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.     

On the investigation of heat transfer in the presence of chemical conversions

The simplest boundary problem of unstationary heat-conduction equation, with the source depending on temperature as exp (—E*/T) is investigated in this paper.

The uniform convergence of successive approximations is proved for the corresponding integral equation; the solutions have been calculated in the first approximation at various limit cases. It has been also shown here that in the absence of “sexplosion” the temperature at each point will not exceed at any moment of time the corresponding stationary temperature.     

PARTICLE SHAPE AND DIFFERENTIAL SHRINKAGE OF STEATITE TALC BODIES *

An attempt has been made to correlate the differential shrinkage of fired steatite pieces with the particle shape of the raw talc used in their manufacture. Various talcs of widely varying particle shape were used in making the steatite test pieces. It was found that the more irregular in shape the talc particles, the greater the differential shrinkage. A method is given for assigning arithmetical values to various particle shapes depending on their deviation from sphericity, this arithmetical value being known as specific shape factor. A direct relationship was found to exist between the differential shrinkage of a talc and its specific shape factor. As the talc particles became more irregular in shape, the “specific shape factor” value increased and the differential shrinkage was found to increase. The proper selection of the talc td be used and blends of various talcs were found to be helpful in the control of differential shrinkage.     

Molecular distillation of a hydrogenated cottonseed oil and certain characteristics of the distilled fractions

Summary 1. A hydrogenated cottonseed oil has been molecularly distilled, and the distilled fractions examined. 2. Fractionation of a molecularly distilled oil occurs, as is to be expected, on the basis of variations in molecular weight of the glycerides. The composition of cottonseed oil is such that there is a considerable separation of the glycerides according to their degree of unsaturation. The composition of peanut oil is such that similar separation can only be slight. Soybean oil is in this respect intermediate between cottonseed oil and peanut oil. 3. Molecular distillation of hydrogenated cottonseed oil causes a segregation of tocopherols and related compounds similar to that observed in peanut oil. However, the fractions first distilled from the oil are relatively weak in antioxygenic properties. It appears probable that their lack of effectiveness is due to the presence of unknown substances capable of inhibiting or counteracting the action of tocopherols. However, the presence of substances other than tocopherols, which respond to or interfere with the Emmerie-Engel test is not to be excluded. The tocopherols in the potent fractions are more effective thana-tocopherol, but less effective than γ-tocopherol. This is one of four regional research laboratories operated by the Bureau of Agricultural and Industrial Chemistry, Agricultural Research Administration, U. S. Department of Agriculture.