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Approximate solutions of heat and momentum transfer in laminar plane wall jet

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Abstract

In the present paper approximate solutions for the fluid and thermal boundary layers in an incompressible laminar plane wall jet with isothermal and adiabatic walls have been studied respectively, and comparisons with the known exact solutions have been made wherever possible. It is found that the present method is simple and straightforward, and gives results being in good agreement with the exact solutions. For moderate values of the Prandtl number the method may be used for calculating the heat transfer from an isothermal wall and temperature recovery factor for an adiabatic wall respectively.

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Abbreviations

a*:

dimensionless temperature gradient at the wall

c p :

specific heat at constant pressure

K :

momentum flux through a cross-section of the jet

Q :

volume flux through a cross-section of the jet

r*:

temperature recovery factor

T :

temperature of the fluid in the boundary layer

T r :

adiabatic wall temperature

T∞ :

temperature of the fluid at rest

u, v :

velocity components along and normal to the plane wall respectively

x, y :

rectangular coordinates along and normal to the plane wall respectively

z :

\( = y\left( {\frac{E}{{v^3 x^3 }}} \right)^{\frac{1}{4}} \)

δ :

fluid boundary layer thickness

δ t, δ T :

thermal boundary layer thickness for an isothermal and an adiabatic wall respectively

η :

dimensionless y-coordinate

θ :

dimensionless temperature difference (T−T ∞)/T ∞

κ :

coefficient of thermal conductivity

μ :

coefficient of viscosity

ν :

coefficient of kinematic viscosity

σ :

Prandtl number

τ w :

shearing stress on the plane wall

References

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  3. Bansal, J. L. and S. S. Tak, The proc. Indian Acad. Sci. 83 A No. 1 (1976) 1.

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Authors and Affiliations

  1. Dept. of Maths., Univ. of Jodhpur, 342001, Jodhpur, India

    J. L. Bansal & S. S. Tak

Authors
  1. J. L. Bansal
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  2. S. S. Tak
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Bansal, J.L., Tak, S.S. Approximate solutions of heat and momentum transfer in laminar plane wall jet. Appl. Sci. Res. 34, 299–311 (1978). https://doi.org/10.1007/BF00418874

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  • DOI: https://doi.org/10.1007/BF00418874

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