Darcy Forchheimer Medium Research Articles

Optimal homotopy analysis of unsteady second-grade tri-hybrid nanofluid flow with radiative impact between parallel disks

The research explored the critical examination of unsteady second-grade Tri-hybrid nanofluid flow between parallel disks within a Darcy-Forchheimer medium with porosity. The study focusses on a fluid comprised of Au, TiO2, and Ag solid nanoparticles within blood, encompassing various shapes such as brick, blade, and platelet. It thoroughly investigated the impacts of Soret and Dufour effects in conjunction with MHD, joule heating, and the presence of a heat source. Furthermore, it elucidated thermally radiative effects and considers slip and convective boundary conditions, as well as mass transfer with a chemical reaction. The research also encompassed the influence of suction/injection on the squeezing flow. As the second-grade fluid parameter increases, the velocity of the fluid rises, especially when the η < 0.4. However, when η > 0.4, the velocity decreases. Additionally, the Biot numbers exhibit different effects depending on their application to the lower and upper disks. Specifically, Bi1 enhances the system's temperature, while Bi2 reduces it. The comprehensive mathematical formulation incorporates all these effects, later transformed into ODEs using similarity transformation conditions. Employing the optimal homotopy analysis technique in Mathematica software, the study graphically characterized velocity, temperature, and concentration profiles. The research's credibility is ascertained through validation against previous work by other researchers.

Melting rheology of Prandtl Eyring hybrid nanofluid flow with slip condition past a Riga Wedge through Darcy-Forchheimer medium

The current matter examines the 2D flow of Prandtl Eyring hybrid (Al2O3+Cu/SA) nanoliquid through a porous media with a velocity slip mechanism along the melted Riga wedge. A combination of Alumina (Al2O3) and Copper (Cu) nanoparticles in a sodium alginate (SA) base liquid is called a hybrid nanofluid. Furthermore, the physical meaning of the flow behavior is explored with Darcy-Forchheimer. Heat sink/source, nonlinear thermal energy, and viscous dissipation, applications all need the computation of heat transference. The current flow problem is modelled in the system of highly nonlinear PDEs based on flow assumptions. We use an appropriate similarity transformation to turn these PDEs into ODEs. We simulate the obtained paired nonlinear higher-order ODEs employing the ideas from the bvp4c Matlab scheme. With the help of the graphics, several physical dimensionless factors are discussed and their unique effects on the flow profile are shown. One of the study's most notable findings is that applying boundary slip and Riga impact can increase velocity because of weak electromagnetic forces. At lower velocities, wedge flow through a Darcy-Forchheimer medium is primarily driven by viscous resistance under Darcy's law, with little in the way of inertial forces. It is also noteworthy that the temperature differential, thermal radiation, nanoparticle volume percentage, and Eckert number all enhance the nanoliquid thermal profile in both Prandtl Eyring fluid and hybrid nanofluid. The Nusselt number is increased for both the melting and fluid parameters.

Analysis of Darcy–Forchheimer flow of magnetized hybrid nanofluid (MoS 2+ZnO/E) with non-linear heat source and quartic autocatalytic chemical reaction

In this article, an effort is made to analyze the 3 − D flow of hybrid nanofluid over a rotating stretching sheet. The hybrid nanofluid contains engine oil as a base fluid amalgamated with nano-particles Mo S 2 and ZnO . The flow is assumed to pass through a Darcy–Forchheimer medium subjected to the influence of an inclined magnetic field. In addition, heat radiation, Joule heating, viscous dissipation, nonlinear heat source, and quartic autocatalytic chemical reaction are applied to discourse heat and mass transfer features. The PDEs representing the physical problem are converted to ODEs with the introduction of similarity transformations. The solution of the problem is determined numerically by using MATLAB built-in bvp4c method. The proposed mathematical model’s validation is ascertained by comparing it with an earlier study in limiting case. In this regard, an excellent consensus is accomplished. The current investigation reveals that the flow along axial direction gets retarded by enhancing the values of rotational parameter, inertial parameter, and magnetic parameter, whereas the flow along radial direction gets accelerated. The increasing value of angle of inclination admirably resists the motion of nanofluid and hybrid nanofluid. The concentration profile gets decreased under the increasing influence of inclination angle and Schmidt number while it enhances for homogeneous reaction parameter. The enhancing values of rotational parameter, solid volume fraction and temperature, and exponential dependent heat generation parameters enhance the value of Nusselt number.

Heat transfer in radiative hybrid nanofluids over moving sheet with porous media and slip conditions: Numerical analysis of variable viscosity and thermal conductivity

Our current numerical investigation aims to estimate the thermal transport properties of hybrid nanofluids on a moving surface that is being shrinked horizontally. The hybrid nanoparticles consist of alumina (Al2O3) and copper (Cu), suspended in water as the base fluid. The transportation phenomenon takes place in a Darcy-Forchheimer medium, which is a porous material that exhibits thermal radiation, variable viscosity, variable thermal conductivity, Joule heating, viscous dissipation, and the effects of velocity and thermal slip conditions. The governing partial differential equations (PDEs) are converted using suitable similarity transformations into non-linear ordinary differential equations (ODEs). The equations were solved using the shooting technique with the RK-IV algorithm in the MATHEMATICA program. Dimensionless velocity, temperature, skin friction, and Nusselt numbers all provide numerical outcomes. Graphs and tables show the results of an investigation into the influence of different physical characteristics on these numbers. The velocity profile exhibits an upward trend when the velocity slip and nanoparticles volume fraction rise, but a downward trend when the viscosity and Prandtl number are varied. if the thermal slip and variable Prandtl number grow, the temperature profile falls. Conversely, if the nanoparticles volume fraction and variable thermal conductivity increase, the temperature profile increases. The skin friction and Nusselt number exhibit an upward trend as the volume percentage of nanoparticles and the viscosity of the system rise. At a Prandtl number of 6.2 and a nanoparticle volume fraction of 1 %, the Xue model demonstrates a heat transfer rate increase that is 5.32 % superior to the Yamada-Ota model and 3.18 % superior to the Hamilton-Crosser model for nanofluid. In the case of hybrid nanofluid, the Xue model exhibits a 19.01 % superiority over the Yamada-Ota model and 12.197 % superior to the Hamilton-Crosser model.

A numerical investigation of the chemically reactive maxwell nanofluid flow over a convectively heated rotating disk using Darcy–Forchheimer porous medium

This study investigates the convective heat transfer characteristics in the vicinity of a stagnation point for the flow of Maxwell nanofluid over a porous rotating disk. The analysis takes into account the complex inert-active effects arising from nonlinear thermal radiation, activation energy, and the presence of a Darcy–Forchheimer medium. Through numerical simulations, the enhancement of heat transfer due to the addition of nanoparticles is explored, considering their impact on heat transport. The rotational and porous characteristics of the disk, coupled with nonlinear thermal radiation and activation energy effects, are crucial factors in shaping the overall heat transfer behavior. The study aims to provide valuable insights into the complicated interactions of these phenomena, contributing to the understanding of advanced heat transfer processes and their potential applications in various engineering systems. Using suitable variables to convert the system of leading equations to dimensionless form has then been evaluated by employing the bvp4c approach. It has been revealed that Radial flow has retarded with an upsurge in Deborah number, inertial factor, and porous factor while has upsurge with growth in rotational factor. Angular velocity has declined with higher values of Deborah number, and porous factor and has upsurged with escalation in inertial and rotational factors. Azimuthal flow has weakened with an upsurge in porous factor and has augmented with growth in Deborah number, inertial factor, and rotational factor. Thermal profiles have augmented with an upsurge in rotational, porous, inertial, thermophoresis, Brownian, and radiation factors, and Deborah number has declined with growth in the Prandtl number. Concentration distribution has declined with an upsurge in Schmidt number, Brownian motion factor, rotation factor, and porous factor, while has grown with the escalation in chemically reactive, thermophoresis, inertial factors, and Deborah number.

Magnetohydrodynamic thermo-bioconvective flow of 3D rotating Williamson nanofluid with Arrhenius activation energy in a Darcy–Forchheimer medium over an exponentially stretching Surface

This paper aims to analyze the heat and mass transfer characteristics of the 3D thermo-bioconvective flow of rotating Williamson nanofluid over an exponentially stretching vertical sheet. The flow distribution considers the influence of nonlinear thermal radiation, Hall and ion-slip currents, joule heating, coupled effects of Dufour and Soret diffusion, internal heat generation, Arrhenius activation energy, Brownian, and thermophoresis diffusion in a Darcy–Forchheimer porous medium. The modeled partial differential equations (PDE) in terms of continuity, momentum, energy, concentration, and density of motile microorganisms are reformed into ordinary differential equations (ODE) forms employing similarity variables. The resulting equations are solved numerically using the spectral local linearization method (SLLM). The successive over-relaxation technique is applied to accelerate and enhance the convergence of the method. The obtained results are graphically and tabularly represented and numerically explored for the effects of pertinent parameters on the velocity, temperature, nanoparticle concentration, and motile microorganism concentration profiles. The rotation and mixed convection parameters dropped the primary velocity curve, while the Williamson and heat source parameters uplifted the microbes density distributions. The temperature field rises with an increase in radiation and microbes Brownian motion and declines with an increase in Hall and ion-slip numbers. Furthermore, with the increase in activation energy from 0.5 to 2 and the mixed convection parameter from 0.6 to 1.3, we observe a respective 3.93% rise and 8.30% fall in mass transfer rates. The current investigation has broad applications, including MHD accelerators, biotechnology, the formation of elastic sheets, the production of polymer solutions, and the synthesis of nanoparticles through microbial processes.

Thermal enhancement in magnetized flow of [formula omitted] nanolubricant over a rotating sphere influenced by nonlinear heat generation and thermal radiation

The nanolubricant ZnO−SAE50 is essentially used in a range of industries, including electronics, renewable energy, automotive, and aerospace. Due to its distinct thermal and lubricating characteristics, it can serve a variety of purposes and has the potential to revolutionize a number of technological fields. The prime motive of this study is to introduce ZnO−SAE50 nanolubricant as a flow fluid around a rotating sphere immersed in a Darcy-Forchheimer medium. To control and direct the flow to the desired direction, an external magnetic field is employed. The thermal performance is assessed considering the effects of thermal radiation, nonlinear heat generation and Joule heating. A MATLAB's built-in solver bvp-4c is used to solve the achieved model numerically. The findings disclose that the implementation of an external magnetic field is quite advantageous in adjusting and directing the fluid flow. In order to achieve an excellent thermal performance, the role of thermal radiations and nonlinear heat generation is pivotal. Furthermore, ZnO−SAE50 nanolubricant maximizes heat transmission while conventional SAE50 is ineffective in achieving optimum heat transfer rates.

Darcy-Forchheimer flow of bioconvective nanofluid over a nonaligned stretching surface with slip effects

The primary objective of this investigation is to explore the effects of velocity and nanoparticle slip mechanism on the hydrodynamic behavior of the Darcy-Forchheimer flow of nanomaterials where the blend of (Fe2O3−H2O) (50%−50%) was used as a working fluid. The bioconvection flow of multi-diffusive nanofluid fluid across sheet surface is investigated taking the consequences of oxytactic microorganisms. The Brownian motion and thermophoretic phenomena is explored using Buongiorno slip mechanism theory while the Tiwari Das model incorporate the volume percentage of nanoparticles. The Darcy-Forchheimer medium appears at the sheet surface that permits the flow in the horizontal direction with the effects of permeability and drag. The flow is subjected to first and second order slip and radiative heat transfer. The action of gyrotactic microbes is supported by bioconvection, which strengthens the phenomena of mass transfer. The fundamental governing equations resulting from computational modelling are turned into ordinary differential equations using suitable rescaling variables. The identified complicated equation was numerically solved using the Runge-Kutta-Fehlberg fourth order procedure with shooting techniques. The volume friction of the nanoparticles and the Knudsen number accelerate the stretching and nonaligned velocities field of the nanofluid. The Darcy number, on the other hand, slows down the velocities near the sheet surface. The temperature profile rises against thermal radiation and volumetric friction, while an inverse tendency is found with higher Prandtl number magnitude. The concentration profile of nanoparticles advances through the thermophoresis parameter. The bioconvection Lewis number and the Peclet number shrink the density profile of gyrotactic motile microbes.

Thermal analysis of magnetized [formula omitted] nanolubricant flow in a Darcy-Forchheimer porous medium with nonlinear heat generation

The nanolubricant ZnO−SAE50 is widely used in automobiles and heat exchange systems to minimize friction and resist corrosion and scrape between moving parts. It also improves system's performance and durability and cuts fuel consumption. In this work, the flow of magnetized ZnO−SAE50 nanolubricant is analyzed over a flat plate with variable temperature immersed in a Darcy-Forchheimer medium. The thermal analysis is carried out in the occurrence of nonlinear heat generation and thermal radiation. Furthermore, the influences of viscous dissipation and Joule heating have also been deliberated. A micro-nano convection model named as Patel model of thermal conductivity has been used in view of rise in thermal conductivity. The governing PDEs are altered to ODEs with the incorporation of similarity transformations and then numerically treated by using an eminent MATLAB's built-in bvp4c method. The influences of different physical parameters on velocity, temperature and Nusselt number are discussed and analyzed graphically and in tabular form. The velocity profile diminishes under the impacts of inertia coefficient and magnetic field. The temperature and exponential dependent heat generation parameters considerably enhance temperature of the nanolubricant ZnO−SAE50. The temperature power coefficient tends to reduce the temperature profile. The enhancing strength of thermal radiations and nonlinear heat generation significantly enhance the value of Nusselt number. Furthermore, an increase in the value of temperature dependent heat generation parameter from 0.2 to 0.6 tends 12.37% increment in the value of Nusselt number in conventional SAE50oil, whereas the nanolubricant ZnO−SAE50 experiences a more significant 26.72% increment in the value of Nusselt number. Thus, better heat transmission rate can be achieved by using ZnO−SAE50 nanolubricant rather than conventional SAE50 oil.

Microrotating chemically reactive hybrid nanomaterial in a high porous medium influenced by Cattaneo-Christov double diffusion and non-linear slip

ABSTRACT A simultaneous heat and mass transfer due to microrotating Darcy-Forchheimer flow of hybrid nanofluid over a moving thin needle is investigated. Darcy-Forchheimer medium accommodating hybrid nanofluid flow yields greater heat transfer rate, thereby leading to greater mass transfer rate over thin needle in industrial applications such as blood flow problems, aerodynamics, transportation, coating of wires, lubrication, and geothermal power generation. The thermophoresis and Brownian motion phenomena are introduced to enrich thermal treatment. Heat and mass transfer are accompanied by Cattaneo-Christov heat and mass flux. The hybrid nanofluid is radiative and dissipative in nature. Arrhenius pre-exponential factor law is introduced. Entropy generation analysis is carried out. The 4th order Runge-Kutta method along with shooting technique is devised to get requisite numerical solution of the transformed non-dimensional system of equations. Darcy-Forchheimer effect to simultaneous heat and mass transfer of microrotating hybrid nanofluid flow over thin needle subject to non-linear slip is the novelty of present study which is beyond of previous investigations. Rise in Forchheimer number (strengthening Darcy Forchheimer medium) leads to surface viscous drag decreases by 11.11% for hybrid nanofluid and 10.78% for pure nanofluid indicating the control of momentum transfer, thereby regulating heat transfer rate effectively.

Impacts of Joule heating and dissipation on magnetohydrodynamic ternary-hybrid nanofluid (Al2O3-TiO2-SiO2/H2O) flow over an elongated sheet with Darcy–Forchheimer medium

Thermal transfer enhancement plays a crucial role in various fields of science and engineering. The trihybrid nanofluid, which demonstrates an enriched heat transmission rate has gained increasing attention due to its pivotal role in energy transport systems, particularly in nuclear reactors, heat exchangers, etc. Stimulated by its applications, the dynamics of hydromagnetized, radiative trihybrid nanofluid [Formula: see text] in a Darcy–Forchheimer flow via an elongated sheet has been comprehensively researched in this study. The energy equation is modeled by simultaneously incorporating viscous dissipation, ohmic heating, and thermal generation/absorption, which boosts the novelty of this investigation. Through the use of similarity variables, the major controlling equations of the model are transformed into dimension-free ordinary differential equations, which are numerically handled via the bvp4c package in MATLAB. A comparative sketch is drawn between the nanofluid, hybrid nanofluid, and trihybrid nanofluid to compute the thermal efficacy. It is perceived that the thermal transfer rate of [Formula: see text] dominates over the hybrid nanofluid to a least of 2% and to a supreme of 3.2% for diverse values of magnetic parameters, while it differs between the ranges of 1.9%–3% for varying porosity parameters. The upshot of this research suggests that triple nanoparticle dispersion results in an enhanced thermal transport mechanism compared to dual and mono nanomaterial dispersion. Research presented in this article has stupendous practical value, particularly in the manufacturing and engineering sectors, which rely on the enhanced rate of thermal transmission.

Second law analysis on cross flow of hybrid nanoliquid in a Darcy–Forchheimer medium with thermal radiative flow

This article’s objective is to examine the optimization of entropy in Darcy–Forchheimer cross-hybrid nanofluids as they flow toward a stretchy surface. There is a current because the surface is being stretched. The energy equation is broken down into its component parts including thermal radiation, heat source sink, and convective flow. In this case, copper oxide ( CuO ) and titanium dioxide ( TiO 2 ) are taken into consideration as nanoparticles, while engine oil (EO) is taken into consideration as a continuous phase fluid. In addition, we carried out an investigation into the relative performance of copper oxide ( CuO ) and titanium dioxide ( TiO 2 ) while they were suspended in water engine oil. The application of the second law of thermodynamics allows for the calculation of the rate of entropy optimization. Using a suitable transformation, nonlinear partial differential equations can be transformed into a standard system. In this work, we use the numerical built-in BVP4c solution method to generate numerical results for the derived nonlinear flow equation. Both copper oxide ( CuO ) and titanium dioxide ( TiO 2 ) undergo a graphical analysis of the effects of varying technical factors on entropy optimization, velocity, the Bejan number, and temperature. Numerical computations of the skin friction coefficient and Nusselt number for a range of fascinating parameters are performed for both nanoparticles ( TiO 2 and CuO ) . It is clear from the data that entropy optimization improves as the size of the radiation and porosity estimates reduces. The porosity parameter exhibits direct relationships to both temperature and velocity. Tabular comparisons of the current study with the previously published literature show a high degree of agreement. Copper and titanium oxide nanoparticles are used to increase Engine oil ( EO ) thermal enactment, making it a more useful base fluid. Further, some significant industrial and engineering applications are related to the present problem discourse.

Numerical simulations of Darcy-forchheimer flow of radiative hybrid nanofluid with Lobatto-IIIa scheme configured by a stretching surface

Heat transport and energy storage continue to be major issues for manufacturers and scientists. So far, the notion of novel heat transfer fluids has been developed, namely nanofluids and hybrid nanofluids. This investigation examines thermal radiation effect on heat transfer in MHD flow using the hybrid nanofluid. It examines a hybrid nanofluid (SWCNT-Al2O3/H2H6O2–H2O and MWCNT-CuO/H2H6O2–H2O) with H2O water base fluid nature passing through a starching surface with thermal radiation, Biot number and melting phenomena. The suitable similarity transformations are used to transmute the main governing system of equation PDEs and the appropriate boundary conditions for computation with the help of well-reputed shooting technique. The graphical and numerical outcomes against dissimilar flow parameters are computed by the mathematical software MATLAB. The velocity distribution profile is decreased by growing values of the Rotation parameter and porosity parameter. The velocity profile is enhanced by increasing the values of Darcy forchheimer medium. The thermal distribution field is enhanced by rising estimations of the thermal radiation parameter and Biot number. Temperature of the fluid is increasing due to increase in thermal conductivity parameter while decreasing due to increase in Marangoni ratio parameter. The present model hybrid nanofluid of heat transmission is evaluated to see if it has higher thermal energy storage efficiency than standard nanofluids. As a result, these novel findings in heat transport might be advantageous in dealing with energy storage issues in the modern technological environment.

Three dimensional flow of Cross nanofluid over bidirectional moving surface in Darcy-Forchheimer medium with Cattaneo-Christov heat flux

The main purpose of this study is to present the mathematical modeling of steady three dimensional boundary layer flow of incompressible non-Newtonian Cross nanofluid over a bidirectional stretching surface. The Buongiorno nanofluid model and Cattaneo-Christov heat flux model are also assumed in present work. It is considered that bidirectional stretching sheet is embedded in Darcy-Forchheimer porous media. Additionally, the motion of fluid flow is induced due to the bidirectional stretching surface. Boundary layer theory is invoked to model the basic partial differential equations of current study. The modeled partial differential equations are reduced to ordinary differential equations with the assistance of appropriate transformation and then solved numerically through Runge Kutta Fehlberg scheme along shooting method. The ranges of involved physical parameters in present study can be explained as 0≤βT≤0.08,0≤βC≤0.25,0≤Fr≤6.0,0≤β≤4.0,0≤We₁≤1.0,0≤We₂≤1.5,0≤Nt≤0.4,0.1≤Nb≤1.2,0≤n≤2,0≤δ≤1.2,0.7≤Pr≤6.2,1≤Sc≤7. It is engrossing to reveal that surface mass transfer rate is an aggrandizing function of concentration relaxation parameter but reverse behavior is noticed for enrich thermal relaxation parameter. Additionally, fluid velocities f′(η) and g′(η) reduce due to the improvement of Forchheimer number and porosity parameter. Furthermore, magnitudes of the surface drag forces along x− and y− directions grow for larger approximation of Weissenberg numbers.

Melting rheology of three-dimensional Maxwell nanofluid (graphene-engine-oil) flow with slip condition past a stretching surface through Darcy-Forchheimer medium

Nanofluid has numerous industrial and engineering applications, especially for the improvement of heat transmission. Engine oil is a highly versatile lubricant that is extensively used across diverse industries and engineering fields for a wide range of applications. The applications of engine oil are the aerospace industry, automotive industry, marine industry, power generation, construction and mining, manufacturing and machinery, railroad and transportation, agriculture, etc. Therefore, in the existing problem, 3D flow of Maxwell nanoliquid along the stretched sheet through the porous medium with a melting heat transport mechanism is studied. Nanofluid is made by a mixture of graphene nanoparticles in the engine oil base liquid. Additionally, the physical significance of the Darcy-Forchheimer is discussed on the flow behavior. The computation for heat and mass transference is performed due to the applications of thermal radiation, heat source/sink, Brownian and thermophoresis diffusivity, and chemical reaction. Simulation of the existing model is made by using the idea of velocity slip conditions along with convective boundary and zero mass concentration conditions. In the flow analysis, the magnetic effect is applied normally to the surface, therefore, the features of the magnetic field are studied. On the basis of flow assumptions, the current flow problem is modeled in the system of highly nonlinear PDEs. Appropriate similarity transformation is exploited for the conversion of these PDEs into ODEs. By using the concepts of the Homotopic method (HAM), the attained coupled nonlinear higher-order ODEs are simulated. The graphs are used to discuss how numerous physical factors affect the flow profile, highlighting their distinctive characteristics. Several noteworthy findings of this study are that both primary and secondary velocities declined due to the Lorentz force by using the applications of magnetic impact. Also, it is distinguished that the nanoliquid thermal profile is amplified for the thermal Biot number. Also, the nanoliquid concentration is lesser for the greater Schmidt number. The present nanofluid problem is also investigated for its significant practical applications. Further, it is examined that the Nusselt number is greater for the thermal Biot number.

Heat and mass transfer analysis for magnetized flow of {mathrm{ZnO}-SAE50} nanolubricant with variable properties: an application of Cattaneo–Christov model

The current study scrutinizes heat and mass transfer features of magnetized flow of {mathrm{ZnO}-SAE50} nanolubricant over Riga plate in a Darcy Forchheimer medium. The effects of variable viscosity, thermal radiation, variable thermal conductivity, viscous dissipation and uniform heat source/sink are examined in this study. The diffusion model presented by Cattaneo–Christov is incorporated in this study to enclose heat and mass transport phenomenon. Additionally, the mass transfer rate is inspected subjected to the effects of variable solutal diffusivity and higher order chemical reaction. Heat and mass transfer phenomena have significant applications in the disciplines of science and technology that can be seen everywhere in nature. This simultaneous transportation phenomenon indicates a variety of applications in manufacturing processes, aerodynamics, cooling systems, environmental sciences, oceanography, food industries, biological disciplines, and energy transport systems etc. The modeled system of PDEs is metamorphosed to nonlinear ODEs with the introduction of appropriate transformations. An eminent bvp4c method in MATLAB has been incorporated to execute the resulting system of ODEs numerically. The outcomes of velocity, temperature and concentration profiles corresponding to various emerging parameters have been exposed graphically. The motion of {mathrm{ZnO}-SAE50} nanolubricant tends to enhance significantly with larger modified Hartmann number, whereas converse behavior is reported by increasing porosity parameter and variable viscosity parameter. The greater heat transfer rate is observed for variable thermal conductivity parameter. The rates of heat and mass transfer slow down for thermal and solutal time relaxation parameters respectively. The concentration profile gets enriched by growing the order of the chemical reaction and variable mass diffusivity parameter. It is concluded that by increasing solid volume fraction up to 1.5%, the viscosity of the nanolubricant enhances up to 12% which consequently slows down motion of the nanolubricant but increases temperature and concentration profiles.

Numerical treatment of MHD Al2O3–Cu/engine oil-based nanofluid flow in a Darcy–Forchheimer medium: Application of radiative heat and mass transfer laws

This computational study was designed to examine the effect of alumina and copper on the flow of a nanofluid based on engine oil through a Darcy–Forchheimer porous media. The flow model incorporates the generalized radiative heat and mass transport rules. The Darcy–Forchheimer terms in the momentum equation and radiation term in the energy equation are integral parts of the governing nonlinear Navier–Stokes equations, which are two-dimensional partial differential equations. Under the constraint of the convective boundary, the stated PDEs are transformed into highly nonlinear versions of the ordinary differential equations. In order to solve the final ODEs, the numerical RK-45 approach is combined with the shooting methodology. Important aspects of the governing model include porosity, magnetohydrodynamics (MHD), a convective boundary, thermal radiation, and viscous dissipation. The final findings show that when the Forchheimer number increases, the velocity decreases because of the inertial effect included in the flow model. In addition, the velocity profile is improved due to the increased volume percentage of both kinds of nanoparticles. The temperature varies greatly depending on the volume fraction. A higher Biot number and the resulting convective border cause a greater heat flow than a non-convective barrier. For two particular examples, with and without MHD influence, interesting streamlines and contour graphs are produced.

Analytical and numerical investigation of Darcy-Forchheimer flow of a nonlinear-radiative non-Newtonian fluid over a Riga plate with entropy optimization

The effects of the Riga plate flow of Williamson fluid with a Darcy-Forchheimer medium and suction/injection are explained in this study. Convective heat and mass circumstances are considered. The energy and concentration equations are developed using Catteneo-Christov dual theory. The heat transfer attributes are analyzed via heat consumption/generation. To estimate total entropy creation, the second law of thermodynamics is applied. The governed mathematical models are transmuted into an ODE model by adopting befitting variables. The MATLAB bvp4c algorithm and the HAM scheme are used to solve these problems numerically and analytically. Novel attributes of various physical parameters are debated through graphs, charts and tables. The fluid flow speed decelerates when enlarging the Weissenberg number and porosity parameters. The fluid temperature enriches when enhancing the radiation parameter. The chemical reaction parameter leads to suppresses the fluid concentration. The higher quantity of heat consumption/generation parameter enriches the heat transfer gradient. The mass transfer gradient accelerates due to more presence of the chemical reaction parameter. We also compared numerical and analytical results and found them in good agreement. When the values of the radiation parameter, Brinkman number, and Reynolds number are increased, the entropy generation increases. The Bejan number downturns when enlarging the modified Hartmann number.

Irreversibility analysis of radiative flow of Prandtl nanofluid over a stretched surface in Darcy-Forchheimer medium with activation energy and chemical reaction

This communication elaborates the irreversibility analysis of the flow of Prandtl nanofluid along with thermal radiation past a permeable stretched surface embedded in a Darcy-Forchheimer medium. The activation and chemical impressions along with effects of thermophoretic and Brownian motion are as well examined. The flow symmetry of the problem is modeled mathematically and leading equations are rehabilitated into nonlinear ordinary differential equations (ODEs) through the assistance of suitable similarity variables. The Keller-box technique in MATLAB is employed to draw the impacts of the contributing elements on the velocity field, temperature distribution, and concentration. The impact of the Prandtl fluid parameter has mounting performance for the velocity whereas conflicting behavior is examined in the temperature profile. The achieved numerical results are matched correspondingly with the present symmetrical solutions in restrictive cases and fantastic agreement is scrutinized. In addition, the entropy generation uplifts for the growing values of the Prandtl fluid parameter, thermal radiation, and Brinkman number and decreases for growing numbers of the inertia coefficient parameter. It is also discovered that the coefficient of friction decreases for all parameters involved in the momentum equation. Features of nanofluids can be found in a variety of real-world fields, including microfluidics, industry, transportation, the military, and medicine.

On convective heat and mass transport of radiative double diffusive Williamson hybrid nanofluid by a Riga surface

Convective heat and mass transport of radiative Williamson hybrid [Formula: see text] nanofluid (NF) by a Riga surface with the novel features of Cattaneo–Christov double-diffusion has been investigated. Thermal contributions of internal heat mechanism and Arrhenius energy in Darcy–Forchheimer medium have also been incorporated in the modeling. Mathematical modeling has been completed by using suitable mathematical expressions for thermophysical features of hybrid nanofluid (HNF). Transport partial differential equations (PDEs) have been transformed into ordinary differential equations (ODEs) by means of similarity variables. Numerical approximation of the transformed system has been obtained by using shooting-based Runge–Kutta–Fehlberg approach. Results have been presented through various graphs and discussed physically in detail. Solution is validated for limited cases. Concentration of the hybrid mixture is reduced for progressive concentration-relaxation parameter. Temperature is alleviated for developing thermal-relaxation parameter. Nusselt number is observed to be higher for Williamson HNF than simple ordinary NF.