Thermoacoustic streaming between parallel plates under magnetic fields

Thermal Rayleigh-type acoustic streaming, the phenomenon in which fluid motion is caused by interacting with acoustic waves having temperature gradient, has been reported to have essential use in a wide range of applications including microfluidic mixing and thermal management applications. However, the combined influence of acoustic streaming and magnetic fields on heat transfer remains insufficiently explored. This research examines the influence of MHD on thermal Rayleigh-type acoustic streaming in a horizontal parallel plate configuration with the help of both analytical and numerical tools. Based on the value of$Pe\ll 1$, the use of the Perturbation method, for$Pe\gg 1$, numerical simulations are employed to solve the mathematical equations. This Computational analysis helps to know in detail about the relationship between acoustic streaming and magnetohydrodynamics with the goal of advancing thermal control strategies in aerospace actuators, microfluidic devices, and ultrasonic systems. The key findings show that the pair of equations present the central velocity as occurring within the flow region as it affirmed that in flow region or flow core, the flow does not depend on the viscosity, and the flow described in this equation is dictated by the magnetic field. For magnetic field on Couette flow has been gathered graphically and results depicted in the graphs affirm that flow has been controlled with the help of magnetic field. Asymptotic expression for $Pe\ll 1$, which denote time and axial direction averaged heat transfer coefficient, Nusselt number are also derived.