An analysis is performed to study the influence of local thermal non-equilibrium (LTNE) on unsteady MHD laminar boundary layer flow of viscous, incompressible fluid over a vertical stretching plate embedded in a sparsely packed porous medium in the presence of heat generation/absorption. The flow in the porous medium is governed by Brinkman-Forchheimer extended Darcy model. A uniform heat source or sink is presented in the solid phase. By applying similarity analysis, the governing partial differential equations are transformed into a set of time dependent non-linear coupled ordinary differential equations and they are solved numerically by Runge-Kutta Fehlberg method along with shooting technique. The obtained results are displayed graphically to illustrate the influence of different physical parameters on the velocity, temperature profile and heat transfer rate for both fluid and solid phases. Moreover, the numerical results obtained in this study are compared with the existing literature in the case of LTE and found that they are in good agreement.

The paper is devoted to a study of steady hydromagnetic fluid flow with heat and mass transfer over an inclined nonlinear shrinking porous sheet in the presence of thermophoresis and heat generation. The problem is formulated as a non-linear boundary value problem. A numerical method is developed to solve the problem. The surface velocity of the shrinking sheet and the applied transverse magnetic field are considered as power functions of the distance from the origin. The viscosity and thermal conductivity of the fluid are considered temperature-dependent. The viscosity is taken to be an inverse function of temperature, while the thermal conductivity is supposed to vary linearly with temperature. By using suitable transformation, the equations governing the flow, temperature and concentration fields are reduced to a system of coupled non-linear ordinary differential equations, which are solved numerically by developing an appropriate numerical method. Velocity, temperature and concentration profiles as well as the skin-friction coefficient and wall heat transfer are studied with particular emphasis. Their variations with different parameters are investigated. The computed numerical results are presented graphically.

This work models and analyses the dynamics of a general spring-mass-damper system that is in frictional contact with its support, taking into account frictional heat generation and a reactive obstacle. Friction, heat generation and contact are modelled with subdifferentials of, possibly non-convex, potential functions. The model consists of a non-linear system of first-order differential inclusions for the position, velocity and temperature of the mass. The existence of a global solution is established and additional assumptions yield its uniqueness. Nine examples of conditions arising in applications, for which the analysis results are valid, are presented.