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An algorithm of velocity field evaluation via temperature field measurement on the basic of streamline-defined coordinates

Leble S., Shaban M.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2017

Vol. 21, No 3

247--259

A new algorithm is presented for evaluating the velocity field of the heat convection flow from a vertical solid flat plate using the temperature field. Using the coordinate transformation of Cartesian coordinates, to coordinates defined via streamlines, and visible in such coordinate approximations, it is possible to express the basic flow fields in terms of the temperature gradients only. After discretization we formulate approximated sufficient finite-difference formulas to evaluate the velocity field using the experimental data.

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.

Some free convection flows over a stretching cone embedded in porous media

Mansour M. A., Aly A. M., El-Anssary N. F.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 3

799-812

Laminar free convection from a stretching cone embedded in porous media with the effects of pressure work and chemical reaction is considered. The governing partial differential equations have been transformed by a similarity transformation into a system of ordinary differential equations, which are solved numerically using a fourth order Runge-Kutta scheme with the shooting method. The results are displayed graphically to illustrate the influences of the parameters characterizing the chemical reaction parameter, pressure work parameter and buoyancy ratio on the velocity, temperature and concentration fields for boundary conditions, namely an isothermal surface, a uniform heat surface and a vertical adiabatic surface.