Analysis of Magnetized Chemical Reaction under Arrhenius Control in the Presence of Navier Slip and Convective Boundary Conditions

DOI: https://doi.org/10.33003/jobasr-2023-v1i1-19

Hamza M. M.

Isa M. M.

Ibrahim Y.

Usman H.

Abstract
The presence of Navier slip and Newtonian heating conditions at the boundary layer flow affects the shear stress distribution and overall flow behavior which causes the thermal boundary layer to be thinner or thicker depending on the relative strength of the slip velocity and Newtonian heating rate. In this paper, the steady state magnetized chemical reaction under Arrhenius control in the presence of Navier slip and Newtonian heating at both walls is studied. Using appropriate dimensionless quantities and parameters, the governing ordinary differential equations in dimensional form have been reduced to dimensionless governing equations. A semi-analytical solution for velocity and temperature are obtained using semi-analytical approach (regular perturbation method). Expressions of skin friction and rate of heat transfer are also displayed. The results show that Navier slip and Newtonian heating conditions affect the flow pattern significantly.
References
Rehman, S. U. and Kam, I. (2018). Analysis of activation energy MHD flow with chemical reaction and second order momentum slip model. Case studies internal engineering https://doi.ogr/10.1016/g.csite.2018.10.007. Adebowale, M. O. (2022). Chemical entropy generation and second order slip condition on hydrodynamic casson Nano-fluid flow embedded in a porous medium a fast- convergent method. Journal of the Egyptian mathematical society (2022) 30:6 https://doi.org/10.1186/542787-022- 00140-3. Akbar, N. S., Khan, Z. H., and Nadem, S. (2014). The combined effects of slip and convective boundary condition on stagnation-point flow of CNT suspended nanofluid over stretching sheet. Alaa Jabbar and Akil, J. H. (2020). The effects of the soret and slip boundary condition on thermo-solutal convective with a Navier-stokes-voigt fluid: physic of fluids (in press) (2022) http://doi.org/10.1063/5.0128993 Chinyoka, T., and Makinde, O. D. (2013). Analysis of entropy generation role in an unsteady channel flow with Navier slip and convective cooling. Entropy 2013,15,2081-2081. Doi:3390/e15062081 Das, S., Jana, R. N., and Chamkha, A. J. (2017). Entropy generation in a unsteady MHD channel flow with Navier slip and assignment convection cooling. Int. J. industrial mathematics Vol, no 2,2017 article ID. IJIM-00549 Fenuga O. J, Safiuma and Omowaye A. J. (2018). Effect of mixed convection and Navier slip on a chemically reaction heat and mass transfer MHD flow over a permeable surface with convective boundary conditions, journal of physical mathematics I SSN:2090-0902,DOI :10.4172/2090-0902. 1000291. Geethan, S. K., Kiran, R. K., Vinod, G. K. and Varma, S. V. K., (2016). Soret and RadiationEffects on MHD Free Convection Slip Flow over an Inclined Porous Plate with Heat andMass Flux, Advances in Science and Engineering,8(3), pp. 1-10. Hamza, M. M. (2016). Free convection slip flow of an exothermic fluid in a convectively heated vertical channel. Ain shams engineering journal. http://dx.doi.org/10.1016/j.osoj-2016.08.011 Hamza, M. M., Abdulsalam, S., and Ahmad, S. K. (2022). Examined the effects of MHD on time- dependent mixed convection flow of an exothermic fluid in a vertical channel.Time- dependent magnetohydrodynamic (MHD) flow of an exothermic Arrhenius fluid in a vertical channel with convective boundary condition hindawi advances in mathematical physic, vol 2023, article ID 1773925, 13 pages https://doi.org/10.1155/2023/7173925. Hamza, M. M., Shehu M. Z., andTambuwal, B. H. (2021). Steady state MHD free convective slip flow of an exothermic fluid in a convectively heated vertical channel. Saudi journal of engineering technical. http//doi:10.36348/sjet. 2021.vobi10.006 Hamza, M. M., Shehu, M. Z., Usman H., and Emmanuel O. (2023). Computational treatment of transient MHD slip flow of an Arrhenious chemical reaction in a convectively heated vertical channel, caliphate journal of science and technology (CojoST) 2705-313X,2705-3121 http://dx.doi.org/10.4314/Cajost.v4i2.13 Hussan, K., Shuaib, M., Ali, A., Rehman, H. U., and Nasir J. (2022). Thermo-convection Arrhenius reaction fluid flow between two parallel plates. Jha, B. K., Aina B., and Isa S. (2015). Fully developed MHD natural convection flow inverticalannular microchannel: an exact solution. Journal of king Saudi University of Science,27,253- 259. Jha, B. K., Altine, M. M. and Hussaini, A. M. (2023). MHD steady natural convection in avertical porous channel in the presence of point/line heat source/sink: An exact solution,Heat Transfer, Wiley, pp. 1-15. DOI: 101002/htj.22903 Joseph, K. M., Ayuba, P., Nyitor, L. N. and Muhammed, S. M. (2015). Effect of Heat and MassTransfer on Unsteady MHD Poiseuille flow between Two Infinite Parallel Porous plates inan Inclined Magnetic Field, International Journal of Scientific Engineering and AppliedScience,1(5). Kalandhar and komuraiah (2017). Homotopy analysis for the influence of Navier slip flow in a vertical channel with cross diffusion effect. Math sci (2017) 11:219-229 Makinde, O. D. (2011). “Aziz A. Boundary layer flow of a nanofluid past a stretching sheet withconvective boundary condition”, Int J Thermal Sci vol. 50, pp. 1326– 32, 2011. Malvand, A.,Hadeyati, F., and Ganji, D. D. (2014). Boundary layer slip flow and heart transfer sheet with convective boundary condition journal of applied fluid mechanics vol 8, no. 1,pp. 151, 2015. Doi:10.36884/jafm.8.01.22766 Mona, D., and Aljoufi, A. E. (2016). Effect of a convective boundary condition on boundary layer slip flow and heat transfer over a stretching sheet in view of the exact solution, journal of theoretical and applied mechanic,sofia vol,46 no.4(2016) pp. 85-95 doi:10.1515/jtam-2016-0022. Nayak, M. K., Show, S., Pandey, V., and Chamkha, J. (2018). Combined effects of slip and convection boundary on MHD 3D stretched flow of nanofluid through porous media inspired by non-linear thermal radiation: Indian J physic (august 2018)98(89):197-1028 hppt://doi.org/10.1007/./2648-018-1188-2 Obalalu A. M., Ajala O. A, Adeosun A. T., Akindele A. O., Oladapo O. A. and Olajide O. A. (2021). Significance of variable electrical conductivity on non-Newtonian fluid flow between two vertical plates in the coexistence of Arrhenius energy and exothermic chemical reaction, Partial Differential Equation in Applied Mathematics,4:100184, pp 1-9 Ojemeri, G., Hamza, M. M., Tambuwal B. H., Bello I. and Shuaibu, A. (2023). Influence of Soret and Radial magnetic field on natural convection of a chemically reactive fluid in anupright porous annulus, UMYU Scientifica, 2(3), 108-120. Ojemeri, G., Onwubuya I. O., Omokhuale, E., Hussaini A. and Shuaibu, A. (2024). Analytical investigation of Arrhenius kinetics with heat source/sink impacts along a heatedsuperhydrophobic microchannel, UMYU Scientifica, 3(1), 61-71. Ojemeri, H. and Hamza, M. M. (2022). Heat transfer analysis of Arrhenius-controlled free convective hydro-magnetic flow with heat generation absorption effect in a micro-channel. Alexandria engineering journal, vol 16, 12797-12811. https://doi.org/10.1016/j.aej.2022.06.058. Okedoye, A. M and Waheed A. A. (2023). Second low analysis of passive control MHD flow in the presence of Arrhenius chemical reaction with heat generation/absorption doi:https//doi.org/10.55248/gengpi.2023.4109 Osman, H. I., Omar, N. F. M., Vieru, D. and Ismail, Z. (2022). A study of MHD free convection flow past an infinite inclined plate, Journal of Advanced Research in fluid Mechanics and Thermal Sciences, 92(1), pp. 18-27. Rundora, L., and Makinde, O. N. (2015). Effects of Navier slip an unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convection boundary condition, science direct journal of hydrodynamics 2015,27(6):934-944 doi:10.1016/51001-6058(15) 60556-x Salehi S., Mardani, M. R. and Ganji D. D. (2020). Investigation of nano-Bioconvective fluid motile microorganisms and nanoparticles flow by considering MHD and thermal radiation,Informatics in Medicine unlocked, DOI: 10.1016/j.imu.2020.100462 Sandeep, N. and Sugunamma, V. (2013). Effect of an Inclined Magnetic Field on Unsteady free Convection flow of a Dusty Viscous fluid between two Infinite flat Plates filled by a Porous medium, International Journal of Applied Mathematics and Modeling, 1(1), pp. 1633. Sharada, K., and Shankar, B. (2017). Effect of partial slip and convective boundary condition MHD mixed convection flow of Williamson fluid over an exponentially stretching sheet in the presence of joule heating. Global journal of pure and applied mathematics. Vol.13 number 9(2017). pp,5965-5975 Shehu, Z. M., Abdullahi, I., and Umar, M. (2022). MHD slip flow of an exothermic fluid in a convectively heated porous vertical channel, Doi:10.36348/sjet. 2022.v09i10.002. Siva, T., Jaangili, S. and Kumbhakar, B. (2021). Heat transfer analysis of MHD and electroosmotic flow of non-Newtonian fluid in a rotating microfluidic channel: an exactsolution, Applied Mathematics and Srinivacharya, D., and Hima, K. Bindu (2015): Entropy generation in a micro polar fluid flow through an inclined channel with and convective boundary condition. Energy 91(2018)72-8 Taid, B. K., and Ahmed, N. B., (2022), MHD free convection flow across an inclined porous plate in the presence of heat source, soret effect and chemical reaction affected by viscous dissipation ohmic heating, Bio- interface Research in Applied Chemistry12(5) pp. 6280- 6296. Torobi, M.,and Aziz, A. (2012). Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective- radiative surface cooling. Int. Commun. Heat transfer 39(10)(2012)1487-1495. Torobi, M., and Zhang, K., (2014). Classical entropy generation analysis in cooled homogenous and functionally graded material slabs with variation of internal heat generation with temperature, and convective- radiative boundary conditions. Energy 65(2014)387-397. Uddin, M. J., Anwar Beg O., and Amin N. (2014). Hydro-magnetic transport phenomena from a stretching or shrinking nonlinear material sheet with Navier slip and convective heating: A model for bio- nano-materials processing. Journal of magnetism and magnetic ma386(2014)252-261 http://dx.doi.org/10.1016/j.jmmm.2014.05.0410304- 8853/ Yale I. D., Uchiri A. M. T., Hamza M. M., and Ojemeri G. (2023). Effect of viscous dissipationfluid in a slit microchannel with heated superhydrophobic surface, Dutse Journal of Pureand Applied Sciences, 9(3b), pp. 290-302.
PDF