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The present study is carried out to investigate the effects of shape factor nanoparticles on the oscillatory MHD flow of a nanofluid in two immiscible liquids in a horizontal porous channel with velocity and thermal slip on the walls. Thermal radiation, Joule heating, viscous and Darcy dissipations have been accounted for in the model. We have considered and as nanoparticles, in the lower region (Region-I) and upper region (Region-II) respectively, with water as a base fluid. The effective ratio of thermal conductivity of the nanofluid is evaluated using the Maxwell-Garnetts model. Graphical behavior of velocity, temperature, and rate of heat transfer distributions have been depicted for the cases of slip and no-slip effects. This study has been made to understand the impact of different nanoparticle shape factors on temperature and heat transfer rate. For various parameters, values of shear stress distribution at the walls and the mass flux are shown in tabular form. Our study asserts that with the increase of the strength of the magnetic field, the velocity of the liquid falls and enhances the temperature of the liquid. The influence of different combinations of nanoparticles, on the flow variables, have also been discussed. In order to validate the analytical results, the numerical evaluation of the closed-form results, for the velocity distribution, has been compared with those of the numerical method, by using the NDSolve command in MATHEMATICA, and a good agreement is observed.

The MHD oscillatory flow of two immiscible, viscous liquids in a porous channel with heat transfer is the subject of this investigation. The two liquid layers with different viscosities flow in both regions. The analytical expressions for velocity and temperature distribution have been derived by solving the governing flow equations using the regular perturbation method. The effects of various parameters on the velocity, temperature, and Nusselt number have been shown graphically, and numerical values of skin friction and flow rate are presented in tabular form and discussed. According to our analysis, the mass flux reduces as the magnetic field strength rises. While the temperature of the liquid enhances with an increase in the Eckert number and the Prandtl number, the temperature distribution rises with a decrease in the thermal conductivity ratio. To validate the results, the analytical solutions are compared with the fourth-order numerical Runge-Kutta method coupled with the shooting approach, and the results are found to be in excellent agreement. [ABSTRACT FROM AUTHOR]