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.
Highlights
The study of laminar flow in tube and channel with permeable walls gained significant attention due to its engineering and industrial applications, for example, in reverse osmosis desalination, transpiration cooling boundary layer control, and design of filters [1,2,3]
An approximate solution of flow of laminar fluid flow in permeable channel with uniform suction/injection was obtained by Yuan [6], who investigated the flow in the case of moderate to high suction or injection velocities across the walls
Terrill et al [7] investigated the flow through permeable channel with different permeability for small Reynolds number
Summary
The study of laminar flow in tube and channel with permeable walls gained significant attention due to its engineering and industrial applications, for example, in reverse osmosis desalination, transpiration cooling boundary layer control, and design of filters [1,2,3]. An approximate solution of flow of laminar fluid flow in permeable channel with uniform suction/injection was obtained by Yuan [6], who investigated the flow in the case of moderate to high suction or injection velocities across the walls. Muthu et al [9,10,11] investigated the flow of viscous fluid in a porous channel, assuming that the bulk flow decreases with an axial distance of the channel. They obtained approximate solutions for velocity components and discussed the flow variations through graphs at different positions.
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