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QUASI STEADY-STATE NATURAL CONVECTIVE HEAT TRANSFER FROM ISOTHERMAL CIRCULAR FLAT SURFACES

DOI: 10.1615/ICHMT.1996.TransientConvHeatTransf.230

Witold M. Lewandowski
Department of Chemical Apparatus and Machniery. Gdansk University of Technology, ul. Narutowicza 11/12, 80-952 Gdansk, Poland

P. Kubski
Technical University of Gdansk, Department of Apparatus and Chemical Machinery, ul.G.Narutowicza 11/12, 80-952 Gdansk, Poland

S. Szymanski
Technical University of Gdansk, Department of Apparatus and Chemical Machinery, ul.G.Narutowicza 11/12, 80-952 Gdansk, Poland

H. Bieszk
Technical University of Gdansk, Department of Apparatus and Chemical Machinery, ul.G.Narutowicza 11/12, 80-952 Gdansk, Poland

T. Wilczewski
Technical University of Gdansk, Department of Apparatus and Chemical Machinery, ul.G.Narutowicza 11/12, 80-952 Gdansk, Poland

T. Seramak
Technical University of Gdansk, Department of Apparatus and Chemical Machinery, ul.G.Narutowicza 11/12, 80-952 Gdansk, Poland

Sinopsis

Theoretical considerations on quasi steady-state convective heat transfer from isothermal circular flat surface have been presented. The physical model of this phenomenon consists of an isothermal cone of inclination angle (φ) by the cone base of the diameter (D). The angle is a parameter of circular surface which varied from (φ = 0 - circular horizontal plate) to (φ = π/2 - vertical cylinder). The temperature of the surface is constant (Tw = const) in the contrary the temperature of ambient fluid which is changing according to relation (T* = T + a sin τ). On the base of Navier-Stokes equations, assuming the parabolic temperature profile in the boundary layer, the velocity profile tangent to the surface has been calculated. Introduction of the mean velocity value in the boundary layer into the balance of energy and mass equations and comparison with the Newton equation leads to the dependence describing the boundary layer thickness. Next the relation of Nusselt and Rayleigh numbers, including a function expressing the influence of the inclination angle (Φ) on the heat transfer process has been derived. Obtained solution describes the natural convective heat transfer process for three characteristic cases of the circular flat surface:
For the boundary cases φ = π/2 (vertical cylinder) and φ = 0 (circular horizontal plate) the solution describing convective heat transfer intensity is:
NuR = 0,669 · RaR1/4 · Θ1/4 for φ = π/2 and NuR = 0,932 · RaR1/5 · Θ1/5 for φ = 0,
For the case (0 < φ < π/2) (cones) the solution has the form:
NuR = 1.680 · Φ1/4 · RaR1/4 · Θ1/4
where (Φ) is a function of the inclination angle (φ) of the generating line of the rotational surface to the base of radius (R) and (Θ) is a coefficient of the temperature fluctuation.

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