A proper analytical analysis of annular step porous fins for determining maximum heat transfer

Highlights: • Annular step porous fins for increasing heat transfer rate. • Differential transform method for an approximate analytical model. • Effects of radiation, heat generation, and enthalpy flux on heat transfer rate. • Demonstration for the superiority of step porous fins. • Optimization analysis based on constraint mass of fins. - Abstract: The annular stepped fin is a common choice for enhancing heat transfer from a cylindrical primary surface. This typical fin shape is easy in manufacturing compared to the taper shape. There is still effort required to increase the heat transfer rate per unit mass of a step fin. With this design point of view, the present study has been carried out. There may be two design aspects to be adopted to satisfy the above design requirement. With consideration of the porous material and moving condition of fins, heat transfer can be increased for a constraint mass of a fin. In the present study, an appropriate analytical method has been developed for an annular step fin of porous material under a moving condition. The effect of internal heat generation in the fin and the radiation mode of heat transfer on the fin performance have been studied elaborately. Unlike previous literature for moving fins, the performance design parameter is dependent on the modified Peclet number instead of the conventional Peclet number. The double differential transform method has been used for the analytical analysis. The optimization analysis has been demonstrated for the maximization of heat transfer through an annular step porous fin (ASPF) under a design constraint of mass of a fin. A comparative study has also been made between the porous and solid fins for an equal mass of fins. It was highlighted that the porous fin transfer always more heat at an optimum condition compared to the solid fin which is a profitable design aspect for selecting the porous condition. The moving condition is also a better approach to increase heat transfer rate and it is clearly demonstrated in the present study. The formulation of the present work is suitable for stationary and annular disk porous fins also by considering an appropriate design variable.