Research Article Time-Dependent Magnetohydrodynamic (MHD) Flow of an Exothermic Arrhenius Fluid in a Vertical Channel with Convective Boundary Condition M. M. Hamza, 1 S. Abdulsalam , 2 and S. K. Ahmad 1 1 Usmanu Danfodiyo University, P.M.B 2346 Sokoto, Nigeria 2 Federal University of Agriculture Zuru, P.M.B 28 Kebbi State, Nigeria Correspondence should be addressed to S. Abdulsalam; shuaibuabdulsalam@gmail.com Received 23 August 2022; Revised 29 December 2022; Accepted 17 January 2023; Published 18 February 2023 Academic Editor: Zine El Abiddine Fellah Copyright © 2023 M. M. Hamza et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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. 1. Introduction According to recent theoretical developments, mixed convec- tion is a flow condition that includes both free and forced con- vection movement. Mixed convection flows develop when buoyant forces alter the circulation, temperature, and species composition regimes. When the attractive force on a force flow is significant, the impact intensities of forced and free convection are comparable, resulting in mixed convection. Mixed convection phenomena have been observed frequently in nature, including astronomical detectors exposed to weather systems, telecommunications devices cooled by fans, nuclear facilities cooled during forced outages, and heat exchangers deployed in low-velocity locations. Madhu and Kishan [1] employed a finite element method and a nonlinear MHD model to analyze the coupled heat and mass transfer flow of a non-Newtonian power-law nanofluid. Abdul and Amer [2] simulated the free and forced magnetohydrody- namic flow of a nanofluid using a computer. In their investiga- tion of mixed convection over a vertically extended sheet, Halim and Noor [3] demonstrated that the aided flow had a higher rate of convective heat transfer than the opposing flow over a moving cylinder with a yawed axis controlled by buoy- ancy. Dinarvand [4] found that hybrid nanofluids are better than base fluids and fluids containing single nanoparticles. Dinarvand et al. [5] examine the mixed convection of incompressible viscous and electrically conducting hybrid nanofluid flow approaching the stagnation point of the planar Hindawi Advances in Mathematical Physics Volume 2023, Article ID 7173925, 13 pages https://doi.org/10.1155/2023/7173925