An investigation is performed to study the effect of suction/injection on unsteady hydromagnetic natural convection flow of viscous reactive fluid between two vertical porous plates in the presence of thermal diffusion. The partial differential equations governing the flow have been solved numerically using semi-implicit finite-difference scheme. For steady case, analytical solutions have been derived using perturbation series method. Suction/injection is used to control the fluid flow in the channel, and an exothermic chemical reaction of Arrhenius kinetic is considered. Numerical results are presented graphically and discussed quantitatively with respect to various parameters embedded in the problem.
The current study analyzes the implications of an Arrhenius‐controlled heat transfer fluid on free convection in a micro‐channel confined by two immeasurable vertical parallel plates that are electrically non‐conductive due to an induced magnetic field (IMF) effect. The governing coupled nonlinear equations are ordinary differential equations, and the dimensionless steady‐state solutions were determined using the homotopy perturbation method (HPM). The derived results were discussed and represented graphically with the help of illustrative line graphs for momentum, IMF, temperature, and volume flow rate for the major controlling parameters, namely arrhenius kinetics, rarefaction, wall ambient temperature difference ratios, and Prandtl magnetic number. Thermo‐physical properties that are of engineering interest, like sheer stress and Nusselt number, are also computed and displayed. It is pertinent to report that the velocity of the fluid increases as a result of chemical reactions and rarefaction factors, whereas strengthening the Prandtl magnetic number decreases the volume flow rate. Also, numerical data was obtained and presented in tabular form to compare this research outcome to those of Jha and Aina, and great consistency was found. Microelectronics and microfluidics are some areas where this study can find relevance.
Unsteady as well as steady natural convection flow in a vertical channel in the presence of uniform magnetic field applied normal to the flow region and temperature dependent variable thermal conductivity is studied. The nonlinear partial differential equations governing the flow have been solved numerically using unconditionally stable and convergent semi-implicit finite difference scheme. For steady case, approximate solutions have been derived for velocity, temperature, skin friction, and the rate of heat transfer using perturbation series method. Results of the computations for velocity, temperature, skin friction, and the rate of heat transfer are presented graphically and discussed quantitatively for various parameters embedded in the problem. An excellent agreement was found during the numerical computations between the steady-state approximate solutions and unsteady numerical solutions at steady-state time. In addition, comparison with previously published work is performed and the results agree well.
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.
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