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Heat and fluid flow from a wavy surface subjected to a variable heat flux

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Summary

The study of heat transfer along a wavy surface with a prescribed heat flux proportional to (1+x 2)m (wherem is constant) is investigated. The governing equations are first cast into a non-dimensional form by using suitable boundary layer variables that substract out the effects of the wavy surface from the boundary conditions. The boundary layer equations are then solved numerically by the implicit finite difference method. The numerical results are presented for various values of exponentm, amplitudea and Prandtl number Pr. It was found that for amplitudea=0.2 a point of separation appears atx=2.8 that makes the solution restricted at this amplitude. In addition the wavelength of the local Nusselt number and surface temperature variation was equal to the wavy surface. The wavelength of the average Nuselt number was half of the wavy surface.

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Abbreviations

a :

Amplitude of the wavy surface

h (x) :

Heat transfer coefficient

h (x) av :

Average heat transfer coefficient

K :

Wave number=2π/L

k :

Thermal conductivity

L :

Wave length

m :

Wall heat flux exponent

N :

Unit vector normal to the surface

Nu (x) :

Local Nusselt number

Nu av (x) :

Average Nusselt number

P :

Pressure

Pr:

Prandtl number

q :

Heat flux

Q :

Integral rate of the heat transfer

Re:

Reynolds number

s :

Distance along the surface, measured from the leading edge

T :

Temperature

u, v :

Velocity components

x, y :

Coordinates

ν:

Kinematic viscosity

ρ:

Density

σ:

Surface geometry function

θ:

Dimensionless temperature

α:

Thermal diffusivity

av :

Average value

w :

Wall surface

∞:

Free stream

x :

Derivative with respect tox

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Author notes

  1. B. Tashtoush & E. Abu-Irshaid

    Present address: Mechanical Engineering Department, Just, P.O. Box 3030, Irdib, Jordan

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    1. B. Tashtoush
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    2. E. Abu-Irshaid
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    Superscript Dimensional quantity

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    Tashtoush, B., Abu-Irshaid, E. Heat and fluid flow from a wavy surface subjected to a variable heat flux. Acta Mechanica 152, 1–8 (2001). https://doi.org/10.1007/BF01176941

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    • DOI: https://doi.org/10.1007/BF01176941

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