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2 TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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Novel analytic-numerical model of free convection: with leading edge considered

Leble S., Lewandowski W. M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2014

Vol. 18, No 2

167--185

A novel solution of the free convection boundary problem is represent ed in analytical form for velocity and temperature for an isothermal vertical plate, as an examp le. These fields are built as a Taylor Series in the x coordinate with coefficients as functions of the vertical coordinate ( y ). We restrict ourselves by cubic approximation for both functions. T he basic Navier-Stokes and Fourier-Kirchhoff equations and boundary conditions give links between coefficients and connected with free convection heat transfer phenomen on which define the analytical form of the solution as a function of the Grashof number only. In t he solution the non zero velocity of a fluid flow through a leading edge of the plate is take n into account. The solution in the form of velocity and temperature profiles is numerically evaluated and illustrated for air.

Analytic-numerical model of a convective boundary layer and heat transfer on a horizontal cone

Leble S., Pelc W.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2009

Vol. 13, No 1-2

133-144

An approximate analytical solution of a two dimensional problem for stationary Navier-Stokes, continuity and Fourier-Kirchhoff equations describing a free convective heat transfer from an isothermal cone is presented. The problem formulation is based on assumptions typical for natural convection: non-compressibility and the Boussinesq approximation. The solution is based on Frobenius expansions at the vicinities of two points: the initial point and the singular point of the boundary layer equation. Numerical matching of the expansions and Nusselt number evaluations are traced.