A novel optimum constructal fork-shaped fin array design for simultaneous heat and mass transfer application in a space-constrained situation

Abstract

The present study deals with the design and analysis of an array of constructal fork-shaped fins adhered to a circular tube and operating under fully wet conditions. Fork-shaped fin arrays with two and three numbers of branches are considered in the current work. The mass transfer process is calculated by using a cubic relation between the humidity ratio of saturated air and the corresponding fin surface temperature. The governing equations are highly non-linear and hence they are solved by using a semi-analytical technique called Homotopy Perturbation method. The optimisation is done by maximising the net heat transfer rate of the fin array and un-finned surface and by imposing certain constraints. The constraints are taken such that the radial space limitations fin material limitations, as well as the minimum fin gap considerations, are taken into account. As the present problem involves a large number of design parameters as well as the interrelated constraints, a bio-inspired metaheuristic algorithm called the Firefly Algorithm has been employed for obtaining the optimum condition. The analysis has been performed for different operating conditions and the results have been compared with the corresponding rectangular fin array. From the study, it has been seen that the heat transfer rate from the optimum fork-shaped fin array with two branches is higher than that from the optimum rectangular fin array. However, in a few cases, it has been found that there is marginal difference in heat transfer rate between the optimum fork-shaped fin array with two branches and the rectangular fin array but the total length of each fin for the former case is found to be smaller and hence fork-shaped fin array with two branches would be a better selection than the rectangular fin array. However, increasing the number of branches of the fork-shaped fins from two to three does not provide any benefit in terms of either lower fin length or higher heat transfer rate.