Variable Wall Permeability Effects on Flow and Heat Transfer in a Leaky Channel Containing Water-Based Nanoparticles

Abstract

This work presents the effects of variable wall permeability on two-dimensional flow and heat transfer in a leaky narrow channel containing water-based nanoparticles. The nanofluid is absorbed through the walls with an exponential rate. This situation arises in reverse osmosis, ultrafiltration, and transpiration cooling in industry. The mathematical model is developed by using the continuity, momentum, and energy equations. Using stream function, the transport equations are reduced and solved by using regular perturbation method. The expressions for stream function and temperature distribution are established, which helps in finding the components of velocity, wall shear stress, and heat transfer rate inside the channel. The results show that velocity components, temperature, wall shear stress, and rate of heat transfer are minimum at the entrance region due to the reabsorption of fluid containing nanoparticles. Additionally, with increasing volume fraction of nanoparticles, the rate of heat transfer enhances at all positions inside the channel. Titanium dioxide (TiO 2 ) nanoparticles show higher wall shear stress compared to copper and alumina. The streamlines confirms that all the fluid is reabsorbed before reaching the exit region of the channel for high reabsorption.