Mixing and chemical reaction in an initially non-uniform temperature field

The development of the velocity, temperature and the concentration profiles in the vicinity of the trailing edge is investigated under the boundary layer approximation for an arbitrary initial temperature profile and an arbitrary value of the parameter B for the chemical kinetics.

A series solution is constructed in terms of a system of “universal functions”, from which the initial development of an arbitrary initial temperature profile can be calculated with or without chemical reaction. The first three terms in the series for the temperature have been tabulated previously and are presented here in a diagram.

In the case of no chemical reaction, the analytical results for a given initial temperature distribution predict that the temperature gradient normal to the dividing stream line tends to increase for a limited distance in the downstream direction. This may not be anticipated from the consideration of thermal diffusion alone. Experimental results confirm this qualitative trend. With the three terms in the series solution for the temperature, the agreement between the analytical and the experimental results appears also quite satisfactory.

The analytical results will enable us to calculate the development of the temperature field with chemical reaction. There are as yet no experimental data for comparison.