Unsteady MHD free convection flow of Jeffrey fluid and Jeffrey nanofluid along a vertical plate with radiation effect

Abstract

Fluid is a substance that continuously deform under the influence of shear stress. Basically, fluid can be classified into two categories which are Newtonian and non-Newtonian. In reality, most fluids belong to the class of non-Newtonian fluids and one of them is Jeffrey fluid. Jeffrey fluid is also known as viscoelastic fluid that exhibits both viscous and elastic characteristics. Recently, this type of fluid have received considerable attention due to their numerous applications in industries especially in polymer industries. Due to this reason, many investigations have been made to study the Jeffrey fluid in various aspects from both analytical and numerical methods. Therefore, in this thesis, the effect of thermal radiation on unsteady magnetohydrodynamics (MHD) free convection flow of Jeffrey fluid with and without nanoparticles past an infinite vertical plate are studied. The fluid is taken electrically conducting in the presence of uniform transverse magnetic field applied in a direction perpendicular to the flow. Specifically, focused of this study is to obtain an exact solution for velocity and temperature distributions under conditions of ramped wall temperature and isothermal plate. Using the constitutive relation of Jeffrey fluid and some assumptions of physical conditions, five specific problems are modelled as partial differential equations. For the first three problems, the fluid is considered as non-rotating fluid, while in the fourth and fifth problems the rotating fluid is analyzed. An appropriate dimensionless variables are employed to the dimensional governing equations and solved analytically with the help of Laplace transform technique. The effect of pertinent parameters such as Jeffrey fluid parameter, rotation parameter, phase angle, Hartmann number, permeability parameter, nanoparticles volume fraction, Grashof number, Prandtl number, radiation parameter and time on velocity and temperature are plotted graphically and discussed in details. Numerical results of Nusselt number and skin friction for various emerging parameters are calculated and presented in tabular forms. In order to authenticate the present results, the limiting cases are provided, where an excellent agreement are found. Results obtained show that, increasing of Hartmann number tends to retard the fluid flow due to the Lorentz force effect. Increasing the values of radiation parameter led to an increase in velocity and temperature fields. Further, in the case of rotating fluid, large values of rotation parameter reduces the primary velocity but enhance in the secondary velocity. On the other hand, increasing nanoparticles volume fraction causes the velocity of non-rotating fluid increases but decreases for rotating fluid. It also found that, the fluid motion for ramped wall temperature is always slower compared to an isothermal plate. Interestingly, Jeffrey fluid can be reduced to a Second grade fluid in the absence of material parameter.