Time-Dependent Magnetohydrodynamic (MHD) Flow of an Exothermic Arrhenius Fluid in a Vertical Channel with Convective Boundary Condition

Abstract

The current study examined the effects of magnetohydrodynamics (MHD) on time-dependent mixed convection flow of an exothermic fluid in a vertical channel. Convective heating and Navier’s slip conditions are considered. The dimensional nonlinear flow equations are transformed into dimensionless form with suitable transformation. For steady-state flow formations, we apply homotopy perturbation approach. However, for the unsteady-state governing equation, we use numerical technique known as the implicit finite difference approach. Flow is influenced by several factors, including the Hartmann number, Newtonian heating, Navier slip parameter, Frank-Kamenetskii parameter, and mixed convection parameter. Shear stress and heat transfer rates were also investigated and reported. The steady-state and unsteady-state solutions are visually expressed in terms of velocity and temperature profiles. Due to the presence of opposing force factors such as the Lorentz force, the research found that the Hartmann number reduces the momentum profile. Fluid temperature and velocity increase as the thermal Biot number and Frank-Kamenetskii parameter increase. There are several scientific and infrastructure capabilities that use this type of flow, such flow including solar communication systems exposed to airflow, electronic devices cooled at room temperature by airflow, nuclear units maintained during unscheduled shutoffs, and cooling systems occurring in low circumstances. The current findings and the literature are very consistent, which recommend the application of the current study.

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

“…By examining the velocity profile over time, this is apparent. Also, it was discovered that fluid velocity rises in proportion to the chemical kinetic exponent m, with the biomolecular process producing the highest velocity profile based on reports by Hamza et al [35]. Figures 9a and 9b demonstrate that the slip parameter is consistent with steady and unsteady momentum patterns.…”

“…In both the manufacturing sector and the chemical sciences, slip conditions are crucial. Bestman [33],Alabraba, et al [34], and Hamza et al [35] considered the Arrhenius activation energy when developing their configurations.This study looks at the free convective slip flow's transient and steady-state MHD chemical kinetic exponent in a vertical channel-filled porous medium. The steady-state analytical solution was addressed with the homotopy perturbation method using the fundamental equations of momentum, energy, and related boundary conditions in dimensionless form.…”

Computational Fluid Dynamics for Cavity Natural Heat Convection: Numerical Analysis and Optimization in Greenhouse Application

“…The discretization equations were solved by the Gauss-Seidel model with super relaxation factor. The iteration method used in this program is a line-by-line procedure, which is a combination of the direct method and the resulting tridiagonal matrix algorithm (TDMA), which is more suitable for fluid computation than the finite-difference method and the finite-element method, and is able to overcome the disadvantage of the discrete Taylor expansion with good conservatism, as well as adapting well to the mesh and more easily obtaining smooth results [15][16][17]. Moreover, the point where the heater meets the rest of the section, i.e., the hot/cold junction, can become a singularity in the numerical calculations, and the FVM solves this problem by taking the mean value of the temperature at this point (Figure 2).…”

“…Saha et al [16] found that in the domain of a vertical plate, the resulting nonlinear method was mapped and then worked out numerically by applying the implicit central finite difference technique with Newton's quasilinearization method. Hamza et al [17] examined the effects of magnetohydrodynamics on time-dependent mixed convection flow of an exothermic fluid in a vertical channel and transformed dimensional nonlinear flow equations into dimensionless form with suitable transformation via homotopy perturbation approach.…”