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On laminar free convection stagnation heat transfer from an isothermal cylinder with internal sources-sinks

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Abstract

An analysis of the laminar free convection stagnation heat transfer from an isothermal horizontal cylinder with internal sources and/or sinks within the fluid is presented. Solutions are given for two cases: one in which only the x-direction momentum equation is used and the other in which the two dimensional Navier-Stokes equations are combined into one momentum equation which makes the heat transfer variable θ′(0) and the velocity and temperature profiles to be determined as explicit functions of the Grashof number. Heat transfer results are obtained for Prandtl number of 0.72. Two temperature dependent heat source functions are investigated. It is found that the consideration of the second momentum equation has a moderate but significant effect on the heat transfer results.

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Abbreviations

a, b, c, d, e :

constants in velocity profile (23)

a′, b′, c′, d′ :

constants in temperature profile (24)

D :

diameter of cylinder

f :

dimensionless stream function (8)

g :

acceleration due to gravity

Gr :

Grashof number, [gβD 3(T w−T∞)/ν 2]

h :

convective heat transfer coefficient, [q″/(T w−T∞)]

k :

thermal conductivity of fluid

Nu :

Nusselt number, [hD/k]

P :

dynamic pressure

Pr :

Prandtl number, [ν/α]

q″:

local heat flux

T :

temperature

u :

tangential velocity component

v :

normal velocity component

x :

coordinate along the wall of the cylinder

y :

coordinate normal to wall of cylinder

α :

thermal diffusivity of fluid

β :

coefficient of thermal expansion of fluid

δ :

boundary layer thickness

ς :

dimensionless second source-sink strength, [λD/α]

ε :

first source-sink strength

η :

dimensionless coordinate (7)

θ :

dimensionless temperature (6)

ρ :

density of fluid

ν :

kinematic viscosity of fluid

ξ :

dimensionless first source-sink strength, [εD 2/α]

ϕ :

angle measured from stagnation point

Ψ :

stream function (8)

∞:

ambient conditions

w:

wall conditions

References

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Authors and Affiliations

  1. Mech. Eng. Dept., Louisiana State University, 70803, Baton Rouge, Louisiana, USA

    O. A. Arnas

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  1. O. A. Arnas
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Arnas, O.A. On laminar free convection stagnation heat transfer from an isothermal cylinder with internal sources-sinks. Appl. Sci. Res. 27, 81–92 (1973). https://doi.org/10.1007/BF00382478

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  • DOI: https://doi.org/10.1007/BF00382478

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