Influence of temperature dependent heat source/sink on transient MHD free convective flow in an infinite rigid impermeable vertical cylinder with chemical reaction

Naveen Dwivedi ^a,b,*, Ashok Kumar Singh ^a, Nirmal C. Sacheti ^c

a. Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi  221005, India
         b. Department of Mathematics, Sahu Jain College, Najibabad, Affiliated to M.J.P. Rohilkhand University, Bareilly 246763, India
         c. Retired Professor, Department of Mathematics, College of Science, Sultan Qaboos University, Al Khod PC 123, Muscat, Sultanate of Oman

Abstract: It is increasingly apparent that the inclusion of mass transfer aspects, together with certain thermal conditions, in the momentum and energy equations governing MHD flows leads to a numbers of real life applications. Keeping this in view, we have attempted an exact analysis of heat and mass transfer aspects in transient hydromagnetic free convective flow of an incompressible viscous fluid through a vertical pipe under an externally applied magnetic field, assuming presence of chemical reaction and heat source/sink. The governing  PDEs, which simplify to a set of 3 linear ODEs in the physical set up considered here, have been solved using Laplace transform technique, with solutions for key physical variables presented in the term of Bessel and modified Bessel functions. The influence of governing non-dimensional parameters, namely, Hartmann number, Schmidt number, source/sink parameter, Prandtl number and chemical reaction parameter, has been illustrated on the developing velocity and some concentration profiles. Some important quantities of engineering interest-surface skin friction and volumetric flow rates- have been computed too and analysed. Some notable finding worth mentioning are: (a) heat source presence causes higher fluid velocity as compared to the heat sink; (b) all important surface shear stress can be suitably controlled, among others, by chemical reaction parameter and Schmidt number. The key challenge of this study has been to obtain exact closed-form solutions of the field equations, including cumbersome Laplace inverses. This study finds innovative applications in the emerging fields such as magnetic materials processing, chemical processes, solar energy systems, etc.

Keywords: Circular cylinder; Hydromagnetic transient flow; Chemical reaction; Source/Sink; Free convection

https:https://doi.org/10.1016/j.jppr.2023.11.003