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Thermal radiation and Hall effects on boundary layer flow past a non-isothermal stretching surface embedded in porous medium with non-uniform heat source/sink and fluid-particle suspension

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Abstract

Theoretical study on hydromagnetic heat transfer in dusty viscous fluid on continuously stretching non-isothermal surface, with linear variation of surface temperature or heat flux has been carried out. Effects of Hall current, Darcy porous medium, thermal radiation and non-uniform heat source/sink are taken into the account. The sheet is considered to be permeable to allow fluid suction or blowing, and stretching with a surface velocity varied according to a linear. Two cases of the temperature boundary conditions were considered at the surface namely, PST and PHF cases. The governing partial differential equations are transferred to a system of non-linear ordinary differential equations by employing suitable similarity transformations and then they are solved numerically. Effects of various pertinent parameters on flow and heat transfer for both phases is analyzed and discussed through graphs in detail. The values of skin friction and Nusselt number for different governing parameters are also tabulated. Comparison of the present results with known numerical results is presented and an excellent agreement is found.

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Abbreviations

A, b, D :

Constants

\(A^{*} ,B^{*}\) :

Parameters of space and temperature dependent heat generation

\(\vec{B}\) :

Magnetic induction vector

B0 :

Magnetic field

\(C_{{f_{x} }} , C_{{f_{z} }}\) :

Local skin friction coefficient along x and z directions

c p :

Specific heat coefficient of fluid (J kg−1 K−1)

c m :

Specific heat coefficient of dust particles (J kg−1 K−1)

e :

Charge of electron

E :

Electric field

Ec :

Eckert number

\(\vec{J}\) :

Current density vector

J x , J y , J z :

Current density components along x, y and z directions

f :

Dimensionless axial velocity of fluid

F :

Dimensionless axial velocity of dust

h :

Dimensionless transverse velocity of fluid phase

H :

Dimensionless transverse velocity of fluid phase

K :

Stokes drag coefficient

\(k^{*}\) :

Permeability of porous medium

k 0 :

Porous parameter

k :

Thermal conductivity (W m−1 k−1)

K + :

Mean absorption coefficient (m−1)

l :

Dust particle mass concentration parameter

\(l^{*}\) :

Characteristic length

m :

Hall parameter

M 2 :

Magnetic parameter

m p :

Mass of dust particle per unit volume

N :

Number density of dust particles

Nu :

Local Nusselt number

Pr :

Prandtl number

p e :

Electronic pressure

\(q^{{{\prime \prime \prime }}}\) :

Space and temperature dependent heat generation/absorption

q w :

Heat flux

q r :

Radiative heat flux (Wm−2)

R :

Thermal radiation parameter

r :

Radius of dust particles

Re x :

Local Reynolds number

S :

Suction/blowing parameter

Sh :

Sherwood number

T :

Fluid phase temperature (K)

u, v, w :

Fluid phase velocity components along x, y and z directions (m s−1)

U w :

Stretching sheet velocity

V w :

Suction/injection velocity

x, y, z :

Coordinates (m)

β v :

Fluid-particle interaction parameter for velocity

β T :

Fluid-particle interaction parameter for temperature

ν :

Kinematic viscosity (m2 s−1)

μ :

Dynamic viscosity (kg m−1 s−1)

σ :

Electrical conductivity of the fluid

\(\sigma^{*}\) :

Stefan–Boltzmann constant (Wm−2 K−4)

θ :

Dimensionless fluid phase temperature (K)

η :

Similarity variable

τ e :

Electron collision time

τ T :

Thermal equilibrium time

τ w :

Surface shear stress

τ v :

Relaxation time of the dust particles

\(\tau_{{w_{x} }}\) :

Surface shear stress in x-direction

\(\tau_{{w_{z} }}\) :

Surface shear stress in z-direction

γ :

Specific heat ratio

ρ :

Density of the fluid (kg m−3)

θ :

Non-dimensional temperature

\(\prime\) :

Derivative with respect to η

p :

Dust phase

w :

Fluid properties at the wall

∞:

Fluid properties at ambient condition

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Acknowledgments

One of the authors (B. J. Gireesha) is thankful to the University Grants Commission, India, for the financial support under the scheme of Raman Fellowship for Post-Doctoral Research for Indian Scholars in USA.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Cleveland State University, Cleveland, OH, 44114, USA

    B. J. Gireesha & Rama Subba Reddy Gorla

  2. Department of Studies and Research in Mathematics, Kuvempu University, Shankaraghatta, Shimoga, 577 451, Karnataka, India

    B. J. Gireesha & B. Mahanthesh

  3. Department of Mathematics, Govt. Science College, Chitradurga, 577 501, Karnataka, India

    P. T. Manjunatha

Authors
  1. B. J. Gireesha
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  2. B. Mahanthesh
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Correspondence to Rama Subba Reddy Gorla.

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Gireesha, B.J., Mahanthesh, B., Gorla, R.S.R. et al. Thermal radiation and Hall effects on boundary layer flow past a non-isothermal stretching surface embedded in porous medium with non-uniform heat source/sink and fluid-particle suspension. Heat Mass Transfer 52, 897–911 (2016). https://doi.org/10.1007/s00231-015-1606-3

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