Unsteady MHD free convection flow of an exothermic fluid in a convectively heated vertical channel filled with porous medium

Abstract

Utilizing porous media in a new mathematical model to improve convective heat transfer characteristics in a variety of applications, such as radiation nuclear disposal storing, evaporation cooling, sieving, geological extraction, crude petroleum refining, and building heating and cooling, is becoming increasingly important. This study proposed a numerical analysis of the unsteady magnetohydrodynamic free convection flow of an exothermic fluid with Newtonian heating. This discovery reveals two types of solutions: steady state and unsteady state. After transforming the governing equation from dimensional form to dimensionless form, the steady state governing equation was solved by the Homotopy Perturbation Method. However, the implicit finite difference approach is used to solve the time-dependent governing equations numerically. The impact of various emerging parameters, namely the Hartmann number, Boit number, Darcy number, Navier slip parameter, and the Frank-Kamenetskii parameter, was discussed and graphically analyzed. During the computations and analysis, it was discovered that a minor rise in the Hartman number results in the Lorentz force, which streamlines the momentum barrier layer and hence slows the fluid flow. The fluid velocity, on the other hand, rose as the porous medium, thermal Biot number, slip parameter, and temperature field increased as the viscous reactive fluid parameter and Newtonian heating increased. The skin friction and Nusselt number were also examined and reported. By comparing the finding to an existing work, a great agreement was revealed.

Insight Into the Fluid Flow Through the Porous Medium Between Two Vertical Walls Due to Buoyancy Forces, Convectively Heating of Left Wall, Space-Dependent Heat Source But Subject to Lorentz Force

“…During the computation, the chemical reaction parameter, chemical kinetic exponent, thermal Biot number, porous medium, and Navier slip parameter were shown to be highly reliant on the spike in momentum and energy profile. Similarly, it was demonstrated throughout the computational process that increasing MHD increases the thickness of the momentum boundary layer, resulting in a dropin fluid velocity following Hamza et al [6]. From a physical standpoint, M = 0 signifies no magnetic impact, and the flow is entirely hydrodynamic.…”

“…An alternative study was also conducted on unsteady MHD free convective flow in a vertical tube covered with absorbent material [5].Porous media are sometimes employed in a unique computational framework to increase convective heat transfer properties for someutilizations, including radioactive waste storage, transpiration cooling, crude oil refining, and building heating and cooling. Hamza and colleagues [6] investigated MHD-free convection flow in a vertical plate embedded with porous material. They identified that porous media had a major impact on fluid flow.…”

Numerical Solution for Both Steady and Unsteady State of Fluid Flow Between Two Heated Parallel Walls

“…The effect of various parameters on fluid velocity is presented graphically, and the time of steady state has been evaluated. The studies [11][12][13][14] presented unsteady flow and heat transfer of a viscous, incompressible electrically conducting fluid through a porous horizontal channel. The associated equations of the problem were transformed to dimensionless form and treated analytically using the perturbation method.…”

A Computational Analysis on Steady MHD Casson Fluid Flow Across A Vertical Porous Channel Affected By Thermal Radiation Effect

“…In a recent work, Hamza et al (2023) used homotopy perturbation method to explore the characteristics of Arrheniuscontrolled heat transfer fluid on free convection affected by an induced magnetic field. Later, Hamza et al (2022) evaluated the convectively heated, MHD-free flow of a chemically reacting fluid in a vertical channel contemplated with porous media. The steady-state component was solved using the homotopy perturbation method while the unsteady state case was analyzed using a numerical technique.…”