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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.

The consequences of chemically reactive fluids have provoked many researchers due to their potential to enhance the behavior of heat. Hence, this article discussed a theoretical investigation to explore the actions of Arrhenius chemical reaction and Hall current on hydro-magnetic free convection of a viscous fluid flowing along an upstanding micro-channel. Subject to the required boundary conditions, the governing coupled equations representing the flow pattern in non-dimensional form were solved using the homotopy perturbation method (HPM). Line graphs are also used to generate expressions for energy, momentum, volume flow rate, drag force, and Nusselt number in both primary and secondary flow directions as a function of regulating parameters like chemical reaction, Hall current, rarefaction, and wall ambient temperature difference ratio. It is worthy of note that the fluid temperature and the fluid flow are substantially propelled by the viscous heating term in the Arrhenius chemical reaction of the system for growing values of the wall ambient temperature difference ratio parameter. Additionally, it is noticeable that volume flow rate performance is seen as a growing influence of viscous heating and rarefaction parameters. The findings of this study can be applied to a wide range of electrically controlled devices, thermal and petro chemical engineering, and the serviceability of industrial products.

The consequence of fully developed free convection with Arrhenius-controlled heat flow for a viscous and an electrically-conducting fluid flowing along an isothermally heated vertical parallel plate in a slit micro-channel is presented in this article. One wall had super-hydrophobic slip (SHS) and a temperature spike, while the other did not. A semi-analytical technique (perturbation series) was utilized to analyze the primary equations. The analytical solutions were thoroughly presented, and the functions of the pertinent parameters were illustrated with the help of various plots. It is revealed from this work that the action of chemically reacting factors is noticed to substantially strengthen the fluid movement in the micro-channel for a constant pressure gradient. In the fields of engineering and medicine, it is essential to understand these fluids' characteristics. Due to the lubrication of micro-channel boundary walls where conductivity and viscosity interact with thermos-physical behavior, the outcomes of the current research can substantially enhance the operations of micro-electro-mechanical systems (MEMS) and micro-devices that rely on micro-fabrication processes.