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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.

Two layered immiscible time-dependent flow in the presence of a magnetic field through a curved corrugated channel has been numerically studied. The flow is driven through a pulsatile pressure gradient and is mathematically formulated using a curvilinear coordinate system. The channel is characterized by sinusoidal corrugations that exhibit periodic behavior. The channel is divided into two regions: Region-I and Region-II. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using perturbation analysis and then solved using R-K $${4^{th}}$$4th-order method in conjunction with the shooting technique. The effects of various arising parameters on the flow variables have been investigated. A substantial effect of the magnetic field on flow has been observed when compared to the hydrodynamic case of liquid flow in a curved corrugated channel. Flow enhancement is observed for small corrugation wavenumbers, with maximum augmentation occurring for totally out-of-phase alignment. Notably, stress decreases as the value of the frequency parameter increases, whereas it increases with an elevation in Hartmann number at the outer wall of the channel. Interestingly, the opposite trend is observed for these parameters in relation to shear stress on the lower wall of the channel. [ABSTRACT FROM AUTHOR]

AbstractThis study presents a mathematical model for layered non-miscible liquid flow in an inclined channel subject to a pulsatile pressure gradient. The Casson hybrid nanofluid (hnf) is sandwiched between the layers of Newtonian ternary hybrid nanofluid (t-hnf) and nanofluid (nf). Additionally, the impact of temperature-dependent viscosity is taken into consideration. Multiwall carbon nanotubes, molybdenum disulfide, and silver are considered nanoparticles, with water and kerosene oil as base fluids. The governing partial differential equations are transformed into coupled non-linear ordinary differential equations (ODEs) using the perturbation technique. The resulting ODEs are solved numerically using MATHEMATICA software with the help of the shooting technique associated with the Runge-Kutta fourth-order scheme. The behaviors of numerous sundry parameters against velocity, temperature, concentration, and shear stress are depicted graphically and in tabular form. The outcomes of the study reveal that if the viscosity is held constant, then the fluid’s velocity is initially low and gradually increases as the viscosity variation parameter rises. The velocity of fluid flow is higher when a Newtonian fluid occupies the middle region of the channel than when Casson fluid does. The increase in the nanoparticle shape factor, at both boundaries, results in an increase in the rate of heat transfer. [ABSTRACT FROM AUTHOR]

This investigation aims to examine the hydromagnetic flow of two liquid flows of fully developed incompressible Newtonian fluid in an inclined channel through the porous medium accounting for radiative heat flux, Joule heating, and viscous dissipation. The walls of the channel are maintained at different temperatures. A double perturbation method is employed to derive analytical results for velocity and temperature. Graphical results are presented for various arising parameters such as Hartmann number, Grashoff number, ratio of viscosity parameter, thermal conductivity ratio, and porous parameter. Further, the results for mass flux are presented in a tabular form and discussed. Reduction in the velocity and temperature distribution is observed by enhancing Darcy dissipation and frequency parameter. As the angle of inclination increases, there is a rise in flow and heat distribution. With the strength of the magnetic field and the rise in the Reynolds number, the mass flux decreases. A comparative study is carried out with the previously published work and the results are found to be in good agreement. [ABSTRACT FROM AUTHOR]

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]

In the present study, the hydromagnetic pulsating flow of Casson fluid between two parallel plates in a porous space, thermal radiation and chemical reaction are investigated. The analytical solutions for flow variables are obtained by using a perturbation technique. The effects of pertinent parameters on velocity, temperature, concentration, Nusselt number and Sherwood number distributions are studied in detail. [ABSTRACT FROM AUTHOR]