Thermal analysis of rough micro-fins of variable cross-section by the power series method

Thermal performance of micro-pin fins of variable diameter and rough surface is calculated by means of an approximate procedure based on truncated power series. The geometric effect of roughness is modeled after Bahrami et al. [9], which greatly increases the intricacy of the fin equation, preventing its analytical solution even by symbolic computer codes. The approximate series solution is developed firstly by estimating an adequate number of terms based on convergence to the (known) exact solution of smooth pin fins of the same geometry. Then, residual convergence for an increasing number of terms is studied for the rough fin. Three selected geometries are analyzed, of hyperbolic, trapezoidal and concave parabolic profiles. Influence of surface roughness is evaluated for a wide range of heat transfer conditions; results are discussed in terms of the two primary quantities of interest in fin design, viz., efficiency and effectiveness. Due to the easiness of the present methodology, it can be safely applied to other geometric arrangements involving straight and annular fins.