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Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets With Variable Viscosity and Variable Thermal Diffusivity

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Abstract

The paper presents a study of the laminar mixed convection adjacent to vertical continuously stretching sheets, taking into account the effects of variable viscosity and variable thermal diffusivity. The similarity solutions are reported for isothermal sheet moving with a velocity of the form uw=Bx0.5 and a continuous linearly stretching sheet with a linear surface temperature distribution. The equations of conservation of mass, momentum and energy, which govern the flow and heat transfer, are solved numerically by using the shooting method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. The numerical results show that, variable viscosity, variable thermal diffusivity, the velocity exponent parameter, the temperature exponent parameter and the buoyancy force parameter have significant influences on the velocity and temperature profiles, shear stress and Nusselt number in two cases air and water.

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Abbreviations

A, B:

Constants in Eq. 4

C f x :

Local friction coefficient

f, g:

Dimensionless stream function and gravitational acceleration

G*, h:

Buoyancy force parameter and local heat transfer coefficient

k :

Thermal conductivity

m, n:

Velocity exponent parameter and temperature exponent parameter

Nu x , Pr:

Local Nusselt number and Prandtl number

q w , Re x :

Local surface heat flux and local Reynolds number

T :

Temperature

u, v:

velocity components in x and y directions

x, y:

Axial and normal coordinates

α,α o :

Thermal diffusivity and thermal diffusivity at temperature Tw

β:

Thermal expansion coefficient

β1,β2:

Variable viscosity and variable thermal diffusivity parameters

η,θ:

Similarity variable and dimensionless temperature

μ,μ o :

Dynamic viscosity and viscosity at temperature Tw

ν,ρ:

Kinematic viscosity and fluid density

τw, ψ:

Local wall shear stress and stream function

∞, w:

Quantities away from the wall and quantities at the wall

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Acknowledgements

The authors are grateful to the reviewers for their useful comments.

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Authors and Affiliations

  1. College of Science, Mathematics Department, Kingdom of Saudi Arabia, Al-Qasseem University, P.B. 237, Buriedah, 81999, KSA

    M. A. Seddeek

  2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt

    A. M. Salem

  3. Department of Mathematics, Faculty of Science, Helwan University, Cairo, 11785, Egypt

    M. A. Seddeek

Authors
  1. M. A. Seddeek
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  2. A. M. Salem
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Correspondence to M. A. Seddeek.

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Seddeek, M.A., Salem, A.M. Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets With Variable Viscosity and Variable Thermal Diffusivity. Heat Mass Transfer 41, 1048–1055 (2005). https://doi.org/10.1007/s00231-005-0629-6

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  • DOI: https://doi.org/10.1007/s00231-005-0629-6

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