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Mixed convection boundary layer flow over a horizontal plate with thermal radiation

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Abstract

The effects of thermal radiation and thermal buoyancy on the steady, laminar boundary layer flow over a horizontal plate is investigated. The plate temperature is assumed to be inversely proportional to the square root of the distance from the leading edge. The set of similarity equations is solved numerically, and the solutions are given for some values of the radiation and buoyancy parameters for Prandtl number unity. It is found that dual solutions exist for negative values of the buoyancy parameter, up to certain critical values. Beyond these values, the solution does no longer exist. Moreover, it is found that there is no local heat transfer at the surface except in the singular point at the leading edge. The radiation parameter is found to increase the local Stanton number.

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Abbreviations

c :

Constant

C f :

Skin friction coefficient

c p :

Specific heat at constant pressure

f :

Dimensionless stream function

g :

Acceleration due to gravity

Gr x :

Local Grashof number

k :

Thermal conductivity

k*:

Mean absorption coefficient

Nu x :

Local Nusselt number

Pr :

Prandtl number

q r :

Radiative heat flux

q w :

Heat flux

Q w :

Total heat flux

Re x :

Local Reynolds number

St x :

Local Stanton number

T :

Fluid temperature

T w :

Plate temperature

T ∞ :

Ambient temperature

u, v :

Velocity components along the x and y directions, respectively

U ∞ :

Free stream velocity

x, y :

Cartesian coordinates along the plate and normal to it, respectively

α :

Thermal diffusivity

β :

Thermal expansion coefficient

η :

Similarity variable

θ :

Dimensionless temperature

λ :

Buoyancy or mixed convection parameter

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Fluid density

σ * :

Stefan-Boltzmann constant

τ w :

Wall shear stress

ψ :

Stream function

w :

At the wall

∞:

In the free stream

′:

Differentiation with respect to η

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Acknowledgments

The author is indebted to the referees for their valuable comments and suggestions, which led to the improvement of the paper. The financial support received in the form of a research grant (Science Fund: 06-01-02-SF0610) from Ministry of Science, Technology and Innovation (MOSTI), Malaysia is gratefully acknowledged.

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Authors and Affiliations

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

    Anuar Ishak

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  1. Anuar Ishak
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Correspondence to Anuar Ishak.

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Ishak, A. Mixed convection boundary layer flow over a horizontal plate with thermal radiation. Heat Mass Transfer 46, 147–151 (2009). https://doi.org/10.1007/s00231-009-0552-3

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  • DOI: https://doi.org/10.1007/s00231-009-0552-3

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