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This study explores the unsteady hybrid nanofluid (NF) flow consisting of cobalt ferrite (CoFe2O4) and copper (Cu) nano particulates with natural convection flow due to an expanding surface implanted in a porous medium. The Cu and CoFe2O4 nanoparticles (NPs) are added to the base fluid water to synthesize the hybrid NF. The effects of second-order velocity slip condition, chemical reaction, heat absorption/generation, temperature-dependent viscosity, and Darcy Forchheimer are also assessed in the present analysis. An ordinary differential equation system is substituted for the modeled equations of the problem. Further computational processing of the differential equations is performed using the parametric continuation method. A validation and accuracy comparison are performed with the Matlab package BVP4C. Physical constraints are used for presenting and reviewing the outcomes. With the increase in second-order velocity slip condition and unsteady viscosity, the rates of heat and mass transition increase significantly with the variation in Cu and Fe2O4 NPs. The findings suggest that the uses of Cu and Fe2O4 in ordinary fluids might be useful in the aerodynamic extrusion of plastic sheets and extrusion of a polymer sheet from a dye.

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al2O3, and titanium oxide TiO2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number Ec$Ec$, radiation parameter Rd$Rd$, and joule heating parameter Jh${J_h}$. [ABSTRACT FROM AUTHOR]

It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation. Therefore, this article aims to investigate the viscous dissipation (VD) effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane. Based on the Atangana-Baleanu operator, the fractional model is developed from the fractional constitutive equations. VD is responsible for the non-linear behavior in the problem. Upon taking the Laplace and Fourier sine transforms, exact expressions have been obtained for momentum and energy equations. The influence of relative parameters on fluid flow and temperature distribution is shown graphically. As special cases, and for the sake of correctness, the corresponding results for second-grade fluid and Newtonian viscous fluid are also obtained. It is interesting to note that fractional parameter provides more than one line as compared to the classical model. This effect represents the memory effect in the fluid which is not possible to elaborate by the classical model. It is also worth noting that the temperature profile of the generalized Jeffrey fluid rises for higher values of Eckert number which is due to the enthalpy difference of the boundary layer. [ABSTRACT FROM AUTHOR]

Electrically conducted viscoelastic fluids have recently caught the attention of scientists and engineers due to their extensive applications in various sectors of research and engineering. It has great importance in cancer therapy (hyperthermia), magnetic resonance imaging (MRI), medication administration, and magnetic refrigeration (MR). The core objective of the present manuscript is to find the exact solution of the fractional convective flow of Walters’-B fluid. The effects of thermal radiations, magnetic field, electro-osmosis, and diffusion thermo have been considered in the present phenomenon. With the help of relative constitutive equations, the governing equations of the present phenomenon have been modeled in terms of second-order partial differential equations. To obtain the closed-form solution for velocity, temperature, and concentration equation, the Laplace transform technique has been implemented. To check the influences of various inserted parameters on fluid, graphs have been plotted. It is very important to mention that electro-osmotic and Walters’-B fluid parameters decline the profile of velocity. [ABSTRACT FROM AUTHOR]