This work is licensed under a Creative Commons Attribution 4.0 Unported License ISSN: 1597 – 9928. Science and Education Development Inst., Nigeria 18 Continental J. Applied Sciences Ojemeri et al. (2023) 18 (1): 18 – 40 Doi: 10.5281/zenodo.7932942 Research Article Arrhenius-Controlled Heat Transfer Fluid Provoked by Porosity Effect through a Vertical Micro-Channel: An Analytical Approach Godwin Ojemeri 1 * Isaac O. Onwubuya 2 Abdulsalam Shuaibu 3 , Emmanuel Omokhuale 4 , Mohammad M. Altine 5 1,3 Department of Mathematics, College of Sciences, Federal University of Agriculture, P. M. B. 28, Zuru, Kebbi State, Nigeria. 2 Department of Mathematics, Faculty of Sciences, Air Force Institute of Technology, P. M. B. 2104, Kaduna State, Nigeria. 4 Department of Mathematics, Faculty of Sciences, Federal University Gusau, P. M. B 1001, Zamfara State. 5 Department of Mathematics, Federal University, Birnin Kebbi, P. M. B. 1157, Kebbi State, Nigeria. *Corresponding Author’s email: godwinojemeri@gmail.com Abstract This article basically focuses on the analytical treatment of Arrhenius-controlled fluid in a vertical micro-channel saturated with porous material. The leading equations are solved in dimensionless form using the homotopy perturbation method (HPM) subject to relevant boundary conditions. The fundamental flow features of temperature, velocity, and volume flow rate is investigated as a function of controlling parameters such as chemical reaction parameters, rarefaction parameter, fluid-wall interaction parameter, wall-ambient temperature difference ratio, and Darcy number. The findings are thoroughly investigated and graphically represented in a number of illustrative plots. It is worth noting that the variations of chemical reaction, Darcy number, rarefaction and wall-ambient temperature difference ratio parameters substantially dictate the fluid flow and volume flow rate respectively. KEYWORDS: Homotopy perturbation method, Arrhenius kinetics, rarefaction, porosity effect, wall ambient temperature ratio, Micro-channel Received: 21 March 2023 Accepted: 11 May 2023