Lie symmetry analysis and numerical solutions for thermo-solutal chemicallyreacting radiative micropolar flow from an inclined porous surface

Steady, laminar, incompressible thermo-solutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction effects are included to represent phenomena encountered in high-temperature materials synthesis operations. Rosseland’s diffusion approximation is used to describe the radiative heat flux in the energy equation. A Lie scaling group transformation is implemented to derive a self-similar form of the partial differential conservation equations. The resulting coupled nonlinear boundary value problem is solved with Runge-Kutta fourth order numerical quadrature (shooting technique). Validation of solutions with an optimized Adomian decomposition method algorithm is included. Verification of the accuracy of shooting is also conducted as a particular case of non-reactive micropolar flow from a vertical permeable surface. The evolution of velocity, angular velocity (micro-rotation component), temperature and concentration are examined for a variety of parameters including coupling number, plate inclination angle, suction/injection parameter, radiation-conduction parameter, Biot number and reaction parameter. Numerical results for steady state skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are tabulated and discussed. Interesting features of the hydrodynamic, heat and mass transfer characteristics are examined

Influence of variable viscosity and thermal conductivity, hydrodynamic and thermal slips on magnetohydrodynamic micropolar flow: a numerical study

Thermophysical and wall slip effects arise in many areas of nuclear technology. Motivated by such applications, in this article the collective influence ofvariable viscosity, thermal conductivity, velocity and thermal slipseffects on a steady two-dimensional magnetohydrodynamic microplar fluid over a stretching sheet are analyzednumerically. The governing nonlinear partial differential equations have been converted into a system of non-linear ordinary differential equations using suitable coordinate transformations. The numerical solutions of the problem are expressed in the form of non-dimensional velocityand temperature profiles and discussed from their graphical representations. Nachtsheim-Swigert shooting iteration technique together withthesixth order Runge-Kutta integration scheme has been applied for the numerical solution.A comparison with the existing results has been done and an excellent agreement is found.Further validation with adomian decomposition method is included for the general model. Interesting features in the heat and momentum characteristics are explored. It is found that greater thermal slip and thermal conductivity elevate thermal boundary layer thickness. Increasing Prandtl number enhances Nusselt number at the wall but reduces wall couple stress (micro-rotation gradient). Temperatures are enhanced with both magnetic field and viscosity parameter. Increasing momentum (hydrodynamic) slip is found to accelerate the flow and elevate temperatures

Pulse Propagation in a Non-Linear Medium

This paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suitable for the study of light pulse propagation in a non-linear optical medium