The objective of this study is to present a mathematical modeling and solution approach for the drying process of spheroidal solids with the application of microwave in capillary porous media based on the Luikov equations, composed of a system of linear and coupled partial differential equations arising from the energy, mass and pressure balances inside the solid matrix. Additionally, the power...

Abstract This paper analyzes A.K. Oppenheim’s original works on the transition of deflagration to detonation and reviews them from perspective new numerical experimental results recently obtained such phenomena. Particular attention is focused processes happening in boundary layer tube walls ahead accelerating flame. The theoretical analyses temperature variations inside developing are presente...

A math e mat i cal model rep re sent ing tem per a ture and mois ture con tent in bread dur ing bak ing is de vel oped. The model em ploys the cou pled par tial dif fer en tial equa tions pro posed by Luikov. Dependences of mass and ther mal prop er ties of dough on tem per a ture and mois ture con tent are in cluded in the model. Re sult ing sys tem of non-lin ear par tial dif fer en tial equa...

using the mean-value theorem for integrals we tried to solved the nonlinear integral equations of hammerstein type . the mean approach is to obtain an initial guess with unknown coefficients for unknown function y(x). the procedure of this method is so fast and don't need high cpu and complicated programming. the advantages of this method are that we can applied for those integral equation...

in this article, we study the analytical solutions of different parabolic heat equations with different boundaryconditions in the form of multi-term fractional differential equations. then we compare these analytical solutions with numerical finite difference methods. this comparison demonstrates the accuracy of the analytical and numerical methods presented here.