The influence of the flow of the reacting gas on the conditions for a thermal explosion

The classical problem of thermal explosion is modified so that the chemically active gas is not at rest but is flowing in a long cylindrical pipe. Up to a certain section the heat-conducting walls of the pipe are held at low temperature so that the reaction rate is small and there is no heat release; at that section the ambient temperature is increased and an exothermic reaction begins. The question is whether a slow reaction regime will be established or a thermal explosion will occur. The mathematical formulation of the problem is presented. It is shown that when the pipe radius is larger than a critical value, the solution of the new problem exists only up to a certain distance along the axis. The critical radius is determined by conditions in a problem with a uniform axial temperature. The loss of existence is interpreted as a thermal explosion; the critical distance is the safe reactor’s length. Both laminar and developed turbulent flow regimes are considered. In a computational experiment the loss of the existence appears as a divergence of a numerical procedure; numerical calculations reveal asymptotic scaling laws with simple powers for the critical distance.

Evolutionary importance for the membrane enhancement of the production of vitamin D3 in the skin of poikilothermic animals.

The photoproduction of vitamin D in the skin was essential for the evolutionary development of terrestrial vertebrates. During exposure to sunlight, previtamin D3 formed in the skin is isomerized to vitamin D3 (calciol) by a temperature-dependent process. Since early land vertebrates were poikilothermic, the relatively slow conversion of previtamin D3 to vitamin D3 at ambient temperature put them at serious risk for developing vitamin D deficiency, thus leading to a poorly mineralized skeleton that could have ultimately halted further evolutionary development of vertebrates on land. We evaluated the rate of isomerization of previtamin D3 to vitamin D3 in the skin of iguanas and found the isomerization rate was enhanced by 1100% and 1700% at 25 degrees C and 5 degrees C, respectively. It is likely that the membrane entrapment of previtamin D3 in its s-cis,s-cis conformation is responsible for the markedly enhanced conversion of previtamin D3 to vitamin D3. The membrane-enhanced production of vitamin D3 ensures the critical supply of vitamin D3 to poikilothermic animals such as iguanas.