Author(s): P. Vasseur; L. Robillard
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Keywords: No Keywords
Abstract: Thermal convection in water near its freezing point is distinct from more common convective systems by the fact that the density of water attains a maximum value at a temperature near 3.98C, thereafter decreasing with decreasing temperature. The effects resulting from this nonlinearity on the free convection flow induced by an isothermal vertical plate adjacent to a mass of cold water are of importance in practical applications as well as in the studies of fundamentals of natural flows. In the present study, a solution to this problem is obtained by solving the partial differential equations describing the conservation of mass, momentum and energy. For large Grashof numbers, it may be shown that the resulting governing equations are of the boundary layer type. Numerical integrations are carried out using the time-dependent form of these equations, successive steps in time being regarded as successive approximations towards the final steady-state solution. With this procedure, it is possible to obtain the transient part as well as the steady state part of the solution for the velocity and temperature fields. The results obtained show that, for the case of water at low temperatures, the nonlinear relationship between density and temperature has an important effect on the velocity and temperature fields. This effect increases while the temperature of the water tends towards 0C. Furthermore, it has been found that for water below 3.98C, the effect of the nonlinearity can be important enough to give rise to a reverse of the velocity profile in the boundary layer. However, for such extreme cases the present theory is not expected, in its present form, to predict accurately such a behaviour.
Year: 1978