Exact and numerical solutions for unsteady heat and mass transfer problem of Jeffrey fluid with MHD and Newtonian heating effects

Abstract

The combined heat and mass transfer of unsteady magnetohydrodynamic free convection flow of Jeffrey fluid past an oscillating vertical plate generated by thermal radiation and Newtonian heating is investigated. The incompressible fluid is electrically conducting in the presence of a uniform magnetic field which acts in a direction perpendicular to the flow. Mathematical formulation of the problem is modeled in terms of partial differential equations with some physical conditions. Some suitable non-dimensional variables are introduced to transform the system of equations. The dimensionless governing equations are solved analytically for exact solutions using the Laplace transform technique. Numerical solutions of velocity are obtained via finite difference scheme. Graphical results for velocity, temperature and concentration fields for various pertinent parameters such as material parameter of Jeffrey fluid (Formula presented.), dimensionless parameter of Jeffrey fluid (Formula presented.), Newtonian heating parameter (Formula presented.), phase angle (Formula presented.), Grashof number (Formula presented.), modified Grashof number (Formula presented.), Hartmann number or magnetic parameter (Formula presented.), Prandtl number (Formula presented.), radiation parameter (Formula presented.), Schimdt number (Formula presented.) and dimensionless time (Formula presented.) are displayed and discussed in detail. This study showed that the magnetic field resists the fluid flow due to the Lorentz force, whereas the thermal radiation and Newtonian heating parameters lead to the enhancement of velocity and temperature fields. Present results are also compared with the existing published work, and an excellent agreement is found.