Consequences of Soret–Dufour Effects, Thermal Radiation, and Binary Chemical Reaction on Darcy Forchheimer Flow of Nanofluids

Analysis of the Time-Dependent magnetohydrodynamic Newtonian fluid flow over a rotating sphere with thermal radiation and chemical reaction

This article presents the magnetohydrodynamic (MHD) flow of a nanoliquid due to a rotating sphere at a stagnation point. The flow is considered to be influenced by the magnetic field, dissipative, thermally radiative, and chemically reactive. Also, the thermophoretic and Brownian motion influences are taken into consideration. Some restrictions in the present analysis are taken: like there is no-slip and convective conditions, joule heating, Hall effects and buoyancy-driven. The solution of the present analysis is derived through the homotopy analysis method (HAM). The significance of several physical parameters on velocities, thermal and concentration profiles are shown with the help of Figures. Also, the significance of different physical factors on skin frictions, local Nusselt number and Sherwood number are demonstrated with the help of Tables. The outcomes show that the Nusselt number is lower for the larger Brownian motion parameter, Eckert number, and thermophoretic parameter, while the increment in the thermal radiation parameter augmented the Nusselt number. It is established that the increasing rotation, magnetic and positive constant parameters have increased the velocity profiles along the x-direction while reducing the velocity profiles along the z-direction of the nanoliquid flow. The increasing positive constant parameter reduces the thermal graph of the nanoliquid flow. Furthermore, the intensifying Eckert number, thermophoresis, Brownian motion, and thermal radiation factor have escalated the thermal profiles of the nanoliquid flow.

Optimal Homotopic Exploration of Features of Cattaneo-Christov Model in Second Grade Nanofluid Flow via Darcy-Forchheimer Medium Subject to Viscous Dissipation and Thermal Radiation

INTRODUCTION

In this article, Optimal Homotopy Analysis Method (oHAM) is used for the exploration of the features of the Cattaneo-Christov model in viscous and chemically reactive nanofluid flow through a porous medium with stretching velocity at the solid/sheet surface and free stream velocity at the free surface.

METHODS

The two important aspects, Brownian motion and Thermophoresis, are considered. Thermal radiation is also included in the present model. Based on the heat and mass flux, the Cattaneo- Christov model is implemented on the Temperature and Concentration distributions. The governing Partial Differential Equations (PDEs) are converted into Ordinary Differential Equations (ODEs) using similarity transformations. The results are achieved using the optimal homotopy analysis method (oHAM). The optimal convergence and residual errors have been calculated to preserve the validity of the model.

RESULTS

The results are plotted graphically to see the variations in three main profiles. i.e. momentum, temperature and concentration profile.

CONCLUSION

The outcomes indicate that skin friction enhances due to the implementation of the Darcy medium. It is also noted that the relaxation time parameter results in enhancement of the temperature distribution. Thermal radiation enhances the temperature distribution and so is the case with skin friction.

Soret and Dufour influences on forced convection of Cross radiative nanofluid flowing via a thin movable needle

The main feature of the current investigation is to analyze the magnetohydrodynamic mixed convection flow of Cross fluid. Flow is due to a movable thin needle with Soret and Dufour effect. Heat generation/absorption and nonlinear heat radiation are used in the energy equation. Characteristics of the chemical reaction and thermal activation are given special attention. Appropriate variables are introduced for the transformation of partial differential equations to ordinary differential equations. With the assistance of Runge–Kutta Fehlberg's fourth- fifth-order method with the shooting technique, we determined the prominent result numerically. The prominent examined parameters range is velocity and temperature ratios, heat generation, Dufour, Hartmann, Schmidt numbers (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.1\le{{\lambda}},{{{\theta}}}_{{{w}}},{{Q}},{{{D}}}_{{{u}}},\boldsymbol{ }{{M}},{{S}}{{c}}\le 0.7$$\end{document}0.1≤λ,θw,Q,Du,M,Sc≤0.7), needle thickness (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0\le {{a}}\le 15$$\end{document}0≤a≤15), radiative parameter (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5\le {{R}}{{d}}\le 8$$\end{document}5≤Rd≤8), and Weissenberg number (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.01\le {{W}}{{e}}\le 0.09$$\end{document}0.01≤We≤0.09), respectively. Graphs for velocity, thermal, concentration, Skin friction coefficient, and heat and mass transport rates are displayed and analyzed for physical parameters. A similar observation of mixed convection and needle thickness parameter is seen on the velocity field. Temperature and heat transfer rate are reverse behavior in the frame of the Dufour effect. Moreover, an enhancement in chemical reaction shows decay to the concentration field.

Rheology of electromagnetohydrodynamic tangent hyperbolic nanofluid over a stretching riga surface featuring dufour effect and activation energy

The present model deals with the consequence of Dufour, activation energy, and generation of heat on electromagnetohydrodynamic flow of hyperbolic tangent nanofluid via a stretching sheet. This offers a broad significance in several engineering fields. With adequate similarity variables, the regulating governing equations of PDEs are renovated into nonlinear ODEs. The numerical output of the produced ordinary differential equations is conducted with MATLAB bvp4c. The influence of increasing features on temperature, velocity, concentration patterns, drag force coefficient, Sherwood number and Nusselt number is depicted graphically and numerically. Hence, the resultant conclusions are confirmed utilising contrast with earlier output. Interestingly, the activation energy retards the nanofluid's tangential hyperbolic concentration distribution and the rise in temperature of the hyperbolic tangential nanofluid flow is traceable to an increase in the Dufour effect, However, the electromagnetohydrodynamic variable increases the velocity distribution, which influences the Power law index. Conclusively, the rate of heat transfer is inhibited when the thermophoresis parameter, heat source and the Weissenberg number are enhanced.

The Novelty of Thermo-Diffusion and Diffusion-Thermo, Slip, Temperature and Concentration Boundary Conditions on Magneto–Chemically Reactive Fluid Flow Past a Vertical Plate with Radiation

The significance of radiation, Soret and Dufour’s effects on MHD flow in a porous media near a stagnation point past a vertical plate with slip, temperature, and concentration boundary conditions were investigated. Local similarity variables are used in the solution, which reduces the PDEs into analogous boundary value problem for ODEs. Symmetry analysis can be used to detect these variations in local similarity. To numerically explain the problem, a shooting approach and the MATLAB bvp4c solver are utilized. As the magnetic field and porous medium parameters are raised, the skin friction increases, and the temperature increases as the radiation pointer is increased. As the Soret number grows, the concentration profile rises.

Thermal Analysis of 3D Electromagnetic Radiative Nanofluid Flow with Suction/Blowing: Darcy-Forchheimer Scheme

This paper discusses the Darcy-Forchheimer three dimensional (3D) flow of a permeable nanofluid through a convectively heated porous extending surface under the influences of the magnetic field and nonlinear radiation. The higher-order chemical reactions with activation energy and heat source (sink) impacts are considered. We integrate the nanofluid model by using Brownian diffusion and thermophoresis. To convert PDEs (partial differential equations) into non-linear ODEs (ordinary differential equations), an effective, self-similar transformation is used. With the fourth-fifth order Runge-Kutta-Fehlberg (RKF45) approach using the shooting technique, the consequent differential system set is numerically solved. The influence of dimensionless parameters on velocity, temperature, and nanoparticle volume fraction profiles is revealed via graphs. Results of nanofluid flow and heat as well as the convective heat transport coefficient, drag force coefficient, and Nusselt and Sherwood numbers under the impact of the studied parameters are discussed and presented through graphs and tables. Numerical simulations show that the increment in activation energy and the order of the chemical reaction boosts the concentration, and the reverse happens with thermal radiation. Applications of such attractive nanofluids include plastic and rubber sheet production, oil production, metalworking processes such as hot rolling, water in reservoirs, melt spinning as a metal forming technique, elastic polymer substances, heat exchangers, emollient production, paints, catalytic reactors, and glass fiber production.

Heat Transfer and Fluid Flow Analysis for Turbulent Flow in Circular Pipe with Vortex Generator

Abstract

The performance of heat transfer enhancement (HTE) using modified inserts (MIs) as a vortex generator in pipe flow and fluid flow analysis using computational fluid dynamics (CFD) are evaluated in this article. The MIs are fastened to the central rod, and the circular sections of the MIs touched the circular wall of the test pipe. Heat transfer and fluid flow analyses are carried out for the various pitch to diameter ratios (P/D) and angles of the MIs. P/D ratios of 3, 4 and 6 and MIs angles of 15°, 30°, 45°, 60° and 90° are considered for experimental analysis. CFD analysis is carried out for P/D ratios of 3, 4 and 6 and MIs angles of 30°, 45° and 90°. Nusselt number (Nu/Nus) and friction factor (f/fs) ratios are evaluated using the same Reynolds number between 8000 and 17,000 in the experimental study. The MIs encourage the wall and core fluid to be combined thus helps in HTE. It is found that, as the P/D ratio increases, the Nu/Nus and f/fs decrease. If the distance between the MIs increases, the mixing of fluid weakens. With decreasing the P/D ratio, Nu/Nus increases. Increased fluid mixing leads to a higher coefficient of heat transfer and higher values of pressure drop. A P/D ratio of 4 and MIs angle of 45° results in greater heat interaction than others. Finally, recommendations for the best P/D ratio and angles of MIs are made for improved HTE on fluid flow through a circular pipe.

Article Highlights

Numerical Analysis of Thermal Radiative Maxwell Nanofluid Flow Over-Stretching Porous Rotating Disk

The fluid flow over a rotating disk is critically important due to its application in a broad spectrum of industries and engineering and scientific fields. In this article, the traditional swirling flow of Von Karman is optimized for Maxwell fluid over a porous spinning disc with a consistent suction/injection effect. Buongiorno’s model, which incorporates the effect of both thermophoresis and Brownian motion, describes the Maxwell nanofluid nature. The dimensionless system of ordinary differential equations (ODEs) has been diminished from the system of modeled equations through a proper transformation framework. Which is numerically computed with the bvp4c method and for validity purposes, the results are compared with the RK4 technique. The effect of mathematical abstractions on velocity, energy, concentration, and magnetic power is sketched and debated. It is perceived that the mass transmission significantly rises with the thermophoresis parameter, while the velocities in angular and radial directions are reducing with enlarging of the viscosity parameter. Further, the influences of thermal radiation Rd and Brownian motion parameters are particularly more valuable to enhance fluid temperature. The fluid velocity is reduced by the action of suction effects. The suction effect grips the fluid particles towards the pores of the disk, which causes the momentum boundary layer reduction.

Magnetized Flow of Cu + Al2O3 + H2O Hybrid Nanofluid in Porous Medium: Analysis of Duality and Stability

In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of Sc≤S and Mc≤M (Sc>S and Mc>M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised.