Chaos, Complexity and Leadership 2012 pp 423-452 | Cite as

# Nonlinear Forced Convective Hydromagnetic Flow of Unsteady Biomagnetic Fluid Over a Wedge with Convective Surface Condition

## Abstract

Nonlinear forced convective hydromagnetic flow of an unsteady biomagnetic fluid over a wedge with convective surface has been analyzed numerically. The highly nonlinear coupled governing equations for the momentum, energy, angular momentum for the blood corpuscles and the magnetic induction are reduced to ordinary differential similarity equations by the introduction of a new similarity transformation. These equations are solved using very robust computer algebra software Maple 13. The effects of the various material parameters on the flow, temperature and microrotation fields are investigated. The results show that unsteadiness significantly controls the flow and heat transfer characteristics of the biomagnetic fluid. Strong unsteadiness may trigger back flow even for an accelerated flow. Due to the strong magnetic effect blood corpuscles may oscillate along the surface of the wedge. Induced magnetic field reduces fluid velocity and gives rise to its temperature significantly, which suggests that in the modeling of biomagnetic fluid the effect of induced magnetic field should be taken into account.

## Keywords

Nusselt Number Boundary Layer Thickness Biot Number Skin Friction Coefficient Momentum Thickness## Nomenclature

*Bi*Biot number

*C*_{f}Skin friction coefficient

*c*_{p}Specific heat at constant pressure

*Ec*Eckert number

*f*Dimensionless stream function

*h*Induced magnetic field parameter

*h*_{f}Heat transfer coefficient

*H**Induced magnetic field intensity

*H*Dimensionless

*H***H*_{0}Applied magnetic field intensity

*H*_{w}Induced magnetic field

*j*Micro-inertia per unit mass

*K*Unsteadiness parameter

*M*Magnetic field parameter

*m*Velocity exponent

*N*Dimensionless microrotation

*Nu*Local Nusselt number

*n*Microrotation parameter

*P*Pressure

*Pm*Magnetic Prandtl parameter

*Pr*Prandtl number

*q*_{w}Surface heat flux

*Re*Local Reynolds number

*S*Coefficient of vortex viscosity

*t*Time

*T*Temperature within boundary layer

*T*_{f}Temperature at the bottom

*T*_{w}Temperature at the surface

*T*_{∞}Temperature of the ambient fluid

*u*Velocity along

*x*-axis*U*Free stream velocity

*U*_{0}Characteristic velocity

*U*_{*}Nondim. free stream velocity

*v*Velocity along

*y*-axis*X*Characteristic length

*x*Coordinate along the surface

*y*Coordinate normal to surface

## Greek Symbols

*ρ*Density of the fluid

*β*Wedge angle parameter

*δ*Length scale

*μ*Dynamic viscosity

*μ*_{e}Magnetic permeability

*υ*Kinematic viscosity

*υ*_{s}Spin-gradient viscosity

- Δ
Vortex viscosity parameter

*ξ*Micro-inertia parameter

*ω*Microrotation

*σ*Fluid electric conductivity

*ψ*Stream function

*κ*Thermal conductivity

*η*Similarity parameter

*τ*_{w}Shear stress

*λ*Nondim boundary layer thickness

*λ*_{1}Dimensionless displacement thickness

*λ*_{2}Dimensionless momentum thickness

*θ*Dimensionless temperature

- Δ
*η* Step size

## Subscripts

*w*Surface condition

*∞*Boundary layer edge

## Notes

### Acknowledgment

M.M. Rahman would like to thank the Sultan Qaboos University for financial support through the research grant IG/SCI/DOMAS/10/02. M.A. Sattar expresses his sincere gratitude to Sultan Qaboos University for proving local hospitality during his visit.

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