Modelling of Unsteady Hydromagnetic Micropolar Nanofluid Flow along a Vertical Plate with Reactive Effects
J.B. Mwamunga
*
Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya.
W. N. Mutuku
Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya.
I. Wattanga
Department of Mathematics and Statistics, Open University of Kenya, Konza Technopolis, Kenya.
A. Wahome
Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya.
J. A. Okello
Department of Mathematics and Actuarial Science, Kenyatta University, Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Micropolar nanofluid synergizes both the properties of the micropolar fluid and those of nanofluid. They possess microstructural properties that permit both translational and rotational motion coupled with enhanced thermal conductivity due to the presence of nanoparticles. They have numerous applications in electronic cooling, coolants in car radiators, working fluid in shell and tube heat exchangers, Lubrication, and in medical use (drug delivery, and cancer treatment). The study examines the effect of magnetic field strength, micropolar parameter, reaction rate, and Schmidt number on the velocity profile, temperature profile, and solute concentration by modelling the unsteady two dimensional Hydromagnetic flow of a micropolar nanofluid along a vertical plate. The magnetic field is imposed perpendicular to the flow. The equations and the accompanying boundary conditions governing the flow are formulated. The gyration and the inertial effect due to the micropolar fluid is infused into the body forces of the momentum equation. The introduction of similarity transformation variables converts the equations to nonlinear systems. The deployment of the state-space method linearizes the ordinary differential equations which numerically solves using the fourth-order Runge-Kutta method with a shooting technique in MATLAB. The bvp5c function is invoked in solving the resulting first order differential equations plus the boundary conditions with a higher order of accuracy. The outputs of the simulation are displayed graphically. The primary and secondary velocities decays with a climb in magnetic field due to the upsurge in Lorentz force. The climb in micropolar fluid parameter dampens the flow due to build up in viscous resistance as a result of increase in micro-rotational motion within the flow. The solute concentration and temperature are declined with elevation in the reaction rate. Enhanced reaction rate consumes the reactants and thermal energy during the reaction process resulting in less solute concentration and low temperature. The Schmidt number lowers solute concentration and upsurges the fluid temperature.
Keywords: Hydromagnetic, Micropolar Nanofluid, Reactive Effects