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An electrically conducting time-dependent flow of water-based nanofluid comprised of Copper and Titanium oxide over a stationary plate embedding with a porous matrix is analyzed in this study. The novelty arises due to the interaction of both the thermal radiation as well as the radiation absorption that affect the heat transport phenomenon. In the single-phase flow, both the variation of particle concentration and the solutal concentration for the inclusion of chemical reaction are taken care of. Also, the influence of the free convection phenomena is explained significantly. The transformed dimensionless system of the governing equations is handled analytically by using the Laplace Transform method. The behavior of the characterizing parameters involved in the governing equations is presented via graphs and the simulation of the numerical results of the rate coefficients like shear rate and rate of heat and solutal transfer is deployed through the table. However, the physical significance of these parameters is deliberated briefly. Finally, the important outcomes are higher heavier species because of lesser solutal diffusivity which attenuates the fluid concentration throughout the domain. Further, radiation absorption causes a significant boost in the nanofluid temperature distribution.

The combined effects of diffusion-thermo and radiative absorption on free convective hydromagnetic heat-generating chemically reactive flow of Cu-water nanofluid past an instantaneously accelerated unlimited vertical plate nested in a porous medium are investigated. A comparative analysis is executed for both isothermal and ramped conditions. The set of transformed domain equations has been obtained using a closed form of the Laplace transform method with the help of the Heaviside step function. Graphical and tabular explanations are provided for the physical characteristics of several flow parameters affecting the problem. Graphs are generated using MATLAB computing software. Findings of the problem manifest that the diffusion-thermo parameter and the radiation absorption parameter intensify the velocity and fluid temperature in the entire fluid area. This augmentation is most prominent for copper nanoparticles. Concentration, temperature, and velocity profiles in the case of ramped conditions are less than in isothermal conditions. Furthermore, the ramped parameter amplifies the heat transfer rate while reversing the mass transfer rate. It is also established that the volume concentration of nanoparticles enhances the heat transfer rate. The present study is of great interest in numerous fields of industry and machine-building applications.

In this work, we investigate the time-dependent MHD free convection of Casson fluid across a vertical semi-infinite plate fitted inside a permeable medium, along with viscous dissipation, radiation absorption, and Soret effect by using several non-dimensional variables. The characteristics of a variety of elements influencing the flow phenomenon are examined using the Casson fluid model. The governing dimensional partial differential equations are transformed into an ordinary differential equation set by introducing the similarity variables. The reduced model is numerically solved via the Galerkin finite element method. The non-dimensional equations with suitable boundary conditions can be mathematically simplified using the efficient Galerkin finite element approach. The restrictions are shown numerically and graphically, and their effects on temperature, velocity, species concentration, and rate coefficients are all shown. This study is to present the influence of radiation absorption along with viscous dissipation on the heat transfer phenomenon. For different flow parameter estimations, graphs are generated for various flow profiles as well as skin friction coefficients. The Nusselt (Nu) and Sherwood (Sh) quantities are also demonstrated via graphs.

In the food industry, electrical conductivity is essential for heating processes. The dependence on temperature conductivity of electricity on the outermost layers flow of the nanofluid is the main topic of this paper. Variable electrical conductivity, viscosity, thermo diffusion, thermal radiation and radiation absorption on convective heat and mass transfer flow Cuo and Al₂O₃-water nano-fluids confined in cylindrical annulus. The non-linear governing equations have been solved by finite element technique with quadratic approximation functions. For various parametric adjustments, the temperature, speed, and nanoconcentration have all been examined. Similar to the cylindrical wall, quantitative evaluations have been made of the surface resistance, temperature rate and mass transport. It is discovered that for both types of nanofluids, a higher thermo-diffusion effect leads to a lower concentration and Sherwood digits on the cylinders. An augment in Q1 enriches the rapidity in CuO-water nanofluidic system as well as decreases in Al₂O₃-water nanofluidic. Increased Q1 lowers the real temperature and nanoconcentration in both types of nanofluids.