Finite element investigation of Dufour and Soret impacts on MHD rotating flow of Oldroyd-B nanofluid over a stretching sheet with double diffusion Cattaneo Christov heat flux model

Nanofluids have better surface stability, thermal absorption, and distribution capacities are produced as heat transfer fluids. In current nanofluid-transport studies, together with the heat transfer mechanisms, entropy reduction in thermo- and non-Newtonian nanofluid models with changing thermophysical characteristics is heavily addressed. The entropy production is examined as thermodynamically stable first-grade viscoelastic nanofluid (FGVNF) flow over a flat penetrable, porous barrier. The uniform porous horizontal stretching of the surface in a Darcy type of pore media results in a fluid motion disturbance. In addition, this study also includes the effects of thermal radiation, viscous dissipation, and slip conditions at the border. Under boundary layer flow and Rosseland approximations, the governing mathematical equations defining the physical features of the FGVNF flow and heat transfer models are summarized. The governing nonlinear partial differential equation is transformed by similarity variables to achieve solutions in nonlinear ordinary differential equations. Approximative solutions for reduced ordinary differential equations are obtained by the Keller Box Scheme. Two distinct types of nanofluids, Copper-Engine Oil (Cu-EO) and Zirconium Dioxide-Engine Oil (ZrO2-EO), are considered in this research. The graphs are produced to examine the effects of the different physical factors for the speed, temperature, and entropy distributions. The significant findings of this study are that the critical characteristics of (boundary layer) BL collectively promote temperature variation, including slip speed, diverse thermal conductivity, and non-Newtonian first-grade viscoelastic nanofluid, the concentration of nanoparticles as well as thermal radiation, and a high porous media. The other noteworthy observation of this study demonstrates that the (Cu-EO) FGVNF is a better conductor than (ZrO2-EO) FGVNF transmission. The entropy of the system grows the Deborah number and volume fraction parameter.

Entropy Optimization of First-Grade Viscoelastic Nanofluid Flow over a Stretching Sheet by Using Classical Keller-Box Scheme

Here, a study for MHD (magnetohydrodynamic) impacts on the rotating flow of Casson Carreau nanofluids is considered. The temperature distribution is associated with thermophoresis, Brownian motion, and heat source. The diffusion of chemically reactive specie is investigated with Arrhenius activation energy. The governing equations in the 3D form are changed into dimensionless two-dimensional form with the implementation of suitable scaling transformations. The Variational finite element procedure is harnessed and coded in Matlab script to obtain the numerical solution of the coupled non-linear partial differential problem. The variation patterns of Sherwood number, Nusselt number, skin friction coefficients, velocities, concentration, and temperature functions are computed to reveal the physical nature of this examination. It is seen that higher contributions of the magnetic force, Casson fluid, and rotational fluid parameters cause a raise in the temperature like thermophoresis and Brownian motion does but also causes a slowing down in the primary as well as secondary velocities. The FEM solutions show an excellent correlation with published results. The current study has significant applications in the biomedical, modern technologies of aerospace systems, and relevance to energy systems.

Finite Element Study of Magnetohydrodynamics (MHD) and Activation Energy in Darcy–Forchheimer Rotating Flow of Casson Carreau Nanofluid

In this article, a Riga plate is exhibited with an electric magnetization actuator consisting of permanent magnets and electrodes assembled alternatively. This exhibition produces electromagnetic hydrodynamic phenomena over a fluid flow. A new study model is formed with the Sutterby nanofluid flow through the Riga plate, which is crucial to the structure of several industrial and entering advancements, including thermal nuclear reactors, flow metres and nuclear reactor design. This article addresses the entropy analysis of Sutterby nanofluid flow over the Riga plate. The Cattaneo–Christov heat and mass flux were used to examine the behaviour of heat and mass relaxation time. The bioconvective motile microorganisms and nanoparticles are taken into consideration. The system of equations for the current flow problems is converted from a highly non-linear partial system to an ordinary system through an appropriate transformation. The effect of the obtained variables on velocity, temperature, concentration and motile microorganism distributions are elaborated through the plots in detail. Further, the velocity distribution is enhanced for a greater Deborah number value and it is reduced for a higher Reynolds number for the two cases of pseudoplastic and dilatant flows. Microorganism distribution decreases with the increased magnitude of Peclet number, Bioconvection Lewis number and microorganism concentration difference number. Two types of graphical outputs are presented for the Sutterby fluid parameter (β = −2.5, β = 2.5). Finally, the validation of the present model is achieved with the previously available literature.

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Entropy Analysis of Sutterby Nanofluid Flow over a Riga Sheet with Gyrotactic Microorganisms and Cattaneo–Christov Double Diffusion

The finite element analysis on the transient magnetohydrodynamic three-dimensional rotating flow of Maxwell and tangent hyperbolic nanofluid flow past a bidirectional stretching sheet with Cattaneo Christov heat flux model has been explored numerically. The thermophoresis and Brownian motion effects are taken into account in the flow governing boundary layer equations. Appropriate similarity transformations are applied for the principal PDEs to transform into nonlinear ODEs. A widely recognized Numerical scheme known as the Finite Element Method is employed to solve the resultant convective boundary layer balances. The portrayal of certain physical parameters on the flow model is portrayed via figures and numerical tables. The temperature and concentration distribution for tangent hyperbolic nanofluid is prominently than that of Maxwell nanofluid, but inverse trend is observed for velocities profiles. An outstanding comparison with existing literature ensures a remarkable accuracy and concludes the rate of convergence is extraordinary for nonlinear differential systems. These examinations are relevant to the field of plastic films, crystal growing, paper production, and cooling of metal sheets.

Finite element analysis on transient MHD 3D rotating flow of Maxwell and tangent hyperbolic nanofluid past a bidirectional stretching sheet with Cattaneo Christov heat flux model

The principal aim of this paper is to analyse the two-dimensional magnetohydrodynamic flow and heat and mass transfer phenomena of water-based nanofluid containing gyrotactic microorganisms over a vertical plate by means of heat generation or absorption. Set of nonlinear ordinary differential equations are derived from the governing partial differential equations of the two-dimensional flow of MHD nanofluid and nanoparticles by utilizing appropriate similarity transformations. The numerical results are obtained with the proposed novel spectral relaxation method. The results revealed that in the heat and mass transfer, the motile microorganism flux rates as well as the velocity profiles are decreased throughout the fluid medium with the impact of magnetic field strength. Moreover, the drag stress rate and motile microorganism profiles are increased with the enhancement of magnetic field. Even though the problem of nanofluid has been broadly investigated, limited discoveries can be found through a gyrotactic microorganisms. Indeed, this paper managed to obtain the numerical analysis is performed. Furthermore, the authors also considered the MHD phenomena, heat generation or absorption effects. Very few studies in the fluid with gyrotactic microorganisms embedded in this parameter in their problems.

Internal heat generation on bioconvection of an MHD nanofluid flow due to gyrotactic microorganisms

MHD rotating flow of a Maxwell fluid with Arrhenius activation energy and non‐Fourier heat flux model

Entropy generation on convectively heated surface of casson fluid with viscous dissipation

The present examination is considered to discuss the steady, two-dimensional flow of heat and mass transfer of nanofluid flow along with the variable suction under the influence of heat source/sink alongside the viscous dissipation. Because of the stretchable surface, flow is generated. Spectral relaxation technique is used to acquire the numerical solution for the altered nonlinear group of differential equations. Thereafter, outcomes which were obtained from the above numerical technique are validated by comparing with the available outcomes in the existing literature and also with MATLAB inbuilt solver bvp4c. All the acquired results from the above numerical system are shown through graphs and tables to discuss different resulting parameters related to the present analysis. The range of the physical parameters is taken as $$- \;0.1 \le f_{w} \le 0.5, \;0.1 \le Nt \le 0.7, \;0.1 \le Nb \le 0.7, \;0 \le Ec \le 1.2, \; - 0.5 \le Q \le 0.5, 1 \le Pr \le 10,\; 1 \le Le \le 5.$$
 The main findings are as follows: For the effect of suction parameter, the profiles of velocity, temperature and mass friction are decreased, and the coefficient of skin friction and Nusselt number is declined for the impact of thermophoresis parameter.

A Spectral Relaxation Approach for Boundary Layer Flow of Nanofluid Past an Exponentially Stretching Surface with Variable Suction in the Presence of Heat Source/Sink with Viscous Dissipation

Gangadhar Kotha

Papers

Internal heat generation on bioconvection of an MHD nanofluid flow due to gyrotactic microorganisms

MHD rotating flow of a Maxwell fluid with Arrhenius activation energy and non‐Fourier heat flux model

Entropy generation on convectively heated surface of casson fluid with viscous dissipation

A Spectral Relaxation Approach for Boundary Layer Flow of Nanofluid Past an Exponentially Stretching Surface with Variable Suction in the Presence of Heat Source/Sink with Viscous Dissipation

Newtonian heating effect on laminar flow of Casson fluids: Thermal analysis