effect of hall current on heat and mass transfer of free … · 2016-11-14 · attia [2] studied...

Nonlinear Analysis and Differential Equations, Vol. 4, 2016, no. 14, 645 - 658

HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/nade.2016.6972

Effect of Hall Current on Heat and Mass Transfer of Free

Convective Flow over a Flat Porous Plate Embedded in

Porous Medium – A Numerical Investigation

K. Sumathi1, T. Arunachalam2 and R. Kavitha3

1Department of Mathematics

P.S.G.R Krishnammal College for Women, Coimbatore - 641 004, India


Kumaraguru College of Technology, Coimbatore - 641 049, India


P.S.G.R. Krishnammal College for Women, Coimbatore - 641004, India

Copyright © 2016 K. Sumathi, T. Arunachalam and R. Kavitha. This article is distributed under the Creative

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium,

provided the original work is properly cited.

Abstract

An analysis of the effect of Hall current on free convective MHD flow along with heat and mass

transfer over a flat porous plate embedded in porous medium has been carried out numerically.

The governing non-linear partial differential equations together with the boundary conditions are

reduced to a system of non-linear ordinary differential equations by using similarity

transformations. The system of non-linear ordinary differential equations is solved by shooting

procedure using fourth order Runge-Kutta Method. The effects of permeability, magnetic

parameter, Schmidt number, Soret number and Hall parameter over velocity, temperature and

concentration profiles, Skin friction, rate of heat and mass transfer at the plate are discussed in

detail.

Keywords: Hall current, MHD, Porous medium, Steady flow, Skin friction, Nusselt number,

Sherwood number

646 K. Sumathi, T. Arunachalam and R. Kavitha

1. Introduction

In recent years, the study of heat and mass transfer of free convective MHD flows plays a

vital role in many engineering fields due to its applications in various areas such as heat

exchanger, petroleum reservoirs, chemical catalytic reactors and processes, geothermal and

geophysical engineering, aerodynamic engineering and others. In Fluid dynamics, Hall current

attains widespread interest due to its applications in many geophysical and astrophysical

situations as well as in engineering problems such as Hall accelerators, Hall effect sensors,

constructions of turbines and centrifugal machines. MHD flows with Hall current effect are

encountered in power generators, MHD accelerators, refrigeration coils, electrical transformers

and in flight magnetohydrodynamics.

The study of magneto hydrodynamic flows, heat and mass transfer with Hall currents has an

important bearing in engineering applications. Study of effects of Hall currents on flows have

been done by many researchers. Anjalidevi et al. [1] employed nonlinear hydromagnetic flow

with radiation and heat source over a stretching surface with prescribed heat and mass flux

embedded in a porous medium. Crane [3] studied steady boundary layer flow caused by a

stretching sheet whose velocity varies linearly with the distance from a fixed point in the sheet.

Hall effects on hydromagnetic flow were studied by Pop [7]. Gupta et al [4] studied heat and

Mass Transfer on a stretching sheet with suction or blowing. Shampa Ghosh [9] studied magneto

hydrodynamic boundary layer flow over a stretching sheet with chemical reaction. Katagiri [6]

investigated the effect of Hall current on the steady boundary layer flow in the presence of a

transverse magnetic field. Hossain et al. [5] studied the effect of Hall current on the unsteady

free convection flow of a viscous incompressible and electrically conducting fluid, in presence of

foreign gases (such as H2 , CO2 , H2O, NH3 ), along an infinite vertical porous flat plate in the

presence of a uniform transverse magnetic field. Soundalgekar [8] studied the effect of Hall

current in MHD Couette flow with heat transfer. Attia [2] studied Hall current effects on the

velocity and temperature fields on an unsteady Hartmann flow using perturbation techniques.

The absence of Hall current in Shampa Ghosh [9] motivated us to take up the present work

wherein we study the effect of Hall current on mass transfer in a steady free-convective flow in

the presence of a uniform transverse magnetic field in porous medium. The governing equations

are transformed by a similarity transformation into a system of non-linear ordinary differential

equations which are solved numerically by fourth order Runge-Kutta Method. Numerical

calculations are performed for various values of the magnetic parameter, Hall current parameter,

Schimdt number and Soret number. The results are given for the coefficients of skin-friction, rate

of heat transfer and rate of mass transfer for various values of magnetic and Hall current

parameters.

Effect of Hall current on heat and mass… 647

2. Mathematical Model

We consider the steady free-convective flow of an incompressible viscous electrically

conducting fluid over a porous flat plate in the presence of transverse magnetic field and Hall

current embedded in porous medium. We introduce a stationary frame of reference (𝑥, 𝑦, 𝑧)

such that x-axis is taken along the direction of motion, y-axis is normal to the surface and z-axis is

normal to the xy-plane. A uniform magnetic field 𝐵 is imposed along y-axis and the effect of Hall

current is taken into account. The temperature and the concentration are maintained at a prescribed

constant values 𝑇𝑤, 𝐶𝑤 at the plate and 𝑇∞ ,𝐶∞ are the fixed values far away from the plate.

Taking Hall effects into account the generalized Ohm’s law taken in the following form,

𝐽 =𝜎

1 + 𝑚2(𝐸 + 𝑉 × 𝐵 −

1

𝑒𝑛𝑒𝐽 × 𝐵)

in which 𝑉, 𝐸, 𝐵, 𝐽, 𝑚 = 𝜎𝐵0

𝑒𝑛𝑒, 𝜎, 𝑒 and 𝑛𝑒 represent the velocity vector, intensity vector of the

electric field, magnetic vector, electric current density vector, Hall parameter, electrical

conductivity, charge of the electron and number density of the electron. The effect of Hall current

gives rise to a force in the z-direction which in turn produces a cross flow velocity in this direction.

Due to the above assumptions, the free-convection flow along with heat and mass transfer

and generalized Ohm’s law with Hall current effect are governed by the following system of

equations:

𝜕𝑢

𝜕𝑥+

𝜕𝑣

𝜕𝑦= 0 (1)

𝑢𝜕𝑢

𝜕𝑥+ 𝑣

𝜕𝑢

𝜕𝑦= 𝜈

𝜕2𝑢

𝜕𝑦2+ 𝑔𝛽(𝑇 − 𝑇∞) + 𝑔𝛽∗(𝐶 − 𝐶∞) −

𝜎𝐵02

𝜌(1+𝑚2)(𝑢 + 𝑚𝑤) −

𝜈

𝑘𝑢

(2)

𝑢𝜕𝑤

𝜕𝑥+ 𝑣

𝜕𝑤

𝜕𝑦= 𝜈

𝜕2𝑤

𝜕𝑦2 +𝜎𝐵0

2

𝜌(1+𝑚2)(𝑚𝑢 − 𝑤) −

𝜈

𝑘𝑤 (3)

𝑢𝜕𝑇

𝜕𝑥+ 𝑣

𝜕𝑇

𝜕𝑦=

𝜅

𝜌𝐶𝑝

𝜕2𝑇

𝜕𝑦2 (4)

𝑢𝜕𝐶

𝜕𝑥+ 𝑣

𝜕𝐶

𝜕𝑦= 𝐷𝑀

𝜕2𝐶

𝜕𝑦2+ 𝐷𝑇

𝜕2𝑇

𝜕𝑦2 (5)


In the above system of equations, (𝑢, 𝑣, 𝑤) are the velocity components along the (𝑥, 𝑦, 𝑧)

directions respectively, 𝑔 is the acceleration due to gravity, 𝛽 is the coefficient of thermal

expansion, 𝛽∗ is the coefficient of expansion with concentration, 𝑇, 𝐶, 𝜇, 𝜌, 𝜎 and 𝜈 =

(𝜇 𝜌) ⁄ represent respectively the temperature, mass concentration, coefficient of viscosity,

density, electrical conductivity and kinematic viscosity of the fluid. The constant parameters in

the system are: 𝑘 the permeability of porous material, 𝐶𝑝 the specific heat at constant pressure,

𝜅 the thermal conductivity of the fluid, 𝐷𝑀 is the molecular diffusivity and 𝐷𝑇 is the thermal

diffusivity.

The appropriate boundary conditions for the velocity, temperature and mass concentration are

given by,

𝑢 = 𝑏𝑥, 𝑣 = 0, 𝑤 = 0 at y=0; 𝑢 = 𝑤 = 0 as 𝑦 → ∞, (6)

𝑇 = 𝑇𝑤 at 𝑦 = 0; 𝑇 → 𝑇∞ as 𝑦 → ∞ , (7)

𝐶 = 𝐶𝑤 at 𝑦 = 0; 𝐶 → 𝐶∞ as 𝑦 → ∞ , (8)

where b > 0 being stretching rate of the sheet.

3. Solution of the Problem

In this work similarity technique is employed to solve the system of equations (1)-(5) along

with the boundary conditions (6)-(8). The similarity transformations are,

𝑢 = 𝑏𝑥𝑓′(𝜂), 𝑣 = −√𝑏𝜈𝑓(𝜂), 𝑤 = 𝑏𝑥𝑔(𝜂), 𝜂 = √𝑏

𝜈 𝑦,

𝜃(𝜂) =𝑇−𝑇∞

𝑇𝑤−𝑇∞, 𝜙(𝜂) =

𝐶−𝐶∞

(𝐶𝑤−𝐶∞)

} (9)

Introducing the above transformations in equations (1)-(5), we obtain the system of ordinary

differential equations,

𝑓′′′ + 𝑓𝑓′′ − 𝑓′2 + 𝐺𝑟𝜃 + 𝐺𝑐𝜙 −𝑀

1+𝑚2 (𝑓′ + 𝑚𝑔) − 𝑘∗𝑓′ = 0, (10)

𝑔′′ + 𝑓𝑔′ − (𝑓′ +𝑀

1+𝑚2+ 𝑘∗) 𝑔 +

𝑀𝑚

1+𝑚2𝑓′ = 0, (11)

𝜃′′ + 𝑃𝑟𝑓𝜃′ = 0, (12)

𝜙′′ + 𝑆𝑐𝑓𝜙′ + 𝑆𝑐𝑆𝑟𝜃′′ = 0. (13)


where 𝑀 = 𝜎𝐵0

2

𝜌𝑏 is the magnetic parameter, 𝐺𝑟 =

𝑔𝛽(𝑇𝑤−𝑇∞)

𝑏2𝑥 is the Local Grashof number, 𝐺𝑐 =

𝑔𝛽∗(𝐶𝑤−𝐶∞)

𝑏2𝑥 is the local modified Grashof number, 𝑚 =

𝜎𝐵0

𝑒𝑛𝑒 is the Hall current parameter, 𝑃𝑟 =

𝜇𝐶𝑝 𝜅⁄ is the Prandtl number, 𝑆𝑐 =𝜈

𝐷𝑚 is the Schmidt number, 𝑆𝑟 =

(𝑇𝑤−𝑇∞)𝐷𝑇

(𝐶𝑤−𝐶∞)𝜈 is the Soret

number, 𝑘∗ = 1 𝐷𝑎𝑥𝑅𝑒𝑥⁄ is the permeability of porous medium, 𝐷𝑎𝑥 = 𝑘 𝑎2 = 𝑘0 𝑥⁄⁄ is the

local Darcy number. Here 𝑘0 is the constant, 𝑅𝑒𝑥 = 𝑏𝑥2

𝜈 is the Reynolds number

The boundary conditions (6)-(8) transform to the following form,

𝑓(𝜂) = 0, 𝑓′(𝜂) = 1 at 𝜂 = 0; 𝑓′(𝜂) → 0 as 𝜂 → ∞ (14)

𝑔(𝜂) = 0 at 𝜂 = 0; 𝑔(𝜂) → 0 as 𝜂 → ∞ (15)

𝜃(𝜂) = 1 at 𝜂 = 0; 𝜃(𝜂) → 0 as 𝜂 → ∞ (16)

𝜙(𝜂) = 1 at 𝜂 = 0; 𝜙(𝜂) → 0 as 𝜂 → ∞ (17)

The nonlinear coupled ordinary differential equations (10)-(13) subject to boundary conditions

(14)-(17) are solved numerically using shooting method with fourth order Runge-Kutta Method.

𝑓′ = 𝑤, 𝑤′ = 𝑣, 𝜃 = 𝑦, 𝜃′ = 𝑧, 𝜙 = 𝑏, 𝜙′ = 𝑒 , 𝑔 = 𝑖, 𝑔′ = 𝑎.

𝑣′ = −𝑓𝑣 + 𝑤2 − 𝐺𝑟𝑦−𝐺𝑐𝑏 +𝑀

1+𝑚2(𝑤 + 𝑚𝑖) + 𝑘∗𝑤, (18)

𝑎′ = −𝑓𝑎 + (𝑤 +𝑀

1+𝑚2+ 𝑘∗) 𝑖 −

𝑀𝑚

1+𝑚2𝑤 (19)

𝑧 ′ = −𝑃𝑟𝑓𝑧, (20)

𝑒 ′ = −𝑆𝑐𝑓𝑒 − 𝑆𝑐𝑆𝑟𝑧′ (21)

and boundary conditions become,

𝑓(0) = 0, 𝑤(0) = 1, 𝑖(0) = 0, 𝑦(0) = 1, 𝑏(0) = 1 (22)

To solve Equations(18),(19), (20) and (21) with Equation(22) as an IVP the initial guess values for

𝑓 ′′(0), 𝑔′(0), 𝜃 ′(0) and 𝜙′(0) are chosen arbitrarily and applying the fourth order Runge-Kutta

method the solutions are obtained. We compare the calculated values of 𝑓′(𝜂), 𝑔(𝜂), 𝜃(𝜂) and

𝜙(𝜂) at large values of 𝜂 with the boundary conditions 𝑓′(𝜂∞) = 0, 𝑔(𝜂∞) = 0, 𝜃(𝜂∞) = 0

and 𝜙(𝜂∞) = 0 and interpolate/extrapolate the initial values accordingly. The step size is taken


as h = 0.1. The process is repeated until we obtain the correct results upto the desired accuracy

of 10−6 level.

4. Parameters of Engineering Interest

The major physical quantities of engineering interest are the skin-friction coefficient 𝐶𝑓 ,

the local Nusselt number 𝑁𝑢𝑥, and the local Sherwood number 𝑆ℎ𝑥 are defined respectively as

follows,

Skin-friction Co-efficient:

𝐶𝑓𝑥 = 𝜏𝑥

𝜇𝑏𝑥√𝑏

𝜈

, Here Shear stress along x-direction

𝐶𝑓𝑧 = 𝜏𝑧

𝜇𝑏𝑥√𝑏

𝜈

, Here Shear stress along z-direction (23)

Local Nusselt Number: 𝑁𝑢𝑥 =𝑞𝑤

𝑘√𝑏

𝜈(𝑇𝑤−𝑇∞)

(24)

Local Sherwood Number: 𝑆ℎ𝑥 = 𝑚𝑤

𝐷√𝑏

𝜈(𝐶𝑤−𝐶∞)

(25)

where 𝜏𝑥 and 𝜏𝑧is the skin-friction along x and z- direction respectively, 𝑞𝑤 is the heat flux

and 𝑚𝑤 is the mass flux at the surface.

𝜏𝑥 = 𝜇 (𝜕𝑢

𝜕𝑦)

𝑦=0= 𝜇𝑏𝑥√

𝑏

𝜈 𝑓′′(0)

𝜏𝑧 = 𝜇 (𝜕𝑤

𝜕𝑦)

𝑦=0= 𝜇𝑏𝑥√

𝑏

𝜈 𝑔′(0) (26)

𝑞𝑤 = −𝑘 (𝜕𝑇

𝜕𝑦)

𝑦=0= −𝑘√

𝑏

𝜈 (𝑇𝑤 − 𝑇∞)𝜃′(0) (27)

𝑚𝑤 = −𝐷 (𝜕𝐶

𝜕𝑦)

𝑦=0= −𝐷√

𝑏

𝜈 (𝐶𝑤 − 𝐶∞)𝜙′(0) (28)

Substituting equations (26),(27) and (28) into the equations (23),(24) and (25), we get

𝑓′′(0) = 𝐶𝑓𝑥

𝑔′(0) = 𝐶𝑓𝑧

−𝜃′(0) = 𝑁𝑢𝑥

−𝜙′(0) = 𝑆ℎ𝑥


5. Results and Discussion

The numerical computations are performed for several values of dimensionless parameters

involved in the equations i.e., magnetic parameter M, Hall current parameter m, Schmidt number

𝑆𝑐, Soret number 𝑆𝑟. In order to examine the computed results and understanding the bahaviour

of various physical parameters of the flow, some graphs are plotted. The results of the

hydrodynamic characteristics are represented by the velocity, heat transfer, concentration and

mass transfer contours.

Figs. 1-3 show the velocity profiles 𝑓 ′(𝜂), 𝑓(𝜂) and 𝑔(𝜂) corresponding to the axial

velocity, transverse velocity and the cross flow velocity i.e. velocity along z-direction for various

values of the magnetic parameter M. These figures indicate that the velocity decreases with the

increase in the magnetic parameter M. Lorentz force opposes the flow and leads to deceleration of

the fluid motion. The cross flow velocity is found to decrease with the increasing magnetic

parameter. Figs. 4 and 5 illustrate that the temperature and concentration increases with the

increase of magnetic parameter 𝑀.

From Fig. 6 and 7 it is evident that velocity increases with the increase in the Hall current

parameter 𝑚. Fig. 8 shows that for a particular or fixed value of 𝑚, 𝑔(𝜂) attains a maximum

value at a certain height 𝜂 and cross flow velocity 𝑔(𝜂 ) decreases gradually in asymptotic

nature.

Fig. 9 and 10 explain about the temperature (𝜂) and concentration profiles 𝜙(𝜂) for

various values of Hall Current parameter 𝑚. These two graphs illustrate that the temperature and

concentration decreases with the increase in Hall Current parameter 𝑚.

Figs. 11-18 depict that the velocity components and concentration profiles decrease with

increase in the Schmidt number 𝑆𝑐 while Soret number has an adverse effect on these profiles i.e,

increase in Soret number increase the velocity components and concentration profiles.

Figs. 19 – 22 we can infer that skin-friction increases due to increase of Hall current

parameter 𝑚, and decreases with increasing magnetic parameter M. The rate of heat transfer

𝜃′(0) and the rate of mass transfer 𝜙′(0) decreases, with increase in Hall current parameter 𝑚

while increase in the magnetic parameter increases the heat and mass flux.


Fig. 1 Axial velocity of 𝑓′(𝜂) for various

values of magnetic parameter 𝑀.

Fig. 2 Transverse velocity of 𝑓(𝜂) for

various values of magnetic parameter 𝑀.

Fig. 3 Cross flow velocity of 𝑔(𝜂) for


Fig. 4 Temperature profiles of (𝜂) for


-0,2

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6

f'(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,m=1.0

M = 0.0, 0.5, 1.0, 2.0

0

0,5

1

1,5

0 0,5 1 1,5 2 2,5 3 3,5 4

f(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,m=1.0

M = 0.0, 0.5, 1.0, 2.0

0

0,04

0,08

0,12

0,16

0 0,5 1 1,5 2 2,5 3 3,5

g(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,m=1.0

M = 0.0

M = 0.5, 1.0, 2.0

0

0,5

1

1,5

0 0,5 1 1,5 2 2,5 3 3,5 4

(

)

Pr=7.0,Sc=0.5,Sr=0.5,Gr=0.5, Gc=0.5,k*=0.2,m=1.0

M = 0.0, 0.5, 1.0, 2.0


Fig. 5 Concentration profiles 𝜙(𝜂) for

various values of magnetic parameter 𝑀


values of Hall Current parameter 𝑚.


various values of Hall Current parameter 𝑚.


various values of Hall Current 𝑚.

0

0,5

1

1,5

0 0,5 1 1,5 2 2,5 3 3,5 4

(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,m=1.0

M = 0.0, 0.5, 1.0, 2.0

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6f'

()

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=1.0

m = 0.0, 1.0, 2.0, 3.0, 5.0

0

0,5

1

1,5

0 2 4 6

f(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=1.0

m = 0.0, 1.0, 2.0, 3.0, 5.0

0

0,05

0,1

0 2 4 6

g(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=1.0

m = 0.0

m = 1.0, 2.0, 3.0, 5.0


Fig. 9 Temperature profiles of (𝜂) for

various values of Hall Current parameter 𝑚.


various values Hall Current parameter 𝑚.


values of 𝑆𝑐.


various values of 𝑆𝑐.

0

0,5

1

1,5

0 2 4 6

(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=1.0

m = 0.0, 1.0, 2.0, 3.0, 5.0

-0,5

0

0,5

1

1,5

0 2 4 6

(

)

Pr=7.0, Sc=0.5,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=1.0

m = 0.0, 1.0, 2.0, 3.0, 5.0

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6

f''(

)

Pr=7.0,Sr=0.5,Gr=0.5,Gc=0.5, k*=0.2,M=2.0, m=1.0

Sc = 0.0, 0.1, 0.3, 0.5, 1.0, 1.5

0

0,2

0,4

0,6

0,8

1

0 2 4 6

f(

)

Pr=7.0,Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=2.0, m=1.0

Sc = 0.0, 0.1, 0.3, 0.5, 1.0, 1.5







values of 𝑆𝑟.


various values of 𝑆𝑟.





-0,03

0

0,03

0,06

0,09

0,12

0,15

0 2 4 6

g(

)

Pr=7.0, Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=2.0, m=1.0

Sc = 0.0, 0.1, 0.3, 0.5, 1.0

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6

(

)

Pr=7.0, Sr=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=2.0, m=1.0

Sc = 0.0, 0.1, 0.3, 0.5

-0,2

0,3

0,8

1,3

0 2 4 6

f'(

)

Pr=7.0, Sc=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=2.0, m=1.0

Sr= 0.0, 0.1, 0.3, 0.5, 1.0, 1.5

0

0,5

1

1,5

0 2 4 6

f(

)

Pr=7.0,Sc=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=2.0, m=1.0

Sr= 0.0, 0.1, 0.3, 0.5, 1.0, 1.5

0

0,05

0,1

0,15

0 2 4 6

g(

)

Pr=7.0, Sc=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=2.0, m=1.0

Sr= 0.0, 0.1, 0.3, 0.5, 1.0, 1.5

-0,2

0

0,2

0,4

0,6

0,8

1

1,2

0 2 4 6

(

)

Pr=7.0, Sc=0.5,Gr=0.5,Gc=0.5,k*=0.2,M=2.0, m=1.0

Sr= 0.0, 0.1, 0.3, 0.5


Fig. 19 Skin-friction coefficient 𝑓′′(0)

against magnetic parameter 𝑀 for various

values of Hall current parameter 𝑚.

Fig. 20 Shear stress in z-direction 𝑔′(0)

against magnetic parameter 𝑀 for various

values of Hall current parameter 𝑚.

Fig. 21 Rate of heat transfer at the plate

𝜃′(0) against magnetic parameter 𝑀 for

various values of Hall current parameter 𝑚.

Fig. 22 Rate of mass transfer at the plate

𝜙′(0) against magnetic parameter 𝑀 for

various values of Hall current parameter 𝑚.

Conclusion

In the present study we have investigated the effect of Hall current on free-convective flow

along with heat and mass transfer of a viscous, incompressible and electrically conducting fluid

over a flat porous plate. The non-linear governing equations together with the boundary

conditions are reduced to a system of non-linear ordinary differential equations by using

similarity transformations. The system of non-linear ordinary differential equations is solved

with shooting procedure using fourth order Runge-Kutta Method.

From the present study, we have concluded that all the instantaneous flow characteristics

are affected by the Hall current parameter 𝑚. The velocity profiles 𝑓′, 𝑓, 𝑔 decrease with increase in

-1,5

-1

-0,5

0

0 1 2 3

f''(

0)

MPr=7.0, Sc=0.5,Sr=0.5, Gr=0.5,

Gc=0.5,k*=0.2

m= 0.0, 1.0, 2.0, 3.0

0

0,1

0,2

0,3

0,4

0,5

0 1 2 3

g'(0

)

M

Pr=7.0, Sc=0.5,Sr=0.5, Gr=0.5, Gc=0.5, k*=0.2

m= 1.0, 2.0, 3.0

m= 0.0

-2

-1,95

-1,9

-1,85

-1,8

-1,75

0 1 2 3

'(

0)

M

Pr=7.0, Sc=0.5,Sr=0.5, Gr=0.5, Gc=0.5,k*=0.2

m= 0.0, 1.0, 2.0, 3.0 -0,08

-0,06

-0,04

-0,02

0

0 1 2 3

'(

0)

M

Pr=7.0, Sc=0.5,Sr=0.5, Gr=0.5, Gc=0.5,k*=0.2

m=0.0, 1.0, 2.0, 3.0


M, while the temperature and concentration profiles increase with the increase in magnetic

parameter M. The velocity profiles 𝑓′, 𝑓 increase with the increase in Hall current 𝑚, in the case

of temperature and concentration a reversal trend is observed.

Velocity components and concentration profiles decrease with increase in the Schmidt

number 𝑆𝑐. Increase in Soret number increase the velocity components and concentration

profiles.

Skin-friction increases due to increase of Hall current parameter 𝑚, and decreases with

increasing magnetic parameter M. The rate of heat transfer 𝜃′(0) and the rate of mass transfer

𝜙′(0) decreases, with increase in Hall current parameter 𝑚 while increase in the magnetic

parameter increases the heat and mass flux.

References

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source over a stretching surface with prescribed heat and mass flux embedded in a porous

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https://doi.org/10.1007/bf01587695

[4] P.S Gupta and A.S Gupta, Heat and Mass Transfer on a stretching sheet with suction or

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https://doi.org/10.1002/cjce.5450550619

[5] M. A. Hossain, R. I. M. A. Rashid, Hall effects on hydromagnetic free convection flow along a

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https://doi.org/10.1143/jpsj.56.97

[6] M. Katagiri, The effect Hall currents on the viscous flow magnetohydrodynamic boundary

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Acta Mech., 20 (1974), 315-318. https://doi.org/10.1007/bf01175933

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https://doi.org/10.1139/cjp-76-9-739

https://doi.org/10.1007/bf01587695

https://doi.org/10.1002/cjce.5450550619



https://doi.org/10.1007/bf01175933


https://doi.org/10.1109/tps.1986.4316600

[9] Shampa Ghosh, Magnetohydrodynamic boundary layer flow over a stretching sheet with

chemical reaction, International Journal of Education and Science Research, 2 (2015), 78-83.

Received: September 20, 2016; Published: November 11, 2016

https://doi.org/10.1109/tps.1986.4316600

effect of hall current on heat and mass transfer of free … · 2016-11-14 · attia [2] studied...

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