Analysis of laminar film condensation over vertical permeable hollow short fins

Abstract

Laminar falling film condensation over vertical short fin is analyzed. The fin is considered to be hollow and permeable in order to account for condensate suction towards its inner core. The present work accounts for the shear stress at the interface caused by the large velocity of the saturated vapor. The continuity, momentum, and energy equations for the film condensate are solved using an iterative and implicit finite-difference method. The condensate flow rate inside the fin is obtained using the conservation of mass principle and the Poiseuille flow equations. The one-dimensional fin equation model is used to relate the fin temperature to the condensate flow convection heat transfer coefficient. Various computational and numerical methods techniques such as advanced linearization and generations of best-fit correlations are implemented. This is to reduce significantly the number of iterations required for solution convergence as all of the aforementioned equations are coupled. It is found that the dimensionless total mass transfer rate increases slightly as vapor Reynolds number increases. It increases apparently as both suction Reynolds number and dimensionless suction length increase. For both large suction Reynolds number and large dimensionless suction length, the flow rate of the condensate in the falling film can be neglected compared to the total suction condensate flow rate. The fin thermal length increases as Reynolds number, dimensionless suction length, and Grashof number increase. This study shows that significant condensation mass flow rate enhancement ratios are obtainable (can be 18 folds) due to suction through a hollow super conductive fin.