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Here the Cattaneo–Christov double diffusion model explores the mixed convective flow of third-grade nanoliquid on a stretchable surface with Riga device diverging from the traditional Fourier and Fick’s law. The model incorporates entropy optimization and Soret–Dufour effects, offering a unique perspective on heat and mass transfer phenomena. By employing relevant transformations, the complex partial differential equations are converted into more manageable ordinary differential systems. An optimal analysis method is then applied to solve the resulting nonlinear differential system, shedding light on the intricate interplay of various physical variable. Through the utilization of plots, the study delves into the impact of these physical variable, providing insights into the behavior of the system under different conditions. This comprehensive approach not only enhances our understanding of the underlying mechanisms governing the convective flow of nano-liquids, but also highlights the significance of considering nonclassical models in thermal and mass transport studies. The key finding of this study is that fluid velocity enhances for material parameters due to low viscosity. Temperature and nanoparticle concentration enhance for higher values of Dufour and Soret numbers, respectively. For higher estimations of Reynold number, entropy of the system decreases.

Laminar mixed convection of an Al${}_{\mathrm{\text{2}}}$O${}_{\mathrm{\text{3}}}$/water nanofluid inside a vertical channel is investigated numerically. Single-phase and two-phase Eulerian models are employed to analyze flow and thermal fields of the nanofluid in conjunction with the suitable expressions for the particle viscosity and effective particle thermal conductivity. The results of two-phase Eulerian model are compared with the single-phase model and with the published experimental data. Effects of the solid volume fraction, Reynolds number and Grashof number on the heat transfer performance of the nanofluid are investigated and discussed in detail.

This paper presents a model for two-phase nanofluid-fluid flow and heat transfer. The nonuniform nanoparticles are transported using Buongiorno model by convection, Brownian diffusion and thermophoresis. This is the first attempt to employ Buongiorno model for two-phase nanofluid-fluid flow. The moving interface between the nanofluid and the immiscible fluid is captured using the level-set method. The model is first verified and then demonstrated for coupled flow and heat transfer in (1) a water–alumina nanofluid-filled cavity with a rising silicone oil drop and (2) stratified flow of water–alumina nanofluid, pure water and silicone oil in a channel.

In this paper, we studying the entropy generation in Sakiadis nanofluid flowing along a moving plate subject to magnetic field and a Cattaneo–Christov heat flux model that may predict the effects of thermal relaxation time on the boundary layer flow. The nonlinear transport equations are solved using a spectral quasi-linearization method. An analysis of the convergence of the method is presented, and the importance of various fluid and physical parameters concerning the behavior of the solutions is explored. Numerical analysis of the residual error and convergence properties of the method are also discussed. One of the benefits of the proposed method is that it is computationally fast and gives very accurate results after only a few iterations using very few grid points in the numerical discretization process. It is shown that the method converges fast and gives accurate results. The results show that entropy generation increases with an increase in the Reynolds number. The Bejan number is strongly affected by variations in the magnetic parameter, Brinkman number and temperature difference parameter.

This study presents the boundary layer flow of a second grade fluid in a rotating reference frame. The model equations are solved numerically using the bivariate spectral quasi-linearization method to obtain the fluid properties. We investigate the effects of measurable quantities such as the rate of rotation, thermal diffusivity, energy dissipation, viscoelastic parameter and other material properties of the fluid on the flow. The results show that slow rotation leads to a quick decline in the thicknesses of the momentum, thermal and concentration boundary layers. There is also a region of reverse flow for fluids with high Prandtl number.

This work tackles the phenomenon of motile microorganisms and nanoliquid flow in the esteem of cross-flow (CF) and stream-wise (SW) direction. The analysis exposed to viscous dissipation, Brownian motion, thermal radiation, magnetic function, and thermophoresis impacts is encountered. The mathematical model consists of the partial differential equations (PDEs) switched into nonlinear ordinary differential equations (ODEs) through proper transformations of new variables. The multiple outcomes of the flow problem are achieved through the Lobatto IIIA formula. The features of controlling constraints are sketched for the motile organism, temperature, velocities (CF and SW), and concentration fields. Also, the Sherwood and the Nusselt numbers along with motile density and friction factor are sketched. One imperative numerical outcome of this research is the existence of dual numerical solutions for the nanofluid flow. The upshots indicate that the profiles of microorganisms decelerate due to bio-convection Schmidt and Péclet numbers. The magnetic function decelerates the velocity in the directions of SW and CF in the branch of the first solution and upsurges in the branch of the second solution. The concentration profile uplifts due to $Nt$ in both solutions while the opposite behavior is observed for different values of $Nb$ in both solutions. The temperature uplifts due to magnetic and radiation effects in both solutions.