Search Results (13)

Activation energy can be elaborated as the minimal energy required to start a certain chemical reaction. The concept of this energy was first presented by Arrhenius in the year 1889 and was later used in the oil reservoir industry, emulsion of water, geothermal as well as chemical engineering and food processing. This study relates to the impacts of mass transfer caused by temperature differences (Soret) and heat transport due to concentration gradient (Dufour) in a Carreau model with nanofluids (NFs), mixed convection and a magnetic field past a stretched sheet. Moreover, thermal radiation and activation energy with new mass flux constraints are presumed. All chemical science specifications of nanofluid are measured as constant. As a result of the motion of nanofluid particles, the fluid temperature and concentration are inspected, with some physical description. A system of coupled partial differential frameworks is used mathematically to formulate the physical model. A numerical scheme named the Runge–Kutta (R-K) approach along with the shooting technique are used to solve the obtained equations to a high degree of accuracy. The MATLAB R2022b software is used for the graphical presentation of the solution. The temperature of the nanofluid encompasses a quicker rate within the efficiency of a Dufour number. An intensifying thermal trend is observed for thermophoresis and the Brownian motion parameter. The Soret effect causes a decline in the fluid concentration, and the opposite trend is observed for rising activation energy. In addition, the local Nusselt number increases with the Prandtl number. Further, the comparative outcomes for drag force are established, with satisfying agreement with the existing literature. The results acquired here are anticipated to be applied to improving heat exchanger thermal efficiency to maintain thermal balancing control in compact heat density equipment and devices. Full article

The current study used a novel Casson model to investigate hybrid Al₂O₃-Cu/Ethylene glycol nanofluid flow over a moving thin needle under MHD, Dufour–Soret effects, and thermal radiation. By utilizing the appropriate transformations, the governing partial differential equations are transformed into ordinary differential equations. The transformed ordinary differential equations are solved analytically using HAM. Furthermore, we discuss velocity profiles, temperature profiles, and concentration profiles for various values of governing parameters. Skin friction coefficient increases by upto 45% as the Casson parameter raised upto 20%, and the heat transfer rate also increases with the inclusion of nanoparticles. Additionally, local skin friction, a local Nusselt number, and a local Sherwood number for many parameters are entangled in this article. Full article

The study is devoted to investigating the effect of an unsteady non-Newtonian Casson fluid over a vertical plate. A mathematical analysis is presented for a Casson fluid by taking into consideration Soret and Dufour effects, heat generation, heat radiation, and chemical reaction. The novelty of the problem is the physical interpretation of Casson fluid before and after adding copper water-based nanoparticles to the governing flow. It is found that velocity was decreased and the temperature profile was enhanced. A similarity transformation is used to convert the linked partial differential equations that control flow into non-linear coupled ordinary differential equations. The momentum, energy, and concentration formulations are cracked by means of the finite element method. The thermal and solute layer thickness growth is due to the nanoparticles’ thermo-diffusion. The effects of relevant parameters such as the Casson fluid parameter, radiation, Soret and Dufour effects, chemical reaction, and Prandtl number are discussed. A correlation of the average Nusselt number and Sherwood number corresponding to active parameters is presented. It can be noticed that increasing the Dufour number leads to an uplift in heat transfer. Fluid velocity increases with Grashof number and decreases with magnetic effect. The impact of heat sources and radiation is to increase the thermal conductivity. Concentration decreases with the Schmidt number. Full article

The focal interest in this article is to investigate the Stefan blowing and Dufour and Soret effects on hybrid nanofluid (HNF) flow towards a stretching cylinder with thermal radiation. The governing equations are converted into ODE by using suitable transformations. The boundary value problem solver (bvp4c), which is a package in the MATLAB, is used to solve the resulting ODE equations. Results show that rise in the Stefan blowing enhances velocity, temperature, and concentration profiles. Heat transfer rate increases by up to 10% in the presence of 4% nanoparticle/HNF but mass transfer rate diminishes. Additionally, skin friction coefficient, Nusselt number and Sherwood number are examined for many parameters entangled in this article. Additionally, results are deliberatively discussed in detail. Full article

Here, our main aim is to examine the impacts of Dufour and Soret in a radiative Darcy–Forchheimer flow. Ohmic heating and the dissipative features are outlined. The characteristics of the thermo-diffusion and diffusion-thermo effects are addressed. A binary chemical reaction is deliberated. To examine the thermodynamical system performance, we discuss entropy generation. A non-linear differential system is computed by the finite difference technique. Variations in the velocity, concentration, thermal field and entropy rate for the emerging parameters are scrutinized. A decay in velocity is observed for the Forchheimer number. Higher estimation of the magnetic number has the opposite influence for the velocity and temperature. The velocity, concentration and thermal field have a similar effect on the suction variable. The temperature against the Dufour number is augmented. A decay in the concentration is found against the Soret number. A similar trend holds for the entropy rate through the radiation and diffusion variables. An augmentation in the entropy rate is observed for the diffusion variable. Full article

The rheology of different materials at the micro and macro levels is an area of great interest to many researchers, due to its important physical significance. Past experimental studies have proved the efficiency of the utilization of nanoparticles in different mechanisms for the purpose of boosting the heat transportation rate. The purpose of this study is to investigate heat and mass transport in a pseudo-plastic model past over a stretched porous surface in the presence of the Soret and Dufour effects. The involvement of tri-hybrid nanoparticles was incorporated into the pseudo-plastic model to enhance the heat transfer rate, and the transport problem of thermal energy and solute mechanisms was modelled considering the heat generation/absorption and the chemical reaction. Furthermore, traditional Fourier and Fick’s laws were engaged in the thermal and solute transportation. The physical model was developed upon Cartesian coordinates, and boundary layer theory was utilized in the simplification of the modelled problem, which appears in the form of coupled partial differential equations systems (PDEs). The modelled PDEs were transformed into corresponding ordinary differential equations systems (ODEs) by engaging the appropriate similarity transformation, and the converted ODEs were solved numerically via a Finite Element Procedure (FEP). The obtained solution was plotted against numerous emerging parameters. In addition, a grid independent survey is presented. We recorded that the temperature of the tri-hybrid nanoparticles was significantly higher than the fluid temperature. Augmenting the values of the Dufour number had a similar comportment on the fluid temperature and concentration. The fluid temperature increased against a higher estimation of the heat generation parameter and the Eckert numbers. The impacts of the buoyancy force parameter and the porosity parameter were quite opposite on the fluid velocity. Full article

The effect of rotation and cross-diffusion on convection in a horizontal sparsely packed porous layer in a thermally conducting fluid is studied using linear stability theory. The normal mode method is employed to formulate the eigenvalue problem for the given model. One-term Galerkin weighted residual method solves the eigenvalue problem for free-free boundaries. The eigenvalue problem is solved for rigid-free and rigid-rigid boundaries using the BVP4c routine in MATLAB R2020b. The critical values of the Rayleigh number and corresponding wave number for different prescribed values of other physical parameters are analyzed. It is observed that the Taylor number and Solutal Rayleigh number significantly influence the stability characteristics of the system. In contrast, the Soret parameter, Darcy number, Dufour parameter, and Lewis number destabilize the system. The critical values of wave number for different prescribed values of other physical parameters are also analyzed. It is found that critical wave number does not depend on the Soret parameter, Lewis number, Dufour parameter, and solutal Rayleigh number; hence critical wave number has no impact on the size of convection cells. Further critical wave number acts as an increasing function of Taylor number, so the size of convection cells decreases, and the size of convection cells increases because of Darcy number. Full article

Aluminum nanoparticles are suitable for wiring power grids, such as local power distribution and overhead power transmission lines, because they exhibit high conductivity. These nanoparticles are also among the most utilized materials in electrical field applications. Thus, the present study investigated the impact of magnetic field on 3D crossflow in the streamwise direction with the impacts of Dufour and Soret. In addition, the effects of activation energy and chemical reaction were incorporated. The viscosity and thermal conductivity of nanofluids were premeditated by KKL correlation. Prominent PDEs (Partial Differential Equations) were converted into highly nonlinear ODEs (Ordinary Differential Equations) using the proper similarity technique and then analyzed numerically with the aid of the built-in bvp4c solver in MATLAB. The impact of diverse important variables on temperature and velocity was graphically examined. Additionally, the influences of pertaining parameters on the drag force coefficient, Nusselt number, and Sherwood number were investigated. Inspections revealed that the mass transfer rate decreases, while the heat transport increases with increasing values of the Soret factor. However, the Nusselt and Sherwood numbers validate the differing trend for rising quantities of the Dufour factor. Full article

This article models a system of partial differential equations (PDEs) for the thermal and solute characteristics under gradients (concentration and temperature) in the magnetohydrodynamic flow of Casson liquid in a Darcy porous medium. The modelled problems are highly non-linear with convective boundary conditions. These problems are solved numerically with a finite element approach under a tolerance of ${10}^{-8}.$ A numerical algorithm (finite element approach) is provided and a numerical procedure is discussed. Convergence is also observed via 300 elements. Simulations are run to explore the dynamics of flow and the transport of heat and mass under parametric variation. To examine the impact of a temperature gradient on the transport of mass and the role of a concentration gradient on the transport of heat energy, simulations are recorded. Remarkable changes in temperature and concentration are noted when Dufour and Soret numbers are varied. Full article

The development of the mathematical modeling of Casson fluid flow and heat and mass transfer is presented in this paper. The model is subjected to the following physical parameters: shrinking parameter, mixed convection, concentration buoyancy ratio parameter, Soret number, and Dufour number. This model is also subjected to the inclined magnetic field and shrinking sheet at a certain angle projected from the y- and x-axes, respectively. The MATLAB bvp4c program is the main mathematical program that was used to obtain the final numerical solutions for the reduced ordinary differential equations (ODEs). These ODEs originate from the governing partial differential equations (PDEs), where the transformation can be achieved by applying similarity transformations. The MATLAB bvp4c program was also implemented to develop stability analysis, where this calculation was executed to recognize the most stable numerical solution. Numerical graphics were made for the skin friction coefficient, local Nusselt number, local Sherwood number, velocity profile, temperature profile, and concentration profile for certain values of the physical parameters. It is found that all the governed parameters affected the variations of the Casson fluid flow, heat transfer, mass transfer, and the profiles of velocity, temperature, and concentration. In addition, a stable solution can be applied to predict the impact of physical parameters on the actual fluid model by using a mathematical fluid model. Full article

This research article aims to investigate the consequences of binary chemical reaction, thermal radiation, and Soret–Dufour effects on a steady incompressible Darcy–Forchheimer flow of nanofluids. Stretching surface is assumed to drive the fluid along positive horizontal direction. Brownian motion, and the Thermophoresis are accounted in particular. The governing highly nonlinear system of problems which are advanced version of Navier–Stokes equations are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations invoking symmetric property of the independent variables. The numerical approach using RK45 in connection with shooting technique is adopted to solve the final equations. Graphical approach is used to interpret the results and the values of important physical quantities are given in tabular data form. Velocity field, temperature distribution and concentration distribution are graphically analyzed for variation in respective fluid parameters. Furthermore, density graphs and stream lines are sketched for the present model. The outputs indicate a rise of temperature field in connection with thermal radiation parameter. A clear decline is noticed in velocity field for elevated values of Forchheimer number and porosity factor. The Dufour effect anticipates a rising factor for temperature distribution and the same is noticed for concentration distribution in lieu of Soret effect. Thermal radiation and binary chemical reaction has strong impact on heat transport mechanism. The results for physical quantities such as skin friction, heat and mass flux rates are given in tabular data form in last section of this study. Full article

This exploration examines the nonlinear effect of radiation on magnet flow consisting of hybrid alloy nanoparticles in the way of stream-wise and cross flow. Many experimental, as well as theoretical explorations, demonstrated that the thermal conductivity of the regular liquid increases by up to 15 to 40% when nanomaterials are mixed with the regular liquid. This change of the thermal conductivity of the nanoliquid depends on the various characteristics of the mixed nanomaterials like the size of the nanoparticles, the agglomeration of the particles, the volume fraction, etc. Researchers have used numerous nanoparticles. However, we selected water-based aluminum alloy (AA7075) and titanium alloy (Ti₆Al₄V) hybrid nanomaterials. This condition was mathematically modeled by capturing the Soret and Dufour impacts. The similarity method was exercised to change the partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). Such nonlinear ODEs were worked out numerically via the bvp4c solver. The influences of varying the parameters on the concentration, temperature, and velocity area and the accompanying engineering quantities such as friction factor, mass, and heat transport rate were obtained and discussed using graphs. The velocity declines owing to nanoparticle volume fraction in the stream-wise and cross flow directions in the first result and augment in the second result, while the temperature and concentration upsurge in the first and second results. In addition, the Nusselt number augments due to the Soret number and declines due to the Dufour number in both results, whereas the Sherwood number uplifts due to the Dufour number and shrinks due to the Soret number in both results. Full article

The principal objective of the current study is to analyze the Brownian motion and thermophoretic impacts on micropolar nanofluid flow over a nonlinear inclined stretching sheet taking into account the Soret and Dufour effects. The compatible similarity transformations are applied to obtain the nonlinear ordinary differential equations from the partial differential equations. The numerical solution of the present study obtained via the Keller-Box technique. The physical quantities of interest are skin friction, Sherwood number, and heat exchange, along with several influences of material parameters on the momentum, temperature, and concentration are elucidated and clarified with diagrams. A decent settlement can be established in the current results with previously published work in the deficiency of incorporating effects. It is found that the growth of the inclination and nonlinear stretching factor decreases the velocity profile. Moreover, the growth of the Soret effect reduces the heat flux rate and wall shear stress. Full article