^{1}

^{2}

^{2}

^{1}

^{2}

We analyse the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium in presence of heat source. An exact solution of the governing equations in dimensionless form is obtained by Laplace transform technique in ramped temperature case. To compare the results obtained in this case with that of isothermal plate, the exact solution of the governing equations is also obtained for isothermal plate and results are discussed graphically in both ramped temperature and isothermal cases.

The study of convective heat transfer from a solid body with different geometries embedded in a fluid saturated porous medium has varied and wide applications in many areas of science and engineering such as geothermal reservoirs, drying of porous solids, chemical catalytic reactors, thermal insulators, nuclear waste repositories, heat exchanger devices, enhanced oil and gas recovery, and underground energy transport. An investigation of an influence of magnetic field on viscous incompressible flow of electrically conducting fluid has its importance in many applications such as extrusion of plastics in the manufacture of rayon and nylon, paper industry, and textile industry and in different geophysical cases and so forth.

Keeping the above applications, Krishna et al. [

The present paper deals with the effects of aligned magnetic field, radiation, and rotation on unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving vertical plate in a porous medium with heat source, under Boussinesq approximation, assuming that the temperature of the plate has a temporarily ramped profile. An exact solution of the governing equations, in dimensionless form, is obtained by Laplace transform technique. To compare the results obtained in this case with that of isothermal plate and exact solution of the governing equations are also obtained for isothermal plate.

We consider an unsteady hydromagnetic free convection flow of a viscous incompressible electrically conducting fluid past an impulsively moving infinite vertical plate embedded in a porous medium and consider the coordinate system in such a way that the

Taking into consideration the assumptions made above, the governing equations for laminar free convection flow of a viscous incompressible electrically conducting fluid past a vertical plate in a uniform porous medium with radiative heat transfer, under Boussinesq approximation, in a rotating frame of reference are

The initial and boundary conditions are

Introduce the following nondimensional variables:

Equations (

The initial and boundary conditions (

It is evident from (

Applying Laplace transform technique, (

The boundary conditions (

Here,

The analytical solution for the fluid temperature and velocity, represented by (

To study the effects of magnetic parameter

From Figure

Velocity field for different values of magnetic field parameter

From Figure

Velocity field for different values of rotation parameter

Figure

Velocity field for different values of radiation parameter

Velocity field for different values of porosity parameter

It is revealed from Figure

Velocity field for different values of time

Figure

Velocity profiles for different values of Aligned angle

Velocity field for different values of heat source parameter

In order to have physical view of fluid temperature, the profiles of fluid temperature are drawn versus boundary layer coordinate

Temperature field for different values of

From Figure

Temperature field for different values of Prandtl number

Temperature field for different values of heat source parameter

The present study investigates the unsteady hydromagnetic free convection boundary layer flow of a viscous incompressible electrically conducting fluid past a ramped temperature impulsively moving plate in a rotating porous medium in the presence of aligned magnetic field, thermal radiation, and heat source. The significant findings are summarized as follows.

For both ramped temperature and isothermal plates,

magnetic field tends to reduce fluid flow in both the ramped and isothermal cases,

increase of radiation rotation decreases the fluid flow in the isothermal plate, whereas it increases the fluid flow in the ramped temperature,

aligned magnetic field angle does not show effect on rotating fluid velocity,

Prandtl number has tendency to increase the fluid temperature,

radiation parameter causes the decrease of temperature in ramped temperature as well as in isothermal case,

heat source parameter causes the increase in fluid velocity at isothermal case but opposite in ramped case,

heat source parameter increases the temperature in both cases.

The authors declare that there is no conflict of interests regarding the publication of this paper.