Bvp4c Technique Research Articles

Exploring slip flow and heat transfer of power-law fluid past an induced magnetic stretching regime subject to Cattaneo-Christov flux theory

This work investigates the heat transmission and boundary layer (BL) slip flow of a power-law fluid induced by stretching surfaces. The power-law fluid, induced magnetic field, and finite thermal relaxation have significant applications in a variety of industrial settings, including thin-layer growth, cooling systems, the extrusion process, and coating and shaping operations in a heat transfer mechanism. With these significant industrial applications, the current study explores BL flow and heat transfer in the context of the of the Cattaneo-Christov theory against the backdrop of an induced magnetic field over a stretching surface. The shear-thinning and thickening features are captured by the power-law fluid model, while the Cattaneo-Christov theory solves the deficiencies of Fourier's law. The BVP4c technique is used to construct and solve BL equations numerically. The surface drag and heat transmission rates at the wall are studied using statistical multi-regression analysis. The findings clarify that the magnetic and power law indices have a favorable effect on the Nusselt number, while their influence on skin friction is conflicting. A lower heat transmission is predicted with thermal relaxation as compared to Fourier's law in the energy equation. The accumulated thermal relaxation parameter produces a non-equilibrium state, delaying the internal thermal processes.

Tetrahybrid nanoparticles through squeezed channel with inclined Lorentz forces

Heat exchangers, nuclear power plants, and other engineering and manufacturing operations all involve high temperatures. These systems have a very big temperature gradient, which has a substantial impact on the fluid's transport characteristics. Under such circumstances, using the linear Boussinesq approximation and taking into account the constant thermophysical parameters for the ambient liquid become meaningless. Thus, under the impact on the angled magnetic field and joule heating, the radiative convection flow of the blood-based tetrahybrid nanoliquid in a squeezing channel is examined in this work. The base fluid that contains the distributed alumina, gold, silver, and titania nanoparticles is blood. Through suitable transformations, the partial governing equations were decreased into nonlinear ordinary differential equation's, which are then resolved mathematically applying the fourth-order accurate BVP4C technique. The increase in the viscous dissipation parameter corresponds toward the notable elevation on the blood temperature profile. The rate of heat transfer 57.4519% improved in Au-Ag-Al2O3-TiO2/blood than that of pure blood.

Significance of magnetic field and Darcy–Forchheimer law on dynamics of non-Newtonian hybrid nanofluid flow over a spinning disc with Arrhenius activation energy and shape factor

Purpose The purpose of the study is to explore the three-dimensional heat and mass transport dynamics of the magneto-hydrodynamic non-Newtonian (Casson fluid) hybrid nanofluid flow comprised of − as nanoparticles suspended in base liquid water as it passes through a flexible spinning disc. The influence of a magnetic field, rotation parameter, porosity, Darcy−Forchheimer, Arrhenius’s activation energy, chemical reaction, Schmidt number and nanoparticle shape effects are substantial physical features of the investigation. Furthermore, the influence of hybrid nanofluid on Brownian motion and thermophoresis features has been represented using the Buongiorno model. The novelty of the work is intended to contribute to a better understanding of Casson non-Newtonian fluid boundary layer flow. Design/methodology/approach The governing mathematical equations that explain the flow and heat and mass transport phenomena for fluid domains include the Navier−Stokes equation, the thermal energy equation and the solutal concentration equations. The governing equations are expressed as partial differential equations, which are then converted into a suitable set of non-linear ordinary differential equations by using the necessary similarity variables. The ordinary differential equations are computed by combining the shooting operation with the three-stage Lobatto BVP4c technique. Findings Graphs and tables are used in the process of analysing the characteristics of velocity distributions, temperature profiles and solutal curves at varying values of the parameters, along with friction drag, heat transfer rate and Sherwood number. It has been revealed that the radial and axial velocities decrease when the Casson parameter value increases and that the rate of heat transmission is higher in hybrid nanofluids with nanoparticles in the shape of a blade. The increase in Brownian motion and thermophoresis parameters causes a rise in the temperature profile. Also, an increase in the activation energy parameter improves the solutal curve. The use of nanoparticles was shown to improve extrusion properties, the rotary heat process and biofuel generation. Originality/value All results are presented graphically and all physical quantities are computed and tabulated. The current results are compared to previous investigations and found to agree significantly with them.

A magnetohydrodynamic flow of a water-based hybrid nanofluid past a convectively heated rotating disk surface: A passive control of nanoparticles

Abstract One of the basic fluid mechanics problems of fluid flows over a revolving disk has both theoretical and real-world applications. The flow over a rotating disk has been the subject of numerous theoretical studies because it has many real-world applications in areas like rotating machinery, medical equipment, electronic devices, and computer storage. It is also crucial for engineering processes. Therefore, this article deals with a time-independent water-based hybrid nanofluid flow containing copper oxide and silver nanoparticles past a spinning disk. The Newtonian flow is taken into consideration in this analysis. The influence of magnetic field, thermophoresis, nonlinear thermal radiation, Brownian motion, and activation energy has been considered. The present analysis is modeled in a partial differential equation form and is then converted to ordinary differential equations using appropriate variables. A numerical solution using the bvp4c technique is accomplished using MATLAB software. The current results are matched with the previous literature and established a close relationship with previous studies. The purpose of this investigation is to numerically investigate the time-independent hybrid nanofluid flow comprising copper oxide and silver nanoparticles over a rotating disk surface. The results show that the increased magnetic parameters increase the friction force at the surface, which decreases the radial and azimuthal velocity distribution. At the sheet surface, the radial velocity of the hybrid nanofluid shows dominant performance compared to the nanofluid. On the other hand, the magnetic factor has dominant behavior on the azimuthal velocity component of the nanofluid flow compared to the hybrid nanofluid flow. The higher volume fraction and magnetic factor enhance the skin friction at the disk surface. Furthermore, greater surface drag is found for the hybrid nanofluid flow. The higher solid volume fraction, temperature ratio, and Biot number enhance the rate of heat transmission. Also, a higher rate of heat transmission is observed for the hybrid nanofluid flow.

A computation analysis with heat and mass transfer for micropolar nanofluid in ciliated microchannel: With application in the ductus efferentes

Inherited heat enhancement capabilities and their significance in the field of medical sciences and industry make nanofluids the focus of research nowadays. Furthermore, due to the remarkable advancements in bionanotechnology and its significance in biomedical fields such as drug delivery systems, cancer tumor therapy, bioimaging, and many others, it has emerged as a key research area. Contribution of cilia for the flow in ductus efferentes of human male reproductive tract is elaborated. A novel mathematical scheme is presented for the heat and mass transfer of MHD micropolar nanofluid transport in an asymmetric channel lined with cilia. The pertinent equations of nanofluid transport are exposed to lubrication approximation theory and solution for the physical problem is examined with efficient bvp4c technique in MATLAB. Fluid rheology is explored with the variations of different transport parameters like Hartmann number, Grashof number, Brownian motion, buoyancy, thermophoresis and Darcy number. It is reported that nanofluid transport is affected with rise in the Lorentz force and show reverse behavior with rising permeability. The temperature of the nanofluid in ciliated microchannel is raised with enhanced value of Hartmann number, Grashof number, Prandtl number, and Darcy number while diffusion phenomenon of nanofluid is slowed down with these parameters. Spinning motion of the nanofluid is enhanced with Grashof number and slow down with nanoparticle Grashof number and different behavior is recorded for Darcy and viscosity parameters in different flow regime. Reported investigation presents crucial findings for ciliary transport of micropolar nanofluid and tackled with appropriate selection of micropolar parameter, Brownian motion parameter, thermophoresis and Grashof number. Moreover, this investigation will be handful for cilia-based actuators which work as micro-mixers in controlling the flow in minute bio-sensors and may prove their worth in micro-pumps employed in various drug-delivery systems.

A numerical analysis of the rotational flow of a hybrid nanofluid past a unidirectional extending surface with velocity and thermal slip conditions

Abstract This work inspects 3D magnetohydrodynamic hybrid nanofluid flow on a permeable elongating surface. The emphasis of this paper is on the study of hybrid nanofluid flow within a rotating frame, taking into account the simultaneous impact of both thermal and velocity slip boundary conditions. The chosen base fluid is water, and the hybrid nanofluid comprises two nanoparticles Cu \text{Cu} and Al 2 O 3 {\text{Al}}_{2}{\text{O}}_{3} . The effect of the magnetic and porosity parameters is taken into account in the momentum equation. The thermal radiation, Joule heating, and heat source are considered in the energy equation. Using a similarity system, we transform the PDEs of the proposed model into ODEs, which are then solved numerically by the bvp4c technique. The magnetic field shows a dual nature on primary and secondary velocities. Enrich magnetic field decreases the primary velocity and enhances the secondary velocity. The rotation parameter has an inverse relation with both velocities. The temperature profile amplified with the escalation in heat source, magnetic field, rotation factor, and Eckert numbers. The skin friction is boosted with magnetic parameters while the Nusselt number drops.

Numerical study of Casson dusty hybrid nanofluid flow with volume fraction over a Darcy–Forchheimer porous medium

AbstractThis study develops a mathematical model for dusty Casson hybrid nanofluid flow over a vertical stretching sheet, considering the influence of volume fractions for the dust particles and nanoparticles, magnetic field and Darcy–Forchheimer penetrating medium. The nanoparticles used are TC4 (Ti‐6Al‐4V) and Nichrome (80% Ni and 20% Cr), suspended in unused engine oil (EO). The governing partial differential equations are transformed into ordinary ones using suitable transforms. Solutions are obtained numerically via the Matlab built‐in program Bvp4c technique and represent graphically the velocity, temperature, and concentration profiles for both the fluid and dust phases. Additionally, tabular forms present wall shear stress and heat transfer rate variations under different parameter values. It is found that the enhancing volume fraction parameter helps to boost the magnitude of shear stress, heat, and mass diffusivity.

Entropy generation analysis on hybrid dusty nanofluid flow over a heated stretching sheet: aerospace technology

Over the last few decades, many kinds of advanced substances that are acceptable for specific aerospace applications have been developed. An aircraft engine has a number of duties that are performed by kerosene oil. These responsibilities include oiling, air conditioning, servicing, preventing corrosion and reducing loudness. Maintenance is a matter of extreme importance. Without maintenance, it is only inevitable that any moving component might have the capacity to run away quickly. This project’s efforts are focused on reducing expenditures by extending the usable lifetimes of aviation components. Additionally, the initiative aims to improve fuel efficiency, load capacity and travel distance. The importance of the heat transfer investigation on MHD dusty hybrid nanofluid across a porous stretching sheet with entropy generation and thermal radiation is examined in the current research. We used the self-similarity transformation to transform the partial differential equation into ordinary differential equations. After applying transformations, for graphical purposes we have used the Bvp4c technique in MATLAB solver. The effect of active important parameters affecting the fluid’s capacity to transfer importance is shown in graphs and tables. For higher values of the magnetic field parameter, the velocity outline decreased, while the opposite nature was noticed in the energy profile. Based on our investigation, we found that mixed nanofluids are more effective in transferring energy carriers compared to dusty tiny fluids.

Buongiorno’s radiative Prandtl-Eyring nanofluid flow through porous medium over a stretching surface with cross-diffusion effects

The main focus of the current analysis is to describe the thermo-magnetic flow, heat and mass transport features of two-dimensional dissipative Prandtl-Eyring nanofluid (PE-NF) flow over a stretching sheet under the influence of porous medium and magnetic Ohmic dissipation numerically. An innovative Buongiorno’s nanofluid model in terms of Brownian motion and thermophoresis is deployed to accurately simulate the nano behavior in Prandtl-Eyring within the boundary layer regime. The thermal radiation and heat source/sink effects are also included to describe the thermal transport process. In addition to this, the thermo-diffusion and diffusion-thermo effect are included to demonstrate the temperature and concentration diffusion mechanism under the presence of chemical reaction process. The emerged coupled nonlinear two-dimensional time-independent partial differential equations are rendered to their dimensionless form through appropriate similarity transformations and solved by deploying Matlab-based BVP4C technique. The graphical visualization showed that, the increasing magnetic number diminished the flow field and enhanced the temperature and concentration profiles in the flow regime. Rising porous parameter decayed the Prandtl-Eyring nanofluid velocity. Increasing radiation and Eckert numbers enhance the temperature field in the flow regime. Magnifying Prandtl-Eyring parameter suppressed the velocity diffusion. Increasing Brownian motion and thermophoresis parameters increases the temperature profile. Amplifying Soret parameter upsurges the concentration profile. Skin-friction coefficient amplified with enhanced magnetic and porous numbers. Heat transfer rate acts as increasing function of thermophoresis and Brownian motion parameters. The main objective of this study is the addition of magnetic Ohmic dissipation, radiation, porous medium, thermal source/sink, Soret and Dufour effects and Buongiorno nanofluid model and this consideration generalizes former studies and gives a new re-defined mathematical formulation of heat and mass transport features of Prandtl-Eyring nanofluid flow over a stretching sheet. Finally, the numerical accuracy of the current similarity results is validated with available solutions and noticed a good agreement.

Magnetized dissipative Soret-Dufour effects on Walter’s-B fluid flow over a stretching sheet with nonuniform heat source/sink and thermal radiation under chemical reaction

The main motivation behind this numerical analysis is to disclose the salient magneto-thermo characteristic features of two-dimensional viscous incompressible magnetized Soret and Dufour effects on the boundary layer flow of Walter’s-B fluid over a stretching sheet under the influence of viscous dissipation. The novel physical effects such as nonuniform heat source/sink and magnetic Ohmic heating are included in the governing equations. Further, prescribed surface temperature condition is introduced in the boundary conditions to describe the thermal transport features. However, the deployed non-Newtonian Walter’s-B fluid rheology model finds its innumerable applications in numerous areas of science and engineering including electronic cooling, polymer processing, nuclear reactor cooling, extraction of polymer sheet, plastic sheet drawing, chemical engineering, metallurgy, injection molding and many more. Therefore, authors have motivated with these applications and advantageous of considered fluid model. Hence, an effort is made to describe the dynamic characteristic features of non-Newtonian Walter’s-B rheology model about a stretching sheet. However, present physical flow model produces highly nonlinear coupled two-dimensional partial differential equations and which are not acquiescent to available analytical methods. Owing to this, a robust MATLAB-based BVP4C technique is deployed to produce the appropriate numerical solutions through suitable similarity transformations. The graphical representations of velocity, temperature and concentration profiles along with skin-friction coefficient, Nusselt and Sherwood numbers are presented. Magnifying magnetic number decays the velocity profile and enhances the thermal and concentration fields. Rising viscoelastic parameter diminishes the thermal and concentration fields and magnifies the velocity field. Rising the radiation parameter diminish the thermal field. Magnifying Soret number raises the concentration field. Rising the space and temperature dependent heat source/sink coefficient amplifies the thermal diffusion field. Magnifying Dufour and Eckert numbers amplifies the thermal field. Finally, the guarantee and accuracy of the investigated problem is presented through a comparison with previous studies.

A numerical study of heat and mass transfer characteristic of three-dimensional thermally radiated bi-directional slip flow over a permeable stretching surface

Within fluid mechanics, the flow of hybrid nanofluids over a stretching surface has been extensively researched due to their influence on the flow and heat transfer properties. Expanding on this concept by introducing porous media, the current study explore the flow and heat and mass transport characteristics of hybrid nanofluid. This investigation includes the effect of magnetohydrodynamic (MHD) with chemical reaction, thermal radiation, and slip effects. The nanoparticles, copper, and alumina are combined with water for the formation of a hybrid nanofluid. Using the self-similar method for the reduction of Partial differential equations (PDEs) to the system of Ordinary differential equations (ODEs). These nonlinear equation systems are solved numerically using the bvp4c (boundary value solver) technique. The effect of the different physical non-dimensional flow parameters on different flow profiles such as velocity, temperature, concentration, skin friction, Nusselt and mass transfer rate are depicted through graphs and tables. The velocity profiles diminish with the effect of magnetic and slip parameters. The temperature and concentration slip parameters reduce the temperature and concentration profile respectively. The higher values of magnetic factor lessened the skin friction coefficient for both slip and no-slip conditions. An elevation in the thermal slip parameter reduced the boundary layer thickness and the heat transfer from the surface to the fluid. The Nusselt number amplified with the climbing values of the radiation parameter. The mass transfer rate depressed with the solutal slip parameter. Comparison is made with the published work in the literature and there is excellent agreement between them.

A computational investigation for heat and fluid transport with electro-osmosis phenomenon in a scraped surface heat exchanger

Scraped surface heat exchangers (SSHEs) have prominently shown their eminence in various food, chemical and in pharmaceutical industries when the regular processing of fluids and pertinent materials is encountered. The heat transfer analysis of Williamson fluid flow with electro osmotic effects in a narrow-gap SSHE is designed by implementing constant temperature difference between the gaps of the rotor and the stator. A fluid model is established by using lubrication approximation theory and Debye-Huckel simplifications. The computational solution is elaborated by implementing renowned BVP4C technique in MATLAB. Exact solution of Poisson-Boltzmann equation for different scenarios of SSHE is gathered, whereas solution for velocity, stream functions and temperature in various parts of SSHE are explored computationally. Impact of various crucial physical flow parameters like, Weissenberg number, mobility of the medium number, electro osmotic parameter on the velocity profile, stream function, temperature profile, and pressure gradient has been explored graphically. The numerical solution is compared with artificial neural network (ANN) and an absolute alignment of BVP4C solution is observed with ANN solution. It is reported that fluid flow is lifted with enhancing the viscoelastic behavior and exhibits dual behavior for electroosmosis phenomenon and mobility of medium parameter. Also, it is seen that temperature of the fluid is significantly declines with Weissenberg number and is surges with enhancing mobility of medium and Brinkman number. By increasing the Brinkman number conduction phenomenon is slow down and heat produced due to viscous dissipation, raises the temperature of the fluid. The viscoelastic effect could be of enormous significance in applications, like Polymer processing in certain heat exchangers, and in mixing and blending foodstuffs etc.

Applications of partial differential equations to transient heat and mass transfer in MHD flow over a porous medium

The flow problem discussed in this research is an investigation of compressible viscous fluid in an unstable 2D MHD laminar driven vortex and stable boundary layer flow, passing a heated stretched sheet at varying speeds via a porous medium exposed to a magnetic field with viscous dissipation, thermal diffusion, thermal radiation, chemical reaction and Dufour effects. With the aid of similarity transformations, PDEs that come out in governing equations of this formulations are converted into non-linear sets of ODEs. Well-defined bvp4c technique used to numerically solve these converted equations. With use of various graphs, the consequences of different factors on the distributions of velocity, temperature and concentration were examined numerically and graphically. Physical parameters for this issue are also discussed.

Optimization of heat transfer properties in micropolar ternary (Al2O3 + TiO2 + SiO2/water) nanofluid with porosity and magnetic field effects

Decades of study provide substantial evidence supporting that nanofluids possess improved heat transmission capabilities. Optimal qualities of nanoliquids may be achieved by manipulating the volume concentration of the nanoparticles. Nevertheless, this method has constraints due to the balance between negative and positive viscosity. A recent advancement has been produced in creating and thoroughly examining a particular form of hydraulic fluid that incorporates three solid nanoparticles scattered inside an existing fluid. This improvement aims to tackle this limitation. This study investigates the characteristics of a micro-rotational incompressible micropolar ternary hybrid nanofluid in a porous media. It considers the influence of magnetohydrodynamics, Darcy-Forchheimer, and linear thermal radiations on a stretched surface. The nanofluid consists mostly of water, which is blended with titanium oxide, aluminum oxide, and silicon oxide nanoparticles. Using dimensionless similarity transformations, the collection of higher-order non-dimensional partial differential equations is converted into higher-order ordinary differential equations. The BVP4C technique in MATLAB software is used to solve these equations and assess the graphical and tabular outcomes. The graphical analysis examines the influence of various physical characteristics. The heat transfer of a ternary hybrid nanofluid is significantly affected by many factors, including the Forchheimer coefficient, Prandtl number, thermal radiation parameter, and magnetic field parameters, as seen. The research demonstrates that an increase in the magnetic field and Darcy-Forchheimer parameters reduces linear momentum. Conversely, increased porosity, magnetic field, and radiation parameters increase the temperature profile.

MHD flow of second‐grade fluid containing nanoparticles having gyrotactic microorganisms across heated convective sheet

AbstractIn order to keep mechanical processes running smoothly, there is a growing need for effective heat transport. The present study aims to explore the variation of heat on time‐dependent maximum hydrodynamic drag (MHD) second‐grade nanofluids perceiving motile gyrotactic microbe with stretchable sheets. We process the analysis of the thermal energy distribution by using the convective boundary conditions. In addition to this, we take both the chemical reaction and the heat radiation into consideration. The governing nonlinear (PDEs) are converted into (ODEs) by a similarity transformation and then computed BVP4c technique. The multiple results are marked in the range of opposing flows only. Then, the effects of numerous physical variables on temperature, concentration, fluid velocity, and motile microorganisms are scrutinized using different graphical representations. The unsteady parameter and second‐grade fluid also strengthen for higher qualities, while inverse conduct is identified for a magnetic field framework. Finally, the temperature field cultivates a more significant assessment of the Biot number, and reverse behavior is observed for the Prandtl number. The obtained results are found appropriate to the existing literature.

Significance of Thompson and Troian slip effects on Fe3O4-CoFe2O4 ethylene glycol-water hybrid nanofluid flow over a permeable plate

This study aims to analyze the electromagnetic, hydro-thermal characteristics of hybrid nanofluid (Fe3O4-CoFe2O4/EG-water) flow over a permeable plate considering the Thompson and Troian slip, and suction/injection effects. By employing suitable similarity transformations, the governing partial differential equations (PDEs) describing the flow are converted into a set of highly nonlinear ordinary differential equations (ODEs). These transformed equations are computationally solved using the “bvp4c technique” in MATLAB. The detailed graphs illustrate the impact of various factors for instance, the Hartmann number, electric parameter, velocity slip parameter, critical shear rate, permeability parameter, heat generation/absorption parameter and suction/blowing parameter on velocity and temperature distributions. Also, the tabular data facilitates a detailed quantitative examination of these influences. The velocity and temperature profiles exhibit opposite nature influenced by factors such as the Hartmann number, velocity slip, critical shear rate, permeability parameter, and suction/blowing effects. Furthermore, as the critical shear rate, velocity slip, permeability and suction/blowing parameters increase, so do the absolute values of the Nusselt number. Conversely, higher heat generation/absorption parameter and Eckert number cause a decrease in these absolute values.

Thermally radiative flow of MHD Powell-Eyring nanofluid over an exponential stretching sheet with swimming microorganisms and viscous dissipation: A numerical computation

This work deals with the study of mass and heat transmission in nanofluid flow in the Powell-Eyring model over a sheet that is exponentially stretched with motile microorganisms. Additionally, viscous dissipation and radiation sources are considered. The governing flow expressions are remodeled into nonlinear ordinary differential equations by implementing the appropriate transformations. The remodeled equations are numerically computed by using the bvp4c technique via MATLAB. The various flow parameters are used to investigate and explain in depth the nanofluid velocity, thermal, nanoparticle volume fraction, and motile microbe density profiles. It is noted that the nanofluid velocity decreases with enlarging the values of the magnetic field parameter. The fluid thermal profile develops for greater quantities of radiation thermophoresis and Brownian motion parameters. The nanoparticle concentration decays when the Prandtl number and Lewis number are increased. The motile microbe density profiles suppress when heightening the values of the Peclet number, bioconvection Lewis number, and bioconvection parameter. The magnetic field parameter leads to a decrease in local skin friction, heat, and mass transfer rates.

Stability analysis of Reiner–Philippoff nanofluid flow due to sinusoidal waves past a nonuniform channel with Brownian and thermophoretic diffusions

The need for understanding peristaltic flow (PF) is growing frequently because of its applicability in several scientific and technical domains, particularly in biological and medical field. The primary objective of this analysis is to examine the PF in tapering network considering Reiner–Philippoff nanofluid (RPF-NF) under the influence of pseudoplastic fluid (PF) and dilatant fluid (DF) performance. In order to examine the heat and mass transportation inquiry, Buongiorno’s nanofluid model (BNFM) is taken into consideration. The suitable alterations are taken to transform the channel from static reference to stirring frame and, then used the dimensionless variables to transform the moving frame to dimensionless form. Since the Reynolds number (RN) is small and the wavelength is long, the underlying equations are simplified. The statistical consequences are gained through bvp4c technique. The motivation of the physical features on the liquefied crescendos is particularized using graphs as well as tables. For the immovability exploration, eigenvalues are figured. The lowest positive eigenvalues suggest the reliable resolutions; however, the negative eigenvalues denote the unreliable solution. It has been shown that altering the RPF parameter causes the velocity of fluid to switch from a dilatant liquid to a Newtonian fluid and from Newtonian to Pseudoplastic. The results show that the temperature curves ascend with increasing Brownian motion and thermophoretic factors and decrease with increasing Prandtl number. Additionally, a brief mathematical and graphical investigation of the effects of each key parameter on the flow characteristics is conducted.

Numerical heat transfer analysis of bio convective flow of non-Newtonian nanofluid with Darcy-Forchheimer effect over a curved stretching surface

The main aim of this study is to investigate the behavior of bio-convective flow of 2nd grade micropolar nanofluid with Darcy-Forchheimer law over a curved porous stretching surface. The fluid flow analysis includes novel aspects such as the nonuniform heat source/sink, Joule heating, magnetic field, chemical reaction, and thermal radiation. Furthermore, the boundary of the stretching surface is acquired the stratification conditions. A suitable conversion method is employed to transform the flow model into a collection of ordinary differential equations, characterized by their nonlinearity. The bvp4c technique on the MATLAB is utilized to acquire numerical solutions for this set of nonlinear equations. The characteristics of various influential parameters on the velocity, temperature, concentration, and microorganism density profiles are observed and discussed. In the present problem, it is observed that by the growth of micropolar parameter enhances the angular fluid velocity. Moreover, larger values of the magnetic parameter, Darcy number, and porosity parameter result in a decrease in the fluid’s linear velocity. The temperature profile exhibits a decreasing pattern with the elevation thermal stratification parameter, while the opposite trend shows by the increment of the radiation parameter and Eckert number. Additionally, the concentration of nanoparticles decreases as the Schmidt number and Brownian motion parameter increases.

Heat and Mass Transformation of Casson Hybrid Nanofluid (MoS2 + ZnO) Based on Engine Oil over a Stretched Wall with Chemical Reaction and Thermo-Diffusion Effect

This study investigates the potential of a hybrid nanofluid composed of MoS2 and ZnO nanoparticles dispersed in engine oil, aiming to enhance the properties of a lubricant’s chemical reaction with the Soret effect on a stretching sheet under the influence of an applied magnetic field. With the growing demand for efficient lubrication systems in various industrial applications, including automotive engines, the development of novel nanofluid-based lubricants presents a promising avenue for improving engine performance and longevity. However, the synergistic effects of hybrid nanoparticles in engine oil remain relatively unexplored. The present research addresses this gap by examining the thermal conductivity, viscosity, and wear resistance of the hybrid nanofluid, shedding light on its potential as an advanced lubrication solution. Overall, the objectives of studying the hybrid nanolubricant MoS2 + ZnO with engine oil aim to advance the development of more efficient and durable lubrication solutions for automotive engines, contributing to improved reliability, fuel efficiency, and environmental sustainability. In the present study, the heat and mass transformation of a Casson hybrid nanofluid (MoS2 + ZnO) based on engine oil over a stretched wall with chemical reaction and thermo-diffusion effect is analyzed. The governing nonlinear partial differential equations are simplified as ordinary differential equations (ODEs) by utilizing the relevant similarity variables. The MATLAB Bvp4c technique is used to solve the obtained linear ODE equations. The results are presented through graphs and tables for various parameters, namely, M, Q, β, Pr, Ec, Sc, Sr, Kp, Kr, and ϕ2* (hybrid nanolubricant parameters) and various state variables. A comparative survey of all the graphs is presented for the nanofluid (MoS2/engine oil) and the hybrid nanofluid (MoS2 + ZnO/engine oil). The results reveal that the velocity profile diminished against the values of M, Kp, and β, and the temperature profile rises with Ec and Q, whereas Pr decreases. The concentration profile is incremented (decremented) with the value of Sr (Sc and Kr). A comparison of the nanofluid and hybrid nanofluid suggests that the velocity f′ (η) becomes slower with the augmentation of ϕ2* whereas the temperature increases when ϕ2* = 0.6 become slower.