Thermal diffusion and variable thermal conductivity effects on unsteady magnetohydrodynamic (MHD), heat and mass transfer flow past an infinite vertical porous plate have been investigated and analyzed numerically. The resultant flow governing equations are resolved numerically by the finite-difference scheme of the Crank-Nicolson type implicit method. The non-dimensional velocity, fluid temperature, and species concentration distributions are conferred through graphs for different fluid parameters involved such as joule-heating parameter, suction parameter, chemical reaction parameter, radiation parameter, etc. The coefficient of skin friction, Nusselt number and Sherwood number were tabulated. The concentration of the fluid rises with an increase in Soret number, whereas the Sherwood number reduces due to its increase.

In rocket engine nozzle design, flow separation is essential and, given the high temperatures and pressures in the thrust chamber, regenerative cooling is critical for maintaining the nozzle wall's integrity. This passage provides a summary of an in-depth numerical analysis of boundary layer separation and heat transfer within a 30°-15° cooled nozzle. The performance of the SST-V turbulence model under these conditions is assessed numerically. A variety of factors are investigated, including wall temperature, turbulent Prandtl number, and constant specific heat ratios (spanning 1.31 to 1.4 for constant fluid properties of N2O, CH4, Cl2, and air). Furthermore, variable specific heat ratios (from 1.39 to 1.66 for variable fluid properties of air, CH4, O2, and Helium) are examined, along with other parameters that affect the location of separated flow and the local wall heat transfer.

The paper presents the procedure of implicit stress integration for constitutive models for soil and rock. The theoretical basis of Mohr-Coulomb, Matsuoka-Nakai, Hoek-Brown and Hyperbolic soil constitutive models are presented. Stress integration was performed using the theory of incremental plasticity. The general procedure of implicit stress integration of the mentioned constitutive models is shown, as well as the algorithm for their implementation. The presented constitutive models are implemented in the general-purpose program PAK intended for static and dynamic, linear and non-linear analysis of structures. Verification of the implemented algorithms are performed using test examples.