Heat transfer simulation in stirring boundary layer using the semiempirical turbulence theory

The dynamic and thermal boundary layer equations are derived for the stirring boundary layer using Prandtl semiempirical turbulence theory. Based on definition of the thermal perturbations front and supplementary boundary conditions the method of constructing an exact analytical solution of the boundary value problem simulating the formation of the thermal boundary layer in the dynamic boundary layer is obtained and applied to find the exact analytical solutions of thermal boundary layer differential equation almost with a given degree of accuracy. The velocity distribution in stirring dynamic boundary layer and its thickness were taken by the well — known relations, found from experiments. The supplementary conditions fulfillment is equivalent to the fulfillment of the initial differential equation in the boundary point and in the thermal perturbations front. So, the more supplementary conditions we use the better fulfillment of the initial differential equation in the thermal boundary layer we have, because the range of thermal perturbations front changing includes the whole range of transverse spatial variable changing. Analysis of calculations results allows to conclude that the layer thickness within a stirring dynamic boundary layer more than twice less than thermal layer thickness in a laminar dynamic boundary layer. The study of the received in this paper criteria-based equation shows that the difference of heat transfer coefficients in the range 20000⩽Re⩽30000 of the Reynolds number on the experimental not exceed 7%

On one method for solving transient heat conduction problems with asymmetric boundary conditions

Using additional boundary conditions and additional required function in integral method of heat-transfer we obtain approximate analytical solution of transient heat conduction problem for an infinite plate with asymmetric boundary conditions of the first kind. This solution has a simple form of trigonometric polynomial with coefficients exponentially stabilizing in time. With the increase in the count of terms of a polynomial the obtained solution is approaching the exact solution. The introduction of a time-dependent additional required function, setting in the one (point) of the boundary points, allows to reduce solving of differential equation in partial derivatives to integration of ordinary differential equation. The additional boundary conditions are found in the form that the required solution would implement the additional boundary conditions and that implementation would be equivalent to executing the original differential equation in boundary points. In this article it is noted that the execution of the original equation at the boundaries of the area only (via the implementation of the additional boundary conditions) leads to the execution of the original equation also inside that area. The absence of direct integration of the original equation on the spatial variable allows to apply this method to solving the nonlinear boundary value problems with variable initial conditions and variable physical properties of the environment, etc