Blasius flow and heat transfer of fourth-grade fluid with slip

This investigation deals with the effects of slip, magnetic field, and non- Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness.

Thermal Analysis of MHD Non-Newtonian Nanofluids over a Porous Media

In the present research,Tiwari and Das model are used for the impact of a magnetic field on non-Newtonian nanofluid flow in the presence of injection and suction.The PDEs are converted into ordinary differential equations(ODEs)using the similarity method.The obtained ordinary differential equations are solved numerically using shooting method along with RK-4.Part of the present study uses nanoparticles(NPs)like TiO_(2) andAl_(2)O_(3) and sodium carboxymethyl cellulose(CMC/water)is considered as a base fluid(BF).This study is conducted to find the influence of nanoparticles,Prandtl number,and magnetic field on velocity and temperature profile,however,the Nusselt number and coefficient of skin friction parameters are also presented in detail with the variation of nanoparticles and parameters.The obtained results of the present study are presented usingMATLAB.In addition to these,some simulations of partial differential equations are also shown using software for graphing surface plots of velocity profile and streamlines along with surface plots and isothermal contours of the temperature profile.

STABILITY OF DENSITY STRATIFIED FLOW IN THE BOUNDARY LAYER

The stability of the laminar flat plate boundary layer is investigated numerically by solving the linear Orr-Sommerfeld equations for the disturbulence amplitude function. These equations include the terms of viscosity, density stratification, and diffusion. Neutral stability curve and the critical Re numbers are computed for various Richardson （Ri） numbers and Schmidt （Sc） numbers. The results show that the larger the Ri, the larger the critical Re for Sc 〈 10. The flow is stable for Ri 〈 0, when Sc is very small or the mass diffusion coefficient is very large. But for Ri 〉 0, the effects of diffusion are reversed for Sc 〈 10. For Sc 〉 10, the critical Re rapidly decreases to zero as the Sc increases for a given Ri number. The critical Re rapidly decreases as the Ri increases.