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Abstract Two dimensional wavy walls rectangular cavity with inclined magnetohydrodynamic has been examined in mixed convection configurations. Triple fins arranged in the upwards ladder were filled within alumina nanoliquid in the cavity. Vertical sinusoidal walls were heated, and the other side was kept cold while both horizontal walls were kept adiabatic. All walls were motionless except the top cavity that was driven to the right. The diversified range of control parameter in Richardson number, Hartmann number, number of undulations, length of the cavity has been performed in this study. The analysis was simulated using finite element method by employing the governing equation formula, and the results were delineated in the form of streamlines, isotherms, heatlines, and comparisons on several relationships between the local velocity in the y-axis line of 0.6, local and average Nusselt number along the heated surface and dimensionless average temperature. The findings revealed that high concentration nanofluids boost the rate of heat transfer without the need to apply any magnetic field. Results found that the best heat mechanisms are natural convection with significant-high Richardson number as well as constructing two waves on the vertical walls in the cavity.

This study investigates a fractional-order time derivative model of non-Newtonian magnetic blood flow in the presence of thermal radiation and body acceleration through an inclined artery. The blood flow is formulated using the Casson fluid model under the control of a uniformly distributed magnetic field and an oscillating pressure gradient. Caputo-Fabrizio's fractional derivative mathematical model was used, along with Laplace transform and the finite Hankel transform technique. Analytical expressions were obtained for the velocity of blood flow, magnetic particle distribution, and temperature profile. These distributions are presented graphically using Mathcad software. The results show that the velocity increases with the time, Reynolds number and Casson fluid parameters, and diminishes when Hartmann number increases. Moreover, fractional parameters, radiation values, and metabolic heat source play an essential role in controlling the blood temperature. More precisely, these results are beneficial for the diagnosis and treatment of certain medical issues.

In this paper, we studied the effect of a magnetic field on the non-isothermal second-grade fluid confined in a vertically oscillating cylinder. The flow solution is magnetized using the perpendicular magnetic field. The resultant fluid flow is due to the oscillating boundary motion and buoyancy force. Here, the MHD flow is modeled using the Caputo-Fabrizio non-integer derivative approach. The exact solution of the governing continuity, momentum and energy equations is obtained by means of Laplace and finite Hankel transforms. The commercial simulation software, Mathematica is used for calculating the roots of the Bessel function. The effects of dimensionless parameters such as Grashof and Prandtl numbers, magnetic field and fractional parameters on the second-grade fluid flow are analyzed. Heat transfer is high at a small Prandtl number. Velocity correlates positively with Grashof number and magnetic field, and negatively with Prandtl number. The heat and mass transfer results obtained from both conventional and fractional models are compared as well.

Many viscoelastic fluid problems are solved using the notion of fractional derivative. However, most researchers paid little attention to the effects of nonlinear convective in fluid flow models with time-fractional derivatives and were mainly interested in solving linear problems. Furthermore, the nonlinear fluid models with a fractional derivative for an unsteady state are rare, and these constraints must be overcome. On the other hand, nanofluids are thought to be trustworthy coolants for enhancing the cooling process in an electrical power system. Therefore, this research has been conducted to analyze the unsteady upper-convected Maxwell (UCM) hybrid nanofluid model with a time-fractional derivative. Incorporating the Cattaneo heat flux into the energy equation has increased the uniqueness of the research. The numerical solutions for the coupled partial differential equations describing velocity and temperature are presented using an efficient finite difference method assisted by the Caputo fractional derivative. Significant changes in heat transfer and fluid flow properties due to governing parameters, including the nanomaterial volume fraction, fractional derivative, relaxation time, and viscous dissipation, are graphically demonstrated. The nanomaterial concentration, the fractional derivative parameter, and the relaxation time parameter must all be substantial to manifest a surface heat increase.