Numerical solution for Sisko nanofluid flow through stretching surface in a Darcy–Forchheimer porous medium with thermal radiation

The heat transfer assessments in a Sisko nanofluid flow over a stretching surface in a Darcy–Forchheimer porous medium with heat generation and thermal radiation are studied. The numerical analysis technique is used to assess the governing nonlinear equations of the model. The influence of Forchheimer number, porosity, heat generation, radiation, and material parameters is examined. The outlines of Nusselt number and skin friction coefficient corresponding to pertinent parameters are revealed. The comparison of Nusselt number outlines of working fluid and Newtonian fluid is depicted. From the analysis, it has been examined that with the increase in Forchheimer number and material parameter values, heat transfer function decreases, whereas heat transfer characteristics of Sisko nanofluid increase with heat generation and material parameters. Moreover, working fluid velocity outlines depreciate when there is an increase in porosity parameter for both shear-thinning and shear-thickening. The comparison of this study with previous research has been conducted.     

Irreversibility analysis of micropolar nanofluid flow using Darcy–Forchheimer rule in an inclined microchannel with multiple slip effects

The present work explores the consequence of the flow of micropolar fluid in an inclined microchannel when exposed to linear radiation in presence of a magnetic field. The microchannel is embedded with a porous medium and the Darcy–Forchheimer model is implemented. The walls of the microchannel facilitate the simultaneous suction and injection of the micropolar fluid. A multiple slip regime and temperature jump conditions were assumed at the boundaries. The equations are modeled and nondimensionalized using nondimensional entities and further solved with the aid of the Runge–Kutta–Fehlberg method. Entropy generated in the medium and ratio of irreversibilities is also computed. Results so obtained deliberate that enhancement in Darcy number has caused an increment in entropy generation rate whereas the opposite nature is attained for the Bejan number. Magnifying the radiation parameter has resulted in diminishing the profile of entropy generation rate and Bejan number.     

Two-dimensional Darcy–Forchheimer flow of a dusty hybrid nanofluid over a stretching sheet with viscous dissipation

The main objective of the present examination is to design a stable mathematical model of a two-phase dusty hybrid nanofluid flow over a stretching sheet with heat transfer in a porous medium, and the Darcy–Forchheimer flow is taken into account with viscous dissipation and melting effect. The equations of motion are reduced to nonlinear ordinary differential equations by considering suitable similarity variables. These dimensionless expressions are solved by a well-known numerical technique known as Runge–Kutta–Fehlberg fourth–fifth order method. The behavioral study and analysis of the velocity and thermal profile in dual phases (fluid phase and dust phase) for diverse values of parameters are estimated using graphs and tables. The result outcome reveals that the velocity gradient declines in the fluid phase and increases in the dust phase for a rise in values of the velocity interaction parameter. Also, the velocity gradients of the both phases diminish for increasing values of the porosity parameter. Furthermore, it is determined that the increase in the value of melting parameter leads to a decline in the thermal gradient of both phases.     

Cattaneo–Christov heat flux model and multiple slip effect on carbon nanofluid over a stretching sheet in a Darcy–Forchheimer porous medium

In several biotechnological processes, multiple slips are the most paramount, such as blood pumping from the heart to different body components, endoscopy treatment, pabulum distribution, and the heat transport phenomenon regulation. In the current research, we have studied the multiple slips, Darcy–Forchheimer, and Cattaneo–Christov heat flux model on a stretching surface exposed to magnetic carbon nanotube nanofluid. We have additionally included a heat source or sink, a chemical reaction for manipulating the heat and mass transport phenomena. The resulting governing partial differential equations have been transformed into ordinary differential equations. With the Runge–Kutta–Fehlberg fourth–fifth-order procedure, the transformed governing equations are numerically solved. Numerical solutions for different parameters for velocity, temperature, and concentration profiles (Eckert number, velocity slip, thermal slip, mass slip, etc.) are highlighted. Graphical and numerical results for the various parameters in the modeled problem have been outlined. The present numerical results are compared with the published ones for some limiting cases. The slip has been found to control the flow of the boundary layer.     

Characteristics of Darcy–Forchheimer drag coefficients and velocity slip on the flow of micropolar nanofluid

The flow of magneto-micropolar nanofluid, that is, the composition of TiO₂ nanoparticles in an organic solvent, kerosene, and the normal water past a stretchable surface has been considered. With effectiveness idea on the application in several areas, the Darcy–Forchheimer inertial drag and the second-order velocity slip approach are vital for the current investigation. The influence of viscous, Joule and Darcy dissipations on the energy transfer cannot be neglected due to the interaction of the body forces characterized by magnetic and porosity of the medium. The dissipative heat energy with the heat generation/absorption is useful for the enhancement in the fluid temperature. Due to the complexity of the problem, a numerical solution is implemented using the in-built code bvp5c with the help of MATLAB software. The physical properties abide by the characterizing parameters that appeared in the flow profiles are presented via graphs and the computed results for the rate coefficients are also displayed through table both for water- and kerosene-based nanofluids. Finally, the main findings of the results are: the growth in the shear rate coefficient is marked due to the inclusion of second-order slip, and an attenuation in the fluid velocity is rendered with an increase in the volume fraction whereas impact is reversed in the case of nanofluid temperature.     

Darcy–Forchheimer electromagnetic flow of entropy optimized microrotating Casson–Carreau nanomaterials

It is apparent that non-Newtonian nanofluids (especially, Casson and Carreau) find their ubiquitous utilization in diverse industrial processes. The magnetohydrodynamics concept is significantly implemented in the engineering design process. Darcy–Forchheimer's effect characterized by inertia and boundary effects ameliorates the rate of heat transportation outstandingly in association with the flow of nanofluids. Entropy optimization analysis is accentuated as its minimization is the best measure to enhance the efficiency of thermal systems. In view of this, the present article is intended to investigate electromagnetic flow and thermal characteristics of Casson and Carreau nanofluids over the exponential stretched surface. Microrotation facets are entailed. Arrhenius pre-exponential factor law and Robin's condition are implemented. The nondimensional governing equations are solved by the spectral quasi-linearization method. The major outcomes of this study are that axial and transverse flow velocities and heat transfer rate get controlled due to strengthening Casson and microinertia density parameters. More thermal stratification augments the rate of heat transportation efficaciously. Amplification of the Weissenberg parameter intensifies the axial and transverse flow velocities and the associated boundary layer widths. Axial and transverse surface viscous drag enervate due to the rise in porosity, inertia, and magnetic parameters. The entropy generation rate is regulated by the varied Reynolds number.     

Transient and non-Darcian effects on natural convection flow in a vertical channel partially filled with porous medium: Analysis with Forchheimer–Brinkman extended Darcy model

The present study addresses the transient as well as non-Darcian effects on laminar natural convection flow in a vertical channel partially filled with porous medium. Forchheimer–Brinkman extended Darcy model is assumed to simulate momentum transfer within the porous medium. Two regions are coupled by equating the velocity and shear stress in the case of momentum equation while matching of the temperature and heat flux is taken for thermal energy equation. Approximate solutions are obtained using perturbation technique. Variations in velocity field with Darcy number, Grashof number, kinematic viscosity ratio, distance of interface and variations in temperature distribution with thermal conductivity ratio, distance of interface are obtained and depicted graphically. The skin-friction and rate of heat transfer at the channel walls are also derived and the numerical values for various physical parameters are tabulated.     

On the onset of thermal convection in rotating nanofluid layer saturating a Darcy–Brinkman porous medium

In this paper, the effect of rotation on the onset of thermal convection in a horizontal layer of nanofluid saturated by a Darcy–Brinkman porous medium is considered. A linear stability analysis based upon normal mode is used to find solution of the fluid layer confined between two free boundaries. The onset criterion for stationary and oscillatory convection is derived analytically and graphically. The effects of the concentration Rayleigh number, Taylor number, Lewis number, Darcy number and modified diffusivity ratio on the stability of the system are investigated. The sufficient conditions for the non-existence of overstability are also derived.     

Overlapping grid spectral collocation approach for electrical MHD bioconvection Darcy–Forchheimer flow of a Carreau–Yasuda nanoliquid over a periodically accelerating surface

The focus of this study is on computational grid-manipulation to enhance the accuracy, convergence, and computational efficiency of the multidomain bivariate spectral local linearization method (MD-BSLLM). The improved method is used in the scrutiny of Darcy–Forchheimer bioconvection flow of Carreau–Yasuda nanofluid induced by an oscillatory moving surface with cross-diffusion, activation energy with binary chemical reactive species, combined electrical and magnetohydrodynamic field effects. The proposed method is utilized in solving the nondimensional form of the flow equations. Sensitivity and error analyses are provided to aid an understanding of the efficiency, stability, convergence rate, and accuracy of the iterative scheme. The impact of different parameter values on fluid properties and transport phenomena is discussed. Numerical simulation has indicated that the overlapping grid MD-BSLLM is computational efficacious, and produces stable and sufficiently accurate results using a few collocation nodes in each respective subinterval and the entire computational domain. Other findings include the fact that fluid properties are enhanced with injection while flow characteristics are improved with suction. Using the Darcy–Forchheimer model in the flow analysis improves the temperature of the nanofluid. The imposition of electric field augments nanofluid velocity, the amplitude of skin friction coefficient, rates of mass, and motile microorganisms transfer while reducing the rate of heat transfer. The considered flow analysis can contribute towards engineering solicitations in paper production, polymer solution, metal extrusion, and glass blowing.     

Heat transfer analysis for particle–fluid suspension thermomagnetohydrodynamic peristaltic flow with Darcy–Forchheimer medium

This theoretical analysis explores the effect of heat and mass transfer on particle–fluid suspension for the Rabinowitsch fluid model with the stiffness and dynamic damping effects through Darcy–Brinkman–Forchheimer porous medium. In this study, we also incorporate slip and transverse magnetic field effects. Using low Reynolds number, to neglect inertial forces and to keep the pressure constant during the flow, channel height is used largely as compared with the ratio of length of the wave. A numerical technique is used to solve flow governing system of differential equations. Particular attention is paid to viscous damping force parameter, stiffness parameter, and rigidity parameter; also, the numerical data for thermal profile, momentum, and concentration distribution are presented graphically. Outcomes are deliberated in detail for different fluid models (thinning, thickening, and viscous models). It is found that velocity profile increases for greater values of viscous damping effect and stiffness and rigidity parameter for shear thinning, but conflicting comportment is showed for thickening nature model. Viscous dissipation effects increases the thermal profile for all cases of fluid models. The scope of the present article is valuable in explaining the blood transport dynamics in small vessels while considering the important wall features with chemical reaction characteristics. The current analysis has extensive applications in biomedical engineering field, that is, peristaltic pumps.     

Hydromagnetic convective diffusion of species in Darcy–Forchheimer porous medium with non-uniform heat source/sink and variable viscosity

In this paper we have analyzed the combined effects of magnetic field and convective diffusion of species through a non-Darcy porous medium over a vertical stretching sheet with temperature dependent viscosity and non-uniform heat source/sink. The boundary layer equations are transformed into ordinary differential equations using self-similarity transformation which are then solved numerically using fifth-order Runge–Kutta Fehlberg method with shooting technique for various values of the governing parameters. The effects of electric field parameter, non-uniform heat source/sink parameters and Schmidt number on concentration profiles are analyzed and discussed graphically. Favorable comparisons with previously published work on various special cases of the problem are obtained.     

MHD mixed convection of Cu–water nanofluid in a two-sided lid-driven porous cavity with a partial slip

ABSTRACT

A numerical simulation of magneto-hydrodynamic mixed convection flow and heat transfer of Cu–water nanofluid in a square cavity filled with a Darcian porous medium with a partial slip is numerically investigated. The left and right walls of the cavity are moving up with a constant speed in vertical direction, and the partial slip effect is considered along these walls. The top and bottom walls of the cavity are assumed to be adiabatic. The right vertical wall of the cavity is assumed to be kept at a lower temperature, while the left vertical wall is kept at a higher temperature. The developed equations of the mathematical model are nondimensionalized and then solved numerically subject to appropriate boundary conditions by the finite-volume method. A parametric study is performed and a set of graphical results is presented and discussed to demonstrate interesting features of the solution.     

Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–Water nanofluid

This work focuses on the study of natural convection heat transfer characteristics in a differentially-heated enclosure filled with a CuO–EG–Water nanofluid for different published variable thermal conductivity and variable viscosity models. The problem is given in terms of the vorticity–stream function formulation and the resulting governing equations are solved numerically using an efficient finite-volume method. Comparisons with previously published work are performed and the results are found to be in good agreement. Various results for the streamline and isotherm contours as well as the local and average Nusselt numbers are presented for a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 6%), and enclosure aspect ratios (½ ≤ A ≤ 2). Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number as the volume fraction of nanoparticles increases depending on the combination of CuO–EG–Water variable thermal conductivity and viscosity models employed. In general, the effects the viscosity models are predicted to be more predominant on the behavior of the average Nusselt number than the influence of the thermal conductivity models. The enclosure aspect ratio is predicted to have significant effects on the behavior of the average Nusselt number which decreases as the enclosure aspect ratio increases.     

Darcy–Forchheimer MHD radiative flow through a porous space incorporating viscous dissipation,heat source,and chemical reaction effect across an exponentially stretched surface

The impacts of viscous dissipation, Brownian motion, and the thermophoresis caused by temperature gradient on the steady two-dimensional incompressible chemically reactive and radiative flow of traditional fluid through an exponentially stretched sheet embedded in a Darcy porous media are explored by approaching boundary layer analysis. A magnetic field effect is also addressed along the transverse direction of the horizontal stretched sheet. With the implementation of some suitable nondimensional quantities, the regulating nonlinear partial differential equations, which represent the flow geometry, are transformed into coupled nonlinear ordinary differential equations. To acquire the numerical findings from this set of equations, a three-stage Lobatto IIIa, in-built MATLAB scheme named, Bvp4c is used. The effects of the dimensionless physical factors on the flow, heat, and concentration profile, as well as on the coefficient of drag force and the rate of thermal and mass transit at the surface, are graphically and numerically depicted. The thermal profile, as well as the magnitude of the coefficient of the drag force and the Sherwood number, is found to be escalated with the Darcy–Forchheimer factor, but the depreciation in the value of temperature gradient at the wall is noticed for the same.     

Numerical simulation of heat and mass transfers radiative–convective fluid flow on a stretching porous surface with temperature-dependent thermophysical properties

This paper is focused on the analysis of heat and mass transfer radiative–convective fluid flow using quadratic multiple regression and numerical approach. The physical phenomenon is analyzed by utilizing partial differential equations (PDEs). Thermophysical properties, such as viscosity, thermal conductivity, and mass diffusivity, are varied and temperature-dependent. This study is unique because of its applications in magnetohydrodynamic power accelerators, drilling operators, and bioengineering. The governing PDEs are transformed into coupled nonlinear ordinary differential equations (ODEs). The transformed ODEs are solved numerically using the spectral homotopy analysis method. Also, a quadratic multiple regression analysis is performed on quantities of engineering interest to show the significance of the flow parameters. It is observed that the heat and mass transfer process is affected by nonlinear buoyancy impact. The Lorentz force produced by the imposed magnetic field decline the thickness of the hydrodynamic boundary layer. Findings revealed that the nonlinear convective parameter and variable thermophysical properties are greatly affected by the rate of heat and mass transfer. Previously published work was used to validate the present one, which conformed with it. The slope of linear regression through data points is adopted to show the rate of change in skin friction, Nusselt, and Sherwood numbers during the flow phenomenon.     

The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid

The paper presents an analytical treatment of double-diffusive nanofluid convection in a porous medium. The problem treated is natural convection past a vertical plate when the base fluid of the nanofluid is itself a binary fluid such as salty water. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, while the Darcy model is used for the porous medium. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. A similarity solution is presented.     

Magnetohydrodynamic free convection flow of water at 4°C through a porous medium

MHD forced and free convection flow of water at 4°C through a porous medium in the presence of a uniform transverse magnetic field is considered. A family of solutions of the coupled non-linear equations is presented using shooting numerical techniques for two point boundary value problems. Velocity and temperature profiles are shown for different values of the parameters Ha²/Re, Gr/Re² and K.     

Heat transport in a sandwiched set-up of MHD Newtonian–Casson–Newtonian fluids through a porous medium

The time-dependent sandwiched flow of immiscible fluids plays a vital role in petroleum extraction, bio-fluid mechanics, blood rheology, and so forth. Owing to their applications, the present study focuses on exploring the unsteady flow of Casson fluid through porous media sandwiched between Newtonian fluids in the channel. The channel is placed in the horizontal position, wherein the Casson fluid layer is in the central region, and Newtonian fluids are in the upper and lower regions. The governing system of equations is numerically solved using the finite difference method to obtain flow and heat transfer profiles. The influence of vital parameters on flow and heat transfer is discussed. Furthermore, the parameters of engineering interest, that is, fluid flow rate, skin friction, and Nusselt number are also analyzed in this study.     

Cattaneo–Christov double-diffusion model with Stefan blowing effect on copper–water nanofluid flow over a stretching surface

We often encounter many processes where the cooling rate is a key factor in deciding the features of a desired product. Due to increasing demands of controlled cooling systems, an effort is made to theoretically study the effect of volume fraction on mixed convective Cu–water nanofluid flow over a stretching surface with activation energy and thermal radiation. The nonlinear dynamical system is simplified using apt similarity variables and the obtained ordinary differential equations are dealt numerically using Runge–Kutta–Fehlberg method and shooting scheme. The thermal and solutal equations are modeled considering Cattaneo–Christov double-diffusion model. The flow problem is studied considering velocity slip and zero mass flux state at the surface. As a novelty, the present case considers the blowing effect at the surface to study massive species transport during nanofluid flow with Cattaneo–Christov double-diffusion model. The results show that an increase in strength of thermal radiation increases temperature and buoyancy ratio parameter, thereby escalating the skin friction coefficient. When thermal relaxation parameter changes from 0.001 to 0.005, heat transfer coefficient improves by 24.36%. Furthermore, with the change in value of the blowing parameter from 0.1 to 0.1015, the maximum value concentration of nanoparticles that is attained during the flow is increased by 7.15%.     

Investigation of flow parameters of Reiner–Philippoff nanofluid flow with higher-order slip properties,activation energy,and bioconvection by artificial neural networks

In this study, the flow parameters of Reiner–Philippoff nanofluid flow with high-order slip properties, activation energy, and bioconvection have been analyzed using artificial neural networks (ANNs). Local Nusselt number (LNN), local Sherwood number (LSN), and motile density number (MDN) are considered as flow parameters. Numerical values have been obtained by numerical methods using flow equations. To estimate the flow parameters, three different ANN models have been designed. The Levenberg–Marquardt training algorithm is used in multilayer perceptron network models with 10 neurons in the hidden layers. In all, 70% of the data set has been used for training the models, 15% for validation, and 15% for testing. The performance analysis of the network models has been made by calculating the determined performance parameters. The R values for the LNN, LSN, and MDN parameters have been calculated as 0.99261, 0.98769, and 0.99102, respectively, and the average deviation values are −0.65%, 0.06%, and −0.11%, respectively. The attained outcomes showed that the ANNs can predict the LNN, LSN, and MDN, which are the flow parameters of the Reiner–Philippoff nanofluid flow, with high accuracy.