The influence of viscous dissipation and joule heating on the viscous flow field between vertical rotating plates

Abstract

This article explores the influence of joule heating and viscous dissipation on the unsteady three-dimensional squeezing flow of Newtonian fluid. The Squeezing flow refers to the fluid flow through a constriction or a narrow opening. The fluid with some external/internal forces compelled to pass through the constriction which results a change in fluid velocity and a decrease in pressure. It can occur in various natural and man-made systems such as rivers flowing through canyons or fluids flowing through pipes or valves. The Pumping of heart, Synovial fluid in the knee joints, and Blood flow in vein and arteries are also include in the physical domain of squeezing flow. Keeping in view these applications, the goals of this article is to explore the viscous fluid flow behavior in a three dimensional system between two rotating plates that are being vertically squeezed together. The flow in a rotating channel with a lower stretched permeable wall is observed under the influence of a uniform magnetic field. The thermal radiation influence is also considered. The mass and heat transfer effect is investigated for Newtonian fluids in a squeezing phenomenon and the mathematical equations are modeled using the four fundamental governing equations of fluid flow, that is, the mass equation, momentum equation, concentration equation, and energy equation. By introducing the suitable transformations (similarity), the modeled highly non-linear partial differential equations are transformed to ordinary differential equations. The solution methodology is developed using the homotopy analysis method though which we obtained the series solution. The influence of several physical parameters including the squeezing parameter, the suction parameter, the magnetic number, the rotation parameter, the Eckert number, the Prandtl number, the Dufour number, the Soret number, the radiation parameter, and the Schmidt number on the velocity profile, energy, and concentration are also discussed with the help of graphs. Additionally, it is observed that enhancing the top plate’s squeezing impact causes a rise in the velocity profile while lowering the temperature and concentration distribution. It is also obtained that for the velocity field, increasing the magnetic number shows a decrease in the value of the velocity field along the y- and z axes, whereas the velocity field along the x-axes exhibits dual behavior, such that it initially falls as the magnetic number intensifies but starts to rise in the upper region of the channel. The impact of the Dufour, Soret, and Eckert numbers on temperature and concentration distribution is also studied. It is found that while these numbers directly affect the temperature distribution, the mass distribution follows the opposite trend. Also, it is noticed that the thermal radiation parameter is an increasing function of temperature and mass distribution.