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Boundary layer flow and heat transfer over an unsteady stretching vertical surface

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Abstract

The solution to the unsteady mixed convection boundary layer flow and heat transfer problem due to a stretching vertical surface is presented in this paper. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching velocity and the surface temperature. The governing partial differential equations with three independent variables are first transformed into ordinary differential equations, before they are solved numerically by a finite-difference scheme. The effects of the unsteadiness parameter, buoyancy parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. Both assisting and opposing buoyant flows are considered. It is observed that for assisting flow, the solutions exist for all values of buoyancy parameter, whereas for opposing flow, they exist only if the magnitude of the buoyancy parameter is small. Comparison with known results for steady-state flow is excellent.

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Abbreviations

a,b,c:

constants

C f :

skin friction coefficient

f :

dimensionless stream function

g :

acceleration due to gravity (m s−2)

Gr x :

local Grashof number

k :

thermal conductivity (W m−1 K)

Nu x :

local Nusselt number

Pr :

Prandtl number

q w :

local heat flux (W m−2)

Re x :

local Reynolds number

T :

fluid temperature (K)

T w :

surface temperature (K)

T ∞ :

ambient temperature (K)

t :

time (s)

u,v:

velocity components in the x and y directions, respectively (m s−1)

U w :

velocity of the stretching surface (m s−1)

x,y:

Cartesian coordinates along the surface and normal to it, respectively (m)

α :

thermal diffusivity (m2 s−1)

β :

thermal expansion coefficient (K−1)

η :

similarity variable

θ :

dimensionless temperature

λ :

mixed convection or buoyancy parameter

ν :

kinematic viscosity (m2 s−1)

μ :

dynamic viscosity (kg m−1s−1)

ρ :

fluid density (kg m−3)

τ w :

wall shear stress (Pa)

ψ :

stream function (m2 s−1)

w :

condition at the surface

∞:

ambient condition

′:

differentiation with respect to η

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Authors and Affiliations

  1. School of Mathematical Sciences, University Kebangsaan Malaysia, 43600, UKM Bangi, Selangor, Malaysia

    Anuar Ishak & Roslinda Nazar

  2. Faculty of Mathematics, University of Cluj, 3400, Cluj, Romania

    Ioan Pop

Authors
  1. Anuar Ishak
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  2. Roslinda Nazar
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  3. Ioan Pop
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Correspondence to Roslinda Nazar.

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Ishak, A., Nazar, R. & Pop, I. Boundary layer flow and heat transfer over an unsteady stretching vertical surface. Meccanica 44, 369–375 (2009). https://doi.org/10.1007/s11012-008-9176-9

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  • DOI: https://doi.org/10.1007/s11012-008-9176-9

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