Optimal Design of Constructal T-Shaped Fin Under Partially Wet Condition for Enhanced Thermal Performance: An Analytical Approach

Abstract

In refrigeration and air conditioning systems, the fin surface may become dry, fully wet or partially wet depending upon the psychometric, thermo-physical and geometric parameters. The current work is intended to determine the length of the dry portion, temperature distribution, performance and optimum design parameters of a T-shaped fin under partially wet condition. Temperature dependent thermal conductivity of the fin material is taken and the humidity ratio of saturated air is considered to vary linearly with the corresponding fin surface temperature. Considering these the governing equation of T-shaped fin becomes nonlinear and it has been solved analytically by using Homotopy Perturbation Method. The point of separation between the dry and wet portions of a T-shaped fin may be located either in the stem or flange part and hence, two cases having different governing equations and boundary conditions are analyzed in the current study. For the optimization study, Lagrange multiplier technique is employed and the results are obtained by maximizing the heat transfer rate for a constant fin volume. Further, a comparative study is presented between insulated and convective fin tip conditions.

Notes on contributors

Saheera Azmi Hazarika graduated in Mechanical Engineering from Assam Engineering College, Assam, India in 2012. She obtained her M. Tech. in Thermal Engineering from National Institute of Technology Silchar, India in 2015. Presently she is a research scholar in the Department of Mechanical Engineering, National Institute of Technology Silchar, Assam, India. Her research areas include simultaneous heat and mass transfer, constructal theory and optimization.

Dipankar Bhanja received his Ph.D. Degree from Jadavpur University, Kolkata, India. Presently he is an Assistant Professor in the Department of Mechanical Engineering, National Institute of Technology Silchar, Assam, India. His research areas are porous fin, constructal theory, computational fluid dynamics, heat and mass transfer, solar energy and optimization. He is a reviewer for many international journals of repute and also published many technical papers in referred international journals.

Sujit Nath received his Ph.D. Degree from Jadavpur University, Kolkata, India. Presently he is an Assistant Professor in the Department of Mechanical Engineering, National Institute of Technology Silchar, Assam, India. His research areas are computational fluid dynamics, heat transfer, atomization and solar energy. He is a reviewer for many international journals of repute and also published many technical papers in referred international journals.