Soret Number Research Articles

Analytical solution for MHD nanofluid flow over a porous wedge with melting heat transfer

This study employs the Hybrid Analytical-Numerical (HAN) method to investigate steady two-dimensional magnetohydrodynamic (MHD) nanofluid flow over a permeable wedge. Analyzing hyperbolic tangent nanofluid flow, the governing time-independent partial differential equations (PDEs) for continuity, momentum, energy, and concentration transform into a set of nonlinear third-order coupled ordinary differential equations (ODEs) through similarity transformations. These ODEs encompass critical parameters such as Lewis and Prandtl numbers, Brownian diffusion, Weissenberg number, thermophoresis, Dufour and Soret numbers, magnetic field strength, thermal radiation, power law index, and medium permeability. The study explores how variations in these parameters impact the velocity field, skin friction coefficient, Nusselt, and Sherwood numbers. Noteworthy findings include the sensitivity of fluid velocity to parameters like Weissenberg number, power law index, wedge angle, magnetic field strength, permeability, and melting heat transfer. The skin friction coefficient experiences a significant increase with specific parameter changes, while Nusselt and Sherwood numbers remain relatively constant. The local Reynolds number significantly affects Nusselt and Sherwood numbers, with a less pronounced impact on the skin friction coefficient. The study's uniqueness lies in employing the analytical HAN method and extracting recent insights from the results.

Heat and mass transfer dynamics in curved Ш-Chip: ISPH simulations and ANN analysis

This research investigates heat and mass transfer behavior in nano-enhanced phase change materials (NEPCM) within reactive systems using incompressible smoothed particle hydrodynamics (ISPH) coupled with artificial neural network (ANN) predictions. It introduces a novel model comprising six vertical rods and one curved rod, forming a unique Ш-Chip configuration. The complexity of the NEPCM model demonstrates its relevance in fluid dynamics and heat transfer analyses applicable across diverse fields including food processing, electronics cooling, chip manufacturing, heat exchangers, and solar energy systems. The study explores the influence of various dimensionless parameters such as the Frank-Kamenetskii number (Fk), Hartmann number (Ha), Soret and Dufour numbers (Sr&Du), Lewis number (Le), Rayleigh number (Ra), and fractional order parameter (α) on heat and mass transfer phenomena. Heat/mass sources from embedded vertical and curved rods filled with NEPCM are considered within the model. An artificial neural network (ANN) model employing a multilayer perceptron (MLP) structure is utilized to accurately predict the average Nusselt (Nu‾) and Sherwood (Sh‾) numbers, demonstrating its applicability in fluid dynamics and heat transfer analyses. Key insights highlight the role of Fk and Ra in enhancing convection flow and nanofluid velocity within the curved Ш-Chip. Furthermore, variations in Ha lead to observable velocity reductions due to intensified Lorentz forces, while increased Le values result in decreased velocities as thermal diffusion becomes dominant. The fractional order parameter (α) aids in the transition from unsteady to steady state. The unique configuration of the curved Ш-Chip, combined with the incorporation of heat/mass sources from embedded particles, offers promising applications across diverse fields such as food processing, electronics cooling, chip manufacturing, heat exchangers, and solar energy systems. This research underscores the crucial role of understanding the pertinent parameters to ensure the effective development of systems tailored to specific needs. Additionally, it emphasizes the practical value of employing ANN models in predictive modeling to tackle the complexities encountered in engineering applications.

Ternary hybrid nanofluid flow through an inclined shrinking sheet when soret, dufour and quadratic thermal radiation are significant: an irreversibility analysis with various shape factors

As nanofluid technology continues to evolve, the knowledge gained from studying flow over an inclined shrinking sheet can be applied to various emerging applications. These could include heat pipes for spacecraft thermal management, thermal management systems for wearable electronics, or even designing microfluidic channels for efficient desalination processes. A ternary hybrid nanofluid (Ethylene Glycol, Copper (II) oxide, Titanium dioxide, and Silicon dioxide) is the main focus of this study, which aims to theoretically analyse its behaviour through a tilted shrinking sheet in the presence of heat source, Dufour, and Soret effects. Governing equations are transformed into a set of ordinary differential equations using appropriate similarity transformations and then solved using bvp4c solver. The main findings of this study are that enhancing the value of the couple stress parameter leads to a decline in fluid velocity, and increasing the Dufour number will upsurge the temperature of the fluid. It has been noticed that the Sherwood number exhibits a decline when the Soret number increases. We find that the Nusselt number noticeably increases by 0.147404161 (spherical), 0.151277029 (brick), and 0.156726935 (cylinder) for values of the Dufour number within the range of 0 to 3.

Magnetic field effects on double diffusion of four sloshing fins in a nanofluid-occupied cavity

ABSTRACT This article offers a novel study on the impacts of magnetic field and Soret-Dufour numbers on the thermosolutal convection of sloshing four fins on the wall sides of a square cavity occupied by a nanofluid. The incompressible condition of smoothed particle hydrodynamics (SPH) entitled ISPH method simulated sloshing four fins inside a nanofluid flow contained by a square cavity. The scales of pertinent parameters are fin length 0.05 ≤ L Fin ≤ 0.3 , Dufour number 0 ≤ Du ≤ 1 , a magnetic field inclination angle 30 ∘ ≤ γ ≤ 90 ∘ , Soret number 0 ≤ Sr ≤ 2 , Hartmann number 10 ≤ Ha ≤ 50 , Rayleigh number 10 4 ≤ Ra ≤ 10 7 , and nanoparticle parameter 0 ≤ ϕ ≤ 0.2 . The simulations of the ISPH method indicated the significant role of the fin’s length in enhancing the nanofluid alterations and transmission of thermal/solutal convection inside a cavity. Besides, the Rayleigh number has a great influence on improving nanofluid velocity and power of temperature/concentration. The Soret/Dufour numbers are successful in boosting the nanofluid speed as well as heat and mass transport, while the Hartmann number and nanoparticles parameter are effective in reducing the nanofluid movements.

Radiative squeezed flow of magnetized Prandtl-Eyring fluid over a sensor surface under Soret effect

The central aim of this numerical analysis is to describe the effects of magnetic body force and thermal radiation on the boundary layer flow of Prandtl-Eyring fluid over a sensor surface suspended between two parallel plates. The considered fluid flow is two-dimensional unsteady electrically conducting and viscous incompressible in nature. A novel Soret effect is included in the concentration equation to reveal the significant features of mass diffusion mechanism under the influence of external squeezing mechanism. Surface permeable velocity concept is also included in the boundary conditions to describe the suction/injection process. However, squeezing flows find their abundant applications in bio-medicine, medical and bio-technology areas. Particularly, the micro-cantilevers with physical or chemical sensor surfaces are effectively used in the bio-medical applications for the finding of various hazardous or bio-warfare agents’, infections, hazardous virus, nuclear reactor cooling, polymer processing, pharmaceutical, blood flow, injection molding and many more. Thus, inspired by these practical applications of squeezing flows, the present problem is modeled based on the investigated geometry. The present physical problem gives the highly nonlinear coupled unsteady two-dimensional partial differential equations and which are not amenable to any of the direct methods. Owing to this reason, the appropriate similarity transformations are used to diminish the dimensional complexity of the emerged partial differential equations (PDEs). Thus, a robust Runge-Kutta -4th order scheme (RK-4) is used as a basic tool to obtain the similar solutions of the governing equations. The graphical visualization is used to analyze the computer generated numerical data in the boundary layer regime for the different set of physical parameters. It is observed that, the enhancing magnetic number ( 0.1 ≤ M ≤ 2.7 ) in the flow region 0 ≤ η ≤ 3 increases the velocity field and decreases the temperature and concentration fields. Increasing squeezed flow index ( 0.1 ≤ b ≤ 2.5 ) in the flow domain 0 ≤ η ≤ 3 decreased the fluid velocity, temperature and concentration fields. This result may be useful in sensor surface cooling process. Rising Prandtl-Eyring fluid parameters in the range 0 ≤ η ≤ 3 decreased the velocity field and enhanced the temperature and concentration profiles. Increasing Soret number ( 0.1 ≤ Sr ≤ 0.9 ) in the flow domain 0 ≤ η ≤ 3 enhances the concentration field. Enhancing magnetic and squeezed flow numbers amplifies the skin-friction coefficient on the sensor surface. Enhancing radiation parameter increases the heat transport rate. Increasing Soret number magnifies the concentration transport rate. Finally, it is explored that, the current similar results displaying good agreement with the formerly published results in the literature and this fact confirms the accuracy and guarantee of the RK-4 method and present similar results.

Numerical solution of an unsteady nanofluid flow with magnetic, endothermic reaction, viscous dissipation, and solid volume fraction effects on the exponentially moving vertical plate

This study analyzes the unsteady nanofluid flow phenomenon adjacent to an accelerating vertical plate under the influence of magnetic fields, chemical reactions,viscous dissipation and solid volume fraction factors. The analysis motivates the understanding of the behavior of complex fluids to improve existing processes and develop new technologies. The finite difference technique, with the help of the boundary and initial conditions, was employed for the numerical result. The numerical solutions were graphically analyzed through MATLAB software. The results reveal intricate flow behaviors, including the influence of magnetic fields and solid volume fraction in reducing the velocity of the nanofluid. Interestingly, a magnetic field drops the temperature of the nanofluid, which can be observed in a particular case. The chemical reaction is found to absorb the heat, leading to a decline in the velocity and concentration due to temperature drop and solute destruction factors. The viscous dissipation raises the temperature of the nanofluid, but the heat sink affects the temperature oppositely. The Soret number essentially quantifies the phenomenon known as thermophoresis, where solutes concentrate more in cooler regions. This analysis provides valuable insights into the design and optimization of systems involving nanofluids subjected to external magnetic fields, with implications for various engineering applications such as thermal management systems and nanofluid-based heat exchangers.

Stratified numerical heat and mass transport mechanism in MHD Maxwell fluid flow with nonuniform heat source/sink

The present boundary layer flow of Maxwell fluid over a stretching sheet has good number of practical applications in metallurgy, drawing of plastics, polymer sheet extrusion including hot rolling extrusion, glass blowing, spinning of fibers, rubber and plastic sheets, crystal growing and many more. Due to these extensive applications of Maxwell fluid in engineering, medicine and manufacturing industries including the above-mentioned applications, authors have motived, inspired and investigated the present problem. However, in this research paper, the influences of Soret and Dufour effects on the steady-state Maxwell fluid flow past a stretching sheet with nonuniform heat source/sink are considered numerically. The thermal and concentration stratifications impacts are also incorporated. The viscous dissipation and magnetic field effects are also included in the respective governing equations. The main novelty and uniqueness of this numerical research is to generalize the earlier studies and describe the salient features of magneto-thermo visco-elastic dissipative Maxwell fluid motion about a stretching sheet with cross-diffusion effects under the influence of double stratification phenomena. To differentiate the non-Newtonian fluids from those of Newtonian fluids, a well-known Maxwell fluid flow model is used in the present study. The investigated physical problem results the highly nonlinear coupled partial differential equations (PDEs) and which are not amenable to any of the direct methods. Suitable similarity transformations are deployed to reduce the highly complex PDEs into the system of ordinary differential equations (ODEs). A robust BVP4C Matlab function is employed to solve the rendered dimensionless system of ODEs. The numerically generated computed data is plotted in terms of velocity, temperature and concentration profiles including engineering quantities of interest such as skin-friction, Nusselt and Sherwood numbers in the flow region. It is evident from the current analysis that, the amplified magnetic field decreases the velocity field and increases the thermal and concentration distribution fields. Accelerating Maxwell’s number diminished the flow velocity and increased the temperature field. Increasing Soret and Dufour numbers enhances the concentration and temperature fields, respectively. Amplifying Maxwell’s number raises the skin-friction coefficient and enlarging the thermal stratification parameter magnifies the thermal transport rate. The mass transport rate amplified with a raise in concentration stratification number in the flow region. Finally, it is provided that, the current results are excellently matching with earlier published results in the literature and it confirms the accuracy of the used numerical method and the produced similarity solutions.

Mathematical modeling of cross diffusion effect on bioconvective Casson nanofluid over multi slips porous stretching surface

Purpose and significance Cross diffusion is a phenomenon that arises when various species are diffusing at the same time in a mixture. These are crucial in many industrial, environmental, and material processes for analyzing and forecasting temperature distribution, concentration profiles, and overall system behavior. Thus, cross-diffusion effects on Casson nanofluid across nonlinear stretching sheet are considered. In addition, the influence of magnetohydrodynamics (MHD) with multi slip boundary conditions implanted in porous regime is examined. The novelty of this study is the complex interactions and phenomenon of non-Newtonian Casson nanofluid with bioconvective multi slips conditions, which has an essential contribution in interdisciplinary nature. Methodology By employing similarity transformation, governing equations undergo a transformation into ordinary differential equations (ODEs), and solved using 5th-order Runge–Kutta–Fehlberg method via shooting technique. Graphical representations are utilized to depict effects of various parameters, accompanied by detailed explanations. Outcome The results obtained affirm that nonlinear stretching parameter leads to a deceleration of velocity profile, while temperature profile is observed to enhance with Eckert and Dufour numbers. Additionally, enhancement in the concentration profile occurred due to the Soret number. The comparison of current findings with prior research revealed great accuracy. Meanwhile, a graphical representation of skin friction, Nusselt number, and Sherwood number are presented. This investigation demonstrates that skin friction decreases by 10% with an improvement of M from 0.4 to 1.6. Furthermore, it is identified that there is a 31% rise in Sherwood number when Lewis number is accelerated from 1.0 to 1.5.

Employing ISPH simulations and artificial intelligence for enhanced heat and mass transfer in a core reactor with nano-enhanced phase change materials

This research investigates the heat and mass transfer characteristics of nano-enhanced phase change material (NEPCM) within a core reactor, employing both the incompressible smoothed particle hydrodynamics (ISPH) simulations and artificial intelligence (AI) analysis. NEPCM holds promise for enhancing thermal energy storage and transfer efficiency, with applications spanning various fields, including nuclear reactors. Through ISPH simulations, this study delves into the intricate fluid dynamics and phase change phenomena within the reactor, providing valuable insights into the thermal behavior of NEPCM. Eight embedded rods are initially settled inside a reactor with high temperature and concentration on four rods and the others are maintained at low temperature and concentration. The effects of various parameters including the Cattaneo–Christov heat parameter ( δ Heat ) , Cattaneo–Christov mass parameter ( δ Mass ) , Dufour number ( Du ) , Hartmann number ( Ha ) , Soret number ( Sr ) , and thermal radiation ( Rd ) are conducted in this work. δ Heat and δ Mass play critical roles in evaluating heat and mass transfer efficiencies. Raising the Dufour number improves temperature distribution while having a minimal impact on concentration. Additionally, increasing the Dufour number from 0 to 1.5 leads to a 30% increase in the velocity field. Elevating the Soret number significantly enhances velocity and concentration, while increasing the thermal radiation parameter improves temperature distribution. These findings are pertinent across multiple domains like combustion, chemical engineering, and geophysics, aiding in process optimization and system design. The ANN model exhibits high precision in predicting Nusselt and Sherwood numbers, highlighting its effectiveness in forecasting.

Incompressible smoothed particle hydrodynamics simulations enhanced by hybrid artificial intelligence for investigating magnetic field influence on double diffusion in an arc-shaped cavity

Optimizing heat and mass transfer of Nano-Enhanced Phase Change Material (NEPCM) within complex geometries has numerous practical applications across various industries. These include enhancing the performance of heat exchangers, improving the efficiency of solar energy systems, optimizing the cooling of electronic devices, designing more efficient energy systems, and enhancing the processing efficiency in food industry applications. The incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence (AI) are joined to handle the thermosolutal convection of NEPCM inside an arc shape. Different lengths of heat/mass sources are considered in this work. The embedded tree fin is maintained at low temperature and concentration with zero velocities. AI predicted accurately the mean Nusselt and Sherwood numbers by integration with the ISPH simulations that have been done. Heat and mass transmission were investigated for various lengths of partial heat/mass sources, fractional time derivative, Frank-Kamenetskii number, Hartmann number, Rayleigh number, buoyancy ratio parameter, Soret number, Lewis number, and Dufour number. Expanded lengths of heat/mass sources in arc borders improved heat and mass transport inside an arc shape. The fractional time derivative helps in reducing the computing time necessary to achieve a steady state. The Rayleigh number supports the buoyancy forces that raise the velocity field and temperature and concentration distributions inside an arc shape. By including an arc-shaped cooling tree fin, the magnetic field, Lewis number, and buoyancy ratio characteristics are reduced. The Frank-Kamenetskii number contributes to better temperature dispersion. Examples of heat/mass transfer in an arc form with a tree fin include heat exchangers, solar cells, energy systems, electronic device cooling, and food processors.

Impact of variable viscosity, thermal conductivity, and Soret–Dufour effects on MHD radiative heat transfer in thin reactive liquid films past an unsteady permeable expandable sheet

AbstractSignificance of magnetohydrodynamic effect on a viscous (temperature‐dependent) and chemically reactive thin fluid film flow past an unsteady permeable stretchable plate with Soret–Dufour effects, nonlinear thermal radiative, and suction under the action of a convective type of boundary condition is analyzed. The problem consists of nonlinear governing basic equations that are highly nonlinear due to the existence of nonlinear thermal radiative terms in the energy equation. Analytical solutions are challenging to achieve for such types of problems, so a numerical scheme adopts the numerical solution. Computed solutions indicate that decreasing the Dufour number (and simultaneously increasing the Soret number) enhances heat flux, whereas the reverse trend is estimated for the concentration gradient field. The influence of magnetization indicates a decrement in the thin liquid film velocity distribution, whereas an increment is observed in temperature and solutal gradient profiles. Further, an enhancement in thermoradiative values focuses on decreasing the heat flux profiles, whereas a decreasing trend is determined in the solutal gradient by incrementing the Schmidt number. The variations of the velocity field, temperature, and concentration gradients are shown for the unsteady parameter lying in the range [0.8, 1.4]. Similarly, the range of different parameters utilized are [0.0, 1.0], [0.0, 2.0], [0.8, 1.5], [0.5, 2.0], [0.0, 1.0], [0.2, 3.0], [1.0, 2.0], [0.0, 3.0], [0.4, 1.0], and [0.4, 1.0]. The novelty of the present study lies in its analysis of complex fluid dynamics phenomena and their implications for various industrial processes and engineering applications, including coating processes, heat exchangers, microfluidics, and biomedical engineering. The insights gained from the study can contribute to developing more efficient and innovative research in these areas. Further, we have compared the present results with those available in the literature under some special cases and found them to be in excellent agreement.

The varying viscosity impact in an inclined peristaltic channel with diffusion‐thermo and thermo‐diffusion

AbstractA mathematical model is constructed to investigate the behavior of peristaltic flow of Jeffrey fluid in an inclined tapered asymmetric porous channel. The fluid viscosity is taken as space dependent variable quantity. Heat absorption, Soret and Dufour effects are also retained in the current scrutiny. These preferences have broad applications in engineering, biology and industry. We began our investigation by taking into account the two‐dimensional inclined asymmetric porous channel. In the context of mathematical modeling, the appropriate dimensional nonlinear equations for momentum, heat and mass transport are simplified into dimensionless equations by applying the essential estimation of long wavelength and low Reynolds number. The solution of the governing equations is executed numerically. A graphical depiction of many crucial physical characteristics on velocity, temperature, concentration, heat transfer rate, Nusselt number and Streamlines have been reported in ending section. Temperature profile exhibits an escalation with the augmentation of Brinkman number and Dufour number . For the growing values of Prandtl number , an increment in temperature profile is observed whilst a reverse tendency is captured for concentration profile. It is noted that concentration profile falls down owing to the enhancement in Soret number and Schmidt number . An oscillatory outlook is noticed for heat transfer rate and Nusselt number. The novelty of this proposed model in the research domain specifically depends on considerations of the combined study of the Variable viscosity, Darcy resistance, Viscous dissipation, Mixed convention, Heat absorption, Soret and Dufour effects in peristaltic flow of non‐ Newtonian Jeffrey fluid in an inclined Asymmetric tapered channel under the influence of convective boundary conditions.

Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion

Abstract Modern heat transport processes such as fuel cells, hybrid engines, microelectronics, refrigerators, heat exchangers, grinding, coolers, machining, and pharmaceutical operations may benefit from the unique properties of nanoliquids. By considering Al 2 O 3 {{\rm{Al}}}_{2}{{\rm{O}}}_{3} nanoparticles as a solo model and Al 2 O 3 – Cu {{\rm{Al}}}_{2}{{\rm{O}}}_{3}{\rm{\mbox{--}}}{\rm{Cu}} as hybrid nanocomposites in a hyperbolic tangent fluid, numerical simulations for heat and mass transfer have been established. To compare the thermal acts of the nanofluid and hybrid nanofluid, bvp4c computes the solution for the created mathematical equations with the help of MATLAB software. The impacts of thermal radiation, such as altering thermal conductivity and cross-diffusion, as well as flow and thermal facts, including a stretchy surface with hydromagnetic, and Joule heating, were also included. Furthermore, the hybrid nanofluid generates heat faster than a nanofluid. The temperature and concentration profiles increase with the Dufour and the Soret numbers, respectively. The upsurge permeability and Weissenberg parameter decline to the velocity. An upsurge variable of the thermal conductivity grows to the temperature profile. Compared to the nanofluids, the hybrid nanofluids have higher thermal efficiency, making them a more effective working fluid. The magnetic field strength significantly reduces the movement and has a striking effect on the width of the momentum boundary layer.

Influence of Slip Boundary Conditions on Jeffrey Fluid Flow in Tapered Conduit with Hall Current and Soret–Dufour Effects

AbstractThe present work examines the computational analysis and mathematical modeling of peristaltic blood flow in a tapered channel, taking into account slip boundary conditions, Hall current, and Soret–Dufour forces. By neglecting the wave number and employing a long‐wavelength approximation to analyze the fluid model, the investigation was conducted within the framework of a low Reynolds number regime. The study reveals that the values of the Soret number, Dufour number, Prandtl number, and Schmidt number exhibit an upward trend as the fluid temperature rises. In contrast, a rise in the thermal slip parameter causes the fluid temperature to fall. It has been shown that when the mass slip parameter increases, the fluid's concentration rises. The skin friction coefficient rises within the range of x = 0.55 to x = 1 as the velocity, concentration slip parameter, Soret number, and Dufour number increase. Conversely, the skin friction coefficient decreases as the thermal slip parameter increases. The selected characteristics exhibit realism since they find use in many fields such as medical biology, biomechanics, heat exchangers, gas turbines, and several other domains.

Non-Darcian MHD flow of ternary-hybrid Cu-TiO2-Al2O3/H2O nanofluid over an inclined sheet with activation energy

This study has been carried out to understand the unsteady MHD slip flow of a water-based ternary hybrid nanofluid including spherical Cu, titanium dioxide TiO2 and cylindrical Al2O3 nanoparticles across an angled sheet. The complicated scenario above investigates how ternary-hybrid nanofluid behaves when it is stretched across an inclined surface in the existence of a magnetic field. In complex thermal systems such as energy-generating technologies and cooling mechanisms, an understanding of this relationship is essential. In the existence of first-order velocity slip, the heat transfer has been examined taking into account the non-Darcy Porous media, activation energy, and heat source. The study is more accommodating because of the Soret effect. The relevant similarity transformations are applied in primary equations and a built-in bvp4c program is employed for solutions. The effectiveness of the numerical approach is demonstrated by a thorough agreement with results that have been published in the past. The key conclusions are as follows: greater values of the first order slip parameter cause the flow to slow down; an increase in Soret number causes the flow to speed up; and in both scenarios—that is, with and without velocity slip, fluid movement drops caused by higher values of the chemical reaction. The Forchheimer parameter lowers fluid velocity while activation energy enhances the fluid concentration.

The Soret-Dufour Effects on Three-Dimensional Magnetohydrodynamics Newtonian Fluid Flow over an Inclined Plane

The three-dimensional (3D) model of the fluid flow model with length, breadth, and height or depth is the advanced and precise version from the two-dimensional (2D) model which just lies on a flat surface. The heat transfer in the boundary layer flow have numerous applications in the production of polymer, plastic films, and paper production. Therefore, this paper solves 3D magnetohydrodynamics Newtonian fluid flow model with the effect of Soret-Dufour parameters. Compared with the previous report where the 3D model is without the inclination angle (all the axes are located at their fixed position), this paper considers the boundary xy-plane being projected by a certain angle from the z-axis. The initial partial differential equations (PDEs) are subsequently reduced to ordinary differential equations (ODEs). The MATLAB bvp4c program is chosen to solve the ODEs and the results velocity profile, temperature profile, concentration profile, skin friction coefficient, local Nusselt number, and local Sherwood number. It can be inferred that the magnetic parameter is responsible to the decrement of the velocity profile and skin frictions coefficient. The enhancement of the temperature and the local Sherwood number are caused by the Dufour number. Besides, concentration and the local Nusselt number are enhancing due to the increasing Soret number.

Radiative bioconvective flow with non-uniform heat source and Soret and Dufour impacts

Background and objectiveThe stretched flow with heat transfer has pivotal role in geothermal energy system, oil extraction, continuous casting, metal spinning and electronic cooling. Owing to this fact, the current analysis focuses on non-linear thermal radiation effect in bio-convective stagnation point flow by a stretchable wedge. Darcy relation is used to discuss the porous space. Convective conditions are deliberated. Non-uniform heat source is addressed. Soret and Dufour outcomes are analyzed. Dissipation and magnetohydrodynamics are discussed. Presence of gyrotactic microorganisms along with chemical reaction is considered. MethodologyRelated non-linear partial differential equations (PDEs) are reduced into dimensionless ordinary differential equations (ODEs) through adequate transformations. Optimal homotopy analysis method (OHAM) is adopted for the computations of related nonlinear differential systems. ResultsFlow, microorganism field, concentration and temperature distribution are graphically explored. Numerical analysis for coefficient of skin friction, microorganism density number and Sherwood and Nusselt numbers against emerging parameters are discussed. It is noted that velocity and skin friction coefficient have similar scenario for modified Hartman number. Thermal transport rate and temperature have reverse trends for non-uniform heat source variable. An augmentation in thermal distribution is seen through thermal Biot number. Larger Dufour number has increasing trend for temperature. An increasing trend for solutal Biot number for concentration is noticed. Larger Soret number leads to concentration enhancement. Microorganism field and motile density number against Peclet number have opposite response. There is reduction for bio-convective Lewis number in motile density number.

Numerical analysis of velocity slip and magnetic Soret effect on dissipative Maxwell liquid motion about a stretching wall with heat source/sink

The main aim of present numerical analysis is to explore the effects of viscous dissipation and velocity slip on the two-dimensional steady-state viscous incompressible flow of Maxwell fluid over a stretching sheet under the infleunce of magnetic field. Novel collective effects of heat source/sink and Soret impacts have been included in the governing equations to explore the salient features of heat and mass transport mechanism. Further, the velocity slip is introduced into the boundary conditions to depict the momentum transport behavior in the flow region. A typical Maxwell fluid model is deployed to separate the non-Newtonian flow behavior from that of classical Newtonian fluids. However, the visco-elastic Maxwell fluid finds its abundant applications in various fields of engineering and medicine such as plastic sheet drawing, metallurgy, polymer sheet extrusion, chemical engineering, electronic cooling, injection molding and nuclear cooling and many others. Inspired by these applications, authors have made an attempt to disclose the magneto-thermo salient features of slip flow of Maxwell fluid over stretching wall under Soret effect. The current physical situation results the highly nonlinear coupled two-dimensional steady-state partial differential equations and which are not amenable to any of the direct techniques. Due to this, the suitable similarity transformations are deployed to reduce the dimensional complexity of the constructed partial differential equations. A robust Matlab-based bvp4c scheme is utilized as a basic tool to produce the similarity solutions of the governing equations. The computer generated numerical data is presented in view of flow, temperature and concentration profiles including physical quantities of interest like skin-friction coefficient, heat and mass transport rates for the various values of physical parameters range such as, 0 ≤ M ≤ 1 , 0 ≤ β ≤ 1 , − 0.3 ≤ λ ≤ 0.6 , − 0.2 ≤ Q ≤ 0.2 , 0 ≤ Ec ≤ 2.2 , 1.2 ≤ Pr ≤ 2.2 , 0 ≤ Sr ≤ 0.5 and 1.2 ≤ Sc ≤ 2.2 . Accordingly, it is noticed that, enhancing magnetic parameter decreases the Maxwell fluid flow and amplifies the temperature and concentration fields. Enlarging Maxwell fluid parameter decreases the velocity field and increases the temperature and concentration profiles. Amplified slip parameter diminished the Maxwell flow inside the flow regime. Increasing heat source/sink parameter amplifies the temperature field. Further, magnifying Soret number amplifies the concentration field. Magnitude of skin-friction coeffiecient enlarged with amplified magnetic and Maxwell fluid parameters. Heat and mass transport rates decayed with enhancement in heat source/sink and Soret parameters. Finally, it is described that, the present similarity solutions showing good agreement with the previously reported solutions in the literature and this fact confirms the accurateness of the used numerical method and the generated similarity solutions.

Optimizing entropy in mixed convective MHD dissipative nanofluid with cross-diffusion and nonlinear velocity slip

Entropy optimization is crucial for enhancing fluid dynamics and heat transfer, leading to improved efficiency, energy conservation, and environmental sustainability. Recognizing its significance, we examine the influence of radiation, Joule heating, heat sources, mixed convection, and nonlinear slip on the entropy-optimized flow of a dissipative nanofluid over a curved surface. To seamlessly integrate within the MATLAB bvp4c framework, we convert the set of multi-order ODEs, derived from fundamental PDEs via a similarity transformation approach, into a system of first-order ODEs. Graphs and analytical discussions are used to evaluate the parameters of the problem. The velocity within the boundary layer, along with entropy, experiences reduction due to the enhancement in both first- and second-order slip velocity parameters, as well as curvature parameters. The temperature plot improves with the increase in parameters such as the Soret number and Dufour number, as well as radiation. Conversely, the temperature plot reduces with the rise in suction values. The study indicates that a higher Brinkman number is associated with a lower Bejan number, while the first- and second-order velocity slip parameters have a contrasting effect, leading to an increase in the Bejan number.

FRACTAL FRACTIONAL MODEL OF RADIATIVE HEAT AND MASS TRANSFER CHARACTERISTICS OF TIME DEPENDENT FLOW WITH VARIABLE VISCOSITY, INDUCED MAGNETIC FIELD, DUFOUR AND SORET EFFECTS: AN ENTROPY GENERATION

: In this article, the Caputo Fabrizio fractal fractional order derivatives operator with an exponential kernel was employed to examine the radiative heat and mass transfer characteristics of time dependent flow with variable fluid viscosity, induced magnetic field, Soret and Dufour effects. The local mathematical model for the flow problem is formulated by take into account the impacts of thermal radiation, heat source, and viscous dissipation. The governing equations in-terms of fractal fractional model with an exponential kernel were solved numerically using finite difference method. The influence of flow variables such as induced magnetic field, concentration field, entropy rate, thermal field, and velocity field profiles against the pertinent parameters are discussed through graphs. Increase the values of magnetic Prandtl number results to rises of induced magnetic field. Higher Dufour number significantly grows the thermal field. The fractal fractional parameters enhance the velocity field, thermal field, Bejan number, entropy rate, concentration field and induced magnetic field profiles. The velocity field profiles recede with higher values of fluid variable viscosity parameter whereas the thermal field and induced magnetic field has an opposite effect. Larger Soret number amplifies the concentration field. Increase of Brinkman number, thermal radiation parameter, and magnetic Prandtl number intensifies the entropy generation rate. Increases of Brinkman number, magnetic Prandtl number, Soret number and Dufour number leads to a decrease of Bejan number whereas Bejan number rises with an increase of thermal radiation parameter and heat source