Motion Equation and Solution of Mushroom Cloud

Using model like hot air bloom with zero-weighted membrane wrapped hot air, surrounded by cold air, this paper sets up a partial differential equation (PDE) of motion of mushroom cloud by modifying Navier-Stokes (N-S) equations. The obtained equation is a vector PDE. It states that the derivative of velocity is with respect to time proportions to the gradient of temperature with respect to trace. Its solution is obtained by the method of separating variables for scalar function. These results have been compared with well agreement with literatures. Highlight: The Principle of Minimum Energy Release (PMER) is used to prove the pulse-mode of explosion of nuclear weapon, as great Earthquake, and optimum path problems.

Virtual internal thermal work evaluation in the multifield variational statements for the analysis of multilayered structures

The principle of virtual displacements(PVDs)extended to elasto-thermo-electric problems includes virtual internal elastic,thermal and electric works.The governing equations have displacement vector,temperature and electric potential as primary variables of the problem,and the elasto-thermal,elasto-electric and pure elastic problems are obtained as particular cases by deleting the appropriate contributions in the general elasto-thermo-electric variational statement.The most sensitive issue is given by thermal coupling because the thermo-elastic and thermo-electric effects change depending on the type of load and analysis considered(mechanical load,temperature or electric potential imposed and free vibration analysis).This feature means that the form of the virtual internal thermal work in such variational statements changes depending on the analysis performed and the load applied.Results about multilayered plates and shells suggest the appropriate extension of the variational statement for each analysis,and they give an exhaustive explanation for several forms of the PVD proposed.