Thermal and mass diffusion on MHD natural convective flow of a rarefied gas along vertical porous plate

The flow of an electrically conducting incompressible rarefied gas due to the combined buoyancy effects of thermal and mass diffusion past an infinite vertical porous plate with constant suction has been studied in the presence of uniform transverse magnetic field. The problem has been solved for velocity, temperature, and concentration fields. It has been observed that mean velocity and the mean temperature are affected by the Grashof numbersG ₁ andG ₂, the slip parameterh ₁, temperature jump coefficienth ₂, concentration jump coefficienth ₃ and magnetic field parameterM. The amplitude and the phase of skin-friction and the rate of heat transfer are affected by frequency in addition to the above parameters. They are shown graphically. The numerical values of the mean skin-friction and the mean rate of heat transfer are also tabulated.

x′, y′ :

coordinate system

u′,v′ :

velocities inx′, y′-directions

B ₀ :

external magnetic field

|B|:

amplitude of skin-friction

B ₄,B _i :

as defined by Equation (34)

C′ :

species concentration

C′ _p :

specific heat at constant pressure

D :

chemical molecular diffusivity

E :

Eckert number

g :

acceleration due to gravity

G ₁ andG ₂ :

Grashof numbers as defined by Equation (8)

h ₁,h ₂,h ₃ :

velocity slip, temperature and concentration jump coefficients

k′ :

thermal conductivity

L ₁,L ₂,L ₃ :

dimensional velocity slip, temperature and concentration jump coefficients

M :

magnetic field parameter

M _r,M _i :

fluctuating parts of velocity

P _r :

Prandtl number

p′ :

pressure

q :

rate of heat transfer

|Q|:

amplitude of rate of heat transfer

Q _m :

mean rate of heat transfer

Q _r,Q _i :

as defined by Equation (41)

S _c :

Schmidt number

T′ :

temperature

t′ :

time

T _r,T _i :

fluctuating parts of temperature

T _m :

mean shear stress

U′ :

free stream velocity

ω′:

frequency

α:

phase angle of skin-friction

β:

phase angle of rate of heat transfer

β*:

volumetric coefficient of thermal expansion

β**:

volumetric coefficient of expansion with concentration

v :

kinematic viscosity

ϱ′:

density

θ:

non-dimensional temperature

θ*:

non-dimensional concentration

ɛ:

very small quantity (ɛ≪1)

σ:

electrical conductivity

w :

value at the wall

∞:

value away from the wall

Authors and Affiliations

1. School of Applied Sciences, Banaras Hindu University, Varanasi, India

   P. C. Ram & R. Nath

2. Department of Mechanical Engineering Institute of Technology, Banaras Hindu University, Varanasi, India

   A. K. Agrawal

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