% compared with the numerical results. Due to the circumferential symmetry of the temperature field, when the heat conductivity principal axis was deflected in the rOφ and φOz planes, it was beneficial to enhance the fins’ heat transfer performance by making the axis, which had a higher principal heat conductivity coefficient along the r and z directions. However, when the axis was deflected in the rOz plane, the optimal deflection angle can be calculated to maximize the heat transfer performance of the fins under given boundary conditions, material properties, and length to diameter ratio. And the maximum heat transfer rate was 2.97 times that of α=0. The results provide a theoretical support for the design of anisotropic pin fins in application.