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Unsteady MHD flow over exponentially stretching sheet with slip conditions

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Abstract

The present paper examines the hydromagnetic three-dimensional flow induced by a stretched surface. An incompressible material saturates the porous medium. Velocity and thermal slip boundary conditions are considered. Suitable transformations are used to obtain the nonlinear ordinary differential equations. Series solutions of the resulting systems are constructed. The effects of various pertinent parameters on the axial velocity and temperature distributions are analyzed graphically. The skin friction and the Nusselt number are computed numerically and graphically.

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Abbreviations

u, v, w :

velocity components/(m·s−1)

x, y, z :

direction components

U 0, V 0 :

reference velocities/(m·s−1)

L :

characteristics length/m

g :

acceleration due to

k*:

thermal conductivity /(W·K−1·m−1)

c p :

specific heat/(m2·s−2)

T :

temperature/K

T ∞ :

ambient fluid temperature/K

T w :

surface temperature

T 0 :

reference temperature

U w, V w :

stretching surface velocities

S :

ratio parameter

k :

porous medium permeability

α 1, α 2, α 3 :

velocity and thermal slip factors

A :

unsteadiness parameter

S :

ratio parameter

Pr :

Prandtl number

Ec :

ASDFSDFSDFSDAF

M :

Hartman number

K :

porosity parameter

C fx , C fy :

local skin friction coefficients

q w :

surface heat flux/(W·m−2)

Nu x :

local Nusselt number

Re xy :

local Reynolds number

B 0 :

uniform magnetic field

f 0, g 0 :

initial approximations for velocity

C i (i = 1, 2, · · ·, 8):

constants

q :

embedded parameter

f*, g*:

particular solution for velocity field

σ :

thermal diffusivity/(m2·s−1)

ρ :

density/(kg·m−3)

μ :

viscosity/(kg·m−2·s−1)

θ :

dimensionless temperature

η :

transformed coordinate

γ1, γ2, γ3:

velocity and thermal slip parameters

τ xz , τ yz :

wall shear stresses

L 1, L 2, L 3 :

linear operators for velocity and temperature

R f m , R g m , R θ m :

mth-order nonlinear operators

ħ f , ħ g , ħ θ :

non-zero auxiliary parameters

θ 0 :

initial approximation for temperature

θ*:

particular solution for temperature field

w, f, ∞:

represents conditions at wall, fluid and in free stream, respectively

p :

constant pressure

m :

mth-order derivative with respect to η

′:

prime represents derivative with respect to η

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Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan

    T. Hayat & A. Shafiq

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

  3. Department of Mathematics, Comsats Institute of Information Technology, Sahiwal, 57000, Pakistan

    S. A. Shahzad

Authors
  1. T. Hayat
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  2. A. Shafiq
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  3. A. Alsaedi
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  4. S. A. Shahzad
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Corresponding author

Correspondence to A. Shafiq.

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Hayat, T., Shafiq, A., Alsaedi, A. et al. Unsteady MHD flow over exponentially stretching sheet with slip conditions. Appl. Math. Mech.-Engl. Ed. 37, 193–208 (2016). https://doi.org/10.1007/s10483-016-2024-8

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  • DOI: https://doi.org/10.1007/s10483-016-2024-8

Keywords

Chinese Library Classification

2010 Mathematics Subject Classification

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