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A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to

Combined heat and mass transfer in fluid-saturated porous media finds applications in a variety of engineering processes such as heat exchanger devices, petroleum reservoirs, chemical catalytic reactors and processes, and others. A thorough discussion of these and other applications is available in the monographs [

An axisymmetric unsteady natural convection boundary layer flow past a vertical cone with transverse magnetic field applied normal to the surface with variable heat and mass flux in a Darcy-Forchheimer fluid saturated porous medium in a cartesian (

Physical Model.

Here

Then under the previous assumptions, the governing boundary layer equations with Boussinesq’s approximation are

Equation (

The transport (

The corresponding nondimensional initial and boundary conditions are given by

In order to solve the unsteady, nonlinear, coupled (

Only selective figures have been reproduced here for brevity. In the numerical computations, the following values for the dimensionless thermophysical parameters are prescribed: Grashof number (

Comparison of local skin friction values at

Pr | Hossain and Paul [ |
Present |
---|---|---|

0.01 | 5.13457 | 5.13424 |

0.05 | 2.93993 | 2.93180 |

0.1 | 2.29051 | 2.29044 |

Comparison of local Nusselt number values at

Pr | Hossain and Paul [ |
Present |
---|---|---|

0.01 | 0.14633 | 0.14648 |

0.05 | 0.26212 | 0.26227 |

0.1 | 0.33174 | 0.33648 |

In Figures

(a) Steady state velocity profiles at

Figures

(a) Transient velocity profiles at

Transient temperature profiles at

Steady state velocity profiles at

Figure

Steady state concentration profiles at

The effect of surface heat flux power exponent (

Steady state temperature profiles at

Steady state concentration profiles at

Effect of Fs on local Nusselt number at

A slight increase in local Nusselt number accompanies the increment in Pr as shown in Figure

Effect of Pr on local Nusselt number at

Steady state temperature profiles at

Steady state temperature profiles at

Steady state velocity profiles at

Numerical solutions have been presented for the buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a non-Darcian isotropic porous regime. Present results are compared with those of [

Increasing Grashof number boosts the translational velocity in the cone surface regime and decreases temperature throughout the flow regime.

Increasing Darcy number accelerates the flow, that is, increases translational velocities. However, the temperature is reduced with a rise in Darcy number.

An increase in the Forchheimer inertial drag parameter is observed to slightly increase the temperature but reduces both velocity and local Nusselt number.

An increase in Prandtl number is observed to decrease both temperature and velocity, but the concentration is slightly increased. A slight increase in local Nusselt number accompanies the increment in Pr.

The concentration is observed to significantly decrease with an increase in Schmidt number.

The temperature is observed to decrease with an increase in buoyancy ratio parameter but decrease with an increase in semivertical angle of the cone. The time taken to reach the steady state increases with increasing

Coordinates along the cone generator and normal to the generator

Velocity components along the

Gravitational acceleration

Local radius of cone

Time

Dimensionless time

Temperature

Dimensionless temperature

Concentration

Dimensionless concentration

Mass diffusion coefficient

Permeability of porous medium

Heat flux (i.e., heat transfer rate per unit area)

Mass flux (i.e., mass transfer rate per unit area)

Thermal conductivity of fluid

Reference length

Dimensionless coordinates along the cone generator and normal to the generator

Dimensionless velocity components along the

Forchheimer geometrical constant

Darcy number

Forchheimer number

Grashof number

Magnetic parameter

Magnetic field strength

Prandtl number

Buoyancy ratio parameter

Schmidt number

Power-law index for surface heat flux relation

Power-law index for surface mass flux relation

Local Nusselt number

Dimensionless local Nusselt number

Local Sherwood number

Nondimensional local Sherwood number

Dimensionless local radius of cone.

Dynamic viscosity of fluid

Kinematic viscosity of fluid

Semivertical cone angle

Thermal diffusivity

Volumetric thermal expansion coefficient

Dimensionless temperature function

Dimensionless time

Dimensionless local shear stress function (skin friction).

Condition on the wall

Free stream condition.