Darcy Forchheimer Research Articles

Exploration of Hall current effect and multiple convections in a Darcy Forchheimer flow of hybrid nanofluid over rotating permeable disk: a Stefan blowing approach

This article explores the slip boundary layer electrically conducting hybrid-nanofluid ( GO - Ti O 2 / H 2 O ) flow over a rotating disk. Flow is considered to be steady and incompressible type. Hall current effect and thermal radiation are considered in flow. We carried out the analysis of heat and mass transmissions in the flow through multiple convections. The surfaces of disk subjected to the influence of Stefan blowing. By completing similarity assessment, we renovate the primary PDEs of presumed flow model into ODEs. The resulting equations are solved numerically by recalling Runge–Kutta–Fehlberg fourth–fifth order scheme through shooting system. Discussions on significance of flow features on flow specific are structured precisely via graphs and charts. The acknowledged numerical concerns are novel and distinguishing. For Forchheimer number heat transmission declines in suction and in injection both cases and rate of heat transmission is higher in injection than suction which supposes in cooling exercise, flow through rotating disk suction stands more appropriate. Process of fluid flow over rotating disk and transportation via porous forms has engineering and scientific applications like gas turbines, oil condensers, nano-bio-materials processing.

Mathematical modeling of entropy generation in MHD mixed convective Cu–Ag-Al2O3/H2O tri-hybrid nanofluid over an exponential permeable shrinking surface with radiation and slip impacts: Multiple solutions with stability analysis

The present investigation aims to determine the existence of a dual solution in magnetohydrodynamic (MHD) mixed convective radiative flow of Cu-Ag- A l 2 O 3 / H 2 O tri-hybrid nanofluid in a permeable Darcy–Forchheimer porous medium over an exponentially shrinking surface by considering velocity, thermal slips, and suction effects at the surface. This study focuses on assessing entropy production in novel coolant applications. To streamline the analysis, the complex nonlinear partial differential equations (PDEs) are simplified by converting them into a set of ordinary differential equations (ODEs) through the utilization of the similarity transformation technique. These ODEs are then solved utilizing the bvp4c numerical MATLAB function. Graphical and tabular analyses are conducted to investigate the impact of emerging variables on entropy generation, as well as velocity, temperature, skin friction coefficient, and Nusselt number. Due to the contraction of the surface, dual solutions are found, but dual solutions cannot be found beyond the critical values. The critical values of S C are 1.58928, 1.48700, and 1.66058, but ξ C are − 1.239499 , − 1.416999 , and − 1.130030 for Cu / H 2 O nanofluid, Cu − Ag / H 2 O hybrid nanofluid, and Cu − Ag − A l 2 O 3 / H 2 O tri-hybrid nanofluid, respectively. A positive minimum eigenvalue γ 1 signifies the existence of the upper stable solution branch, while a negative minimal eigenvalue indicates the presence of the lower unstable solution branch. The tri-hybrid nanofluid exhibits superior thermal properties compared to nanofluid and hybrid fluids. Adding nanoparticles to traditional fluids is perceived as improving their ability to transmit heat. The analysis has demonstrated that the thermal radiation and temperature slip parameters significantly influence the heat transfer rate. Thermal radiation is found to speed up the creation of entropy. Additionally, in the case of a stable solution, an increase in the Forchheimer number results in a deceleration of the liquid flow, an effect which is further amplified by the presence of the magnetic field and velocity slip parameter.

Effects of Variable Thermal Conductivity on MHD Fluid Flow on Rotating Vertical Cone in the Presence of Darcy Forchheimer, Soret and Dufour Effects through a Porous Medium

This research investigated the effects of Variable Thermal Conductivity on MHD fluid on a Rotating Vertical Cone in the Presence of Darcy Forchheimer, Soret and Dufour effects through a porous medium. The system of nonlinear differential equations were transformed into first order differential equations and solved using shooting technique in Matlab package Bvp4c.Furthermore, the effects of various parameters over the main physical quantities are shown graphically and also extensively discussed. The result shows that Thermal conductivity increases Tangential Velocity, Temperature and decreases Normal Velocity. Dufour increases Tangential Velocity and decreases Normal Velocity. Radiation parameter R enhances Tangential Velocity and Temperature.

Chelyshkov wavelet-based numerical technique for the solution of Darcy–Forchheimer flow of Erying–Powell radiated dusty fluid over a stretching sheet with Cattaneo–Christov heat flux

This article presents the Chelyshkov wavelet-based numerical technique (CWBNT) for the solution of the system of non-linear differential equations arising in the study of Darcy–Forchheimer flow of Erying–Powell radiated dusty fluid over a stretching sheet with Cattaneo–Christov heat flux. Initially, the proposed technique is implemented on the test problem having exact solution. The obtained results are highly accurate in comparison with the solutions obtained by shooting technique based Runge–Kutta Fehlberg 4th–5th order method. The proposed technique is applied to the governing equations of the considered dusty fluid problem. The results obtained for some fixed values of parameters resemble the previously published results. The comparisons validate the method. The flow behavior of dusty fluid is analyzed and the effect of various factors on the velocity and thermal attribute of the dust and fluid phase are studied. It is inferred that the Erying–Powell fluid parameters ε and α have entirely different effects on temperature, velocity profiles, and skin-friction coefficient. The local inertia parameter decreases the velocity and thermal relaxation parameter decreases the temperature. Enhancement in temperature ratio and radiation parameters escalates the temperature and Nusselt number. The proposed technique is simple, reliable, efficient tool to solve the differential equations arising in dusty fluid flow problems.

The significant role of Darcy–Forchhiemer with integrated hybrid nanoparticles (Graphene and TiO 2) on dusty nanofluid flow subjected to heat conduction

The thermal analysis of two-phase models that deal with the fluid and dusty phases has been considered. This study instigates the flow of a non-miscible, dusty hybrid nanofluid over a stretching cylinder with Darcy–Forchheimer permeability in the presence of thermal radiation. The mathematical model is based on the single-phase nanofluid model, which features modified thermophysical characteristics. This innovative flow model explores how important it is to enhance the concentration of dust particles in fluid dynamics. Hybrid nanoparticles are substituted for nanoparticles in a conventional case to accelerate the heat transfer rate of the fluid. Therefore, in this study, the magnetohydrodynamic flow of hybrid nanofluids and heat transfer of non-Newtonian dusty fluids with suspensions of hybrid nanoparticles have been examined. The appropriate dimensionless variables are used to convert the governing periodic model into a non-dimensional form. The finite-difference-based bvp5c algorithm is used through Matlab for numerical analysis of the set of obtained ordinary differential equations. The graphs explored the influences of relatable factors over the profiles of mass, heat, and velocity transfers. It is observed that with intensifying values of Eckert number (Ec) and Biot number (Bi), the temperature of both phases increased at a significant level, and the velocity decreased with increasing intensity of the magnetic field. The computational results of velocity, core temperature, and intensity dispersion are significant for both aspects. Furthermore, it is observed that both the fluid and dust phases exhibit declining behavior as a result of the impact of porosity, mass concentration, and magnetism on the flow stream. Moreover, it is noticed that both the dust phase temperature θ p ( η ) and fluid phase temperature θ ( η ) intensified with the high intensity of magnetic field and thermal radiation. The missile nozzles, nuclear power plants for aerospace and gaseous-core nuclear rocket systems, and the radiation are considered for evaluating heating significance.

Sensitivity analysis and response surface methodology for entropy optimization in the exponentially stretching stratified curved sheet for Casson–Williamson nanofluid flow

The current study explains the parametric entropy optimization by using response surface methodology and sensitivity analysis. It also reveals the effects of thermal radiation and exponential heating on Casson–Williamson nanofluid flow over an exponentially stretching curved sheet. The Darcy–Forchheimer model is used and stratification, Navier slip, and suction-injection are used as the boundary constraints. The 4–5th ordered Runge–Kutta Fehlberg approach is enacted to exhibit the modeled flow. Response surface methodology is used to build the statistical design for the Weissenberg number, magnetic parameter, and Brinkmann number. The thermal stratification parameter, according to the findings, lowers temperature. Entropy grows as Brinkmann number and magnetic parameter increase. When the thermal buoyancy factor assumes the minimum value, little shear stress is seen for high Forchheimer number. The squared co-efficient is confirmed to be 99.99 %. The Pareto chart confirms that point 2.2 is the important point. Entropy surface diagrams in three dimensions demonstrate that with high magnetic parameter, high Brinkman number levels and low Weissenberg number levels, high entropy is obtained. For low and medium levels of magnetic parameter, Weissenberg number exhibits positive sensitivity, whereas for high and medium levels of magnetic parameter, it exhibits negative sensitivity.

Irreversibility analysis of Darcy-Forchheimer flow of a Williamson hybrid nanofluids near a stagnation-point across a vertical plate with buoyancy force

PurposeA novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.Design/methodology/approachBy applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.FindingsThe shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.Practical implicationsThe findings may be highly beneficial in raising the energy efficiency of thermal systems.Originality/valueThe originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.

Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle

Abstract The thermo-diffusion applications of nanofluid subject to variable thermal sources have been presented. The significance of Darcy–Forchheimer effects is attributed. The flow comprises the mixed convection and viscous dissipation effects. Furthermore, the variable influence of viscosity, thermal conductivity, and mass diffusivity is treated to analyze the flow. The analysis of problem is referred to convective mass and thermal constraints. The analytical simulations are proceeded with homotopy analysis method. The convergence region is highlighted. Novel physical contribution of parameters is visualized and treated graphically. It is noted that larger Brinkman number leads to improvement in heat transfer. The concentration pattern boosted due to Soret number. The wall shear force enhances with Hartmann number and variable thermal conductivity coefficient.

Thermal analysis of 3D Darcy–Forchheimer flow of SWCNT–MWCNT/sodium alginate on Riga plate

Thermal analysis of 3D Darcy–Forchheimer flow of SWCNT–MWCNT/sodium alginate on Riga plate

Heat transfer analysis of ternary hybrid nanofluid through variable characteristic porous medium: Non-similar approach

This paper aims at developing non-similar solutions for heat transfer augmentation in ternary hybrid nanofluids. Nanofluid is composed of three distinct (Silver, Copper, Aluminum oxide) nanosize particles while water is considered as a base fluid. Darcy–Forchheimer expression with variable porosity and permeability is adopted. Joule heating and viscous dissipations are also considered. Non-similar approach is utilized. Numerical solutions are computed by bvp4c solver of MATLAB. Graphical illustrations for flow and thermal fields behavior are provided. Comparative results are obtained for ternary hybrid nanofluid and nanoliquid. Physical quantities such as skin drag coefficient and Nusselt number are computed and interpreted. Our results reveal that rate of heat transfer augments substantially for Ag/water nanofluid in comparison to other classes of nanofluid.

Blood-Based CNT Nanofluid Flow Over Rotating Discs for the Impact of Drag Using Darcy–Forchheimer Model Embedding in Porous Matrix

Blood-Based CNT Nanofluid Flow Over Rotating Discs for the Impact of Drag Using Darcy–Forchheimer Model Embedding in Porous Matrix

Darcy Forchhiemer imposed exponential heat source-sink and activation energy with the effects of bioconvection over radially stretching disc

The Darcy–Forchheimer model is a commonly used and accurate method for simulating flow in porous media, proving beneficial for fluid separation, heat exchange, subsurface fluid transfer, filtration, and purification. The current study aims to describe heat and mass transfer in ternary nanofluid flow on a radially stretched sheet with activation energy. The velocity equation includes Darcy–Fochheimer porous media effects. The novelty of this study is enhanced by incorporating gyrotactic microorganisms which are versatile and in nanofluid can greatly improve the thermal conductivity and heat transfer properties of the base fluid, resulting in more efficient heat transfer systems. Furthermore, the governing PDEs are reduced to ODEs via appropriate similarity transformations. The influence of numerous parameters is expanded and physically depicted through the graphical illustration. As the Forchheimer number escalates, so do the medium's porosity and drag coefficient, resulting in more resistive forces and, as a result, lowering fluid velocity. It has been discovered that increasing the exponential heat source/sink causes convective flows that are deficient to transport heat away efficiently, resulting in a slower heat transfer rate. The concentration profile accumulates when the activation energy is large, resulting in a drop in the mass transfer rate. It is observed that the density of motile microorganisms increases with a rise in the Peclet number. Further, the results of the major engineering coefficients Skin-friction, Nusselt number, Sherwood number, and Microorganism density number are numerically examined and tabulated. Also, the numerical outcomes were found to be identical to the previous study.

On viscous stratified Darcy–Forchheimer flow in a horizontal porous layer with thermal anisotropy and variable permeability

This study analyzes the effect of anisotropy and the internal heat source in a Darcy–Forchheimer porous layer. It is well known that the variations in viscosity can be attributed to the temperature. Therefore, in the present problem, we consider a linear variation in viscosity with temperature for simplicity. We first derived the linear instability theory and then established global stability using the energy functional approach. In the global stability analysis, we show that working with the L2 norm fails to give a sufficient condition for global stability by exhibiting that the associated maximization problem is unbounded in the underlying stability measure space. Then, we show that a conditional stability bound can be achieved by restricting the internal heat source parameter Q with higher-order norms. The eigenvalue problems obtained in linear and nonlinear theories were integrated numerically. The linear and nonlinear instability thresholds are then compared to identify the potential regions of sub-critical instabilities. It is observed that the system is stabilized when the horizontal component of thermal diffusivity dominates and is unstable when the vertical component of thermal diffusivity dominates. We also found that increasing the variable permeability parameter λ destabilized the system. It is observed that increasing viscosity stabilizes the system, and decreasing viscosity encourages the start of convection. It is also interesting that, in the presence of an internal heat source, the region of subcritical instability increases with increasing viscosity effect but reduces with increasing vertical permeability λ.

Unsteady, two-dimensional magnetohydrodynamic (MHD) analysis of Casson fluid flow in a porous cavity with heated cylindrical obstacles

This research presents an analysis of entropy generation during natural convection in a porous medium using triangular heated cylindrical obstacles with equal spacing. The study consists of three cylindrical obstacles arranged in a triangular pattern. Each cylinder is uniformly spaced from its neighboring cylinders, creating equilateral triangles throughout the arrangement. All of these cylindrical obstacles are heated. The triangular arrangement guarantees an even distribution of obstacles across the experimental space. The governing equations, with entropy, are numerically solved using the finite element method. The study aims to investigate the interactions between several key elements in fluid dynamics: Casson fluid, magnetohydrodynamics, the Darcy–Forchheimer model, entropy, and natural convection. The goal is to gain insights into the individual behaviors of these elements and their interactions in combined systems. The results indicate that the Casson fluid parameter has an impact on the flow and heat transfer characteristics, while the Hartmann and Nusselt numbers exhibit control mechanisms for the intensity of natural convection and affect the patterns of isotherms, streamlines, and entropy.

Buoyancy driven bioconvective Casson nanofluid flow over a vertical stretching cylinder in Darcy–Forchheimer permeable medium with Arrhenius activation energy and chemical reaction

A mathematical framework is conceived to analyze the flow of Darcy–Forchheimer Casson nanofluid around a vertically stretchable cylinder, taking into account the convective boundary conditions. The heat and mass transport phenomena are visualized in the existence of activation energy and gyrotactic microorganisms with buoyancy effects. Additionally, an external magnetic field is applied to the flow problem. This particular model finds applications in biomedical engineering, the oil and gas industry, heat exchangers and thermal systems, environmental engineering, and renewable energy. By employing suitable transformations to transform partial differential equations into ordinary ones, the MATLAB function bvp4c package is utilized to numerically solve the equations. The findings presented through graphs illustrate the influence of various parameters on velocity, heat and mass transfer, and the density of gyrotactic microorganisms. The analysis revealed that fluid momentum decreases with increasing porosity numbers, while higher activation energy values enhance concentration. Moreover, an increase in the Peclet number reduces the microorganism’s distribution. Tables compute the motile microorganism’s density, Nusselt number, and Sherwood number. A substantial rise in activation energy prominently increases concentration, accompanied by a decrease in the Sherwood number. The density of microorganisms rises with higher values of the curvature parameter, Prandtl number, and Brownian motion parameter, but decreases with an increasing Hartman number. Noteworthy concordance is noted when juxtaposing the findings of this investigation with those of earlier scholarly research.

Arrhenius activation energy and thermal radiation effects on oscillatory heat-mass transfer of Darcy Forchheimer nanofluid along heat generating cone

The main goal of present research is to illustrate the frequency and amplitude behavior of heat and mass transfer of Darcy Forchheimer nanofluid flow with Arrhenius activation energy and thermal radiation effects. The impact of heat generation and chemical reaction on Darcy Forchheimer nanofluid along vertical porous cone is investigated to improve heating durability of thermodynamic systems in this research. The governing mathematical model is moderated in suitable format to construct physical coefficients. The oscillating stokes and primitive coefficients are used to differentiate the model into oscillating and steady forms. The Gaussian elimination and implicit finite difference techniques are used to address the numerical findings. To construct pertinent algorithm in FORTRAN system, the primitive-type variables are used on steady and oscillating models with first law of thermodynamics, nanoparticles and heat generation. The results under defined conditions are reported in numerical and graphical sequence through Tec-plot 360. It is found that the amplitude of surface temperature increases as heat generation increases because heat generation improves the excessive thermal transport. It is depicted that the Darcy-Forchheimer porous material decreases the fluid temperature. It is found that amplitude of mass transfer increases as activation energy and chemical reaction coefficient increases. The oscillating frequency of heat and mass transfer increases as Prandtl number increases. The current mechanism of mass and heat transfer of nanofluid has several uses in mineralogy, cutting tools, lubricating oils, machining operations, heat exchangers, coating sheets, petroleum drilling and cooling of metallic cones.

A non‐similar solution to dissipative Eyring‐Powell nanofluid flow over a nonlinear stretching surface with an inclined magnetic field and active/passive nanoparticles flux

AbstractAmongst numerous non‐Newtonian fluid models, Eyring‐Powell fluid is prominent owing to its shear thinning, pseudoplastic, and yield stress unique characteristics. It has varied industrial applications including the modeling of polymer melts, food products, and blood flow. This study discusses the Darcy Forchheimer flow of Eyring‐Powell nanoliquid along a nonlinear stretched surface influenced by an inclined magnetic flux. The mass and heat transmissions are supported by active and passive control of nanoparticles respectively. The unique effect of viscous dissipation is introduced to influence the liquid velocity and temperature. Unlike the majority of the research being published that espouses similar solutions, we adopted the non‐similar analysis of the proposed problem to eradicate the chance of the variable in the parameters. This was a challenging task and was taken as a mathematical art rather than a science. The established Buongiorno model is followed to compute the thermophoretic and Brownian motion effects. The numerical computation of this mathematical system is performed using the bvp4c algorithm. The results are described through graphs and in numerically calculated tabulated values. It is determined that wall drag is stronger when the magnetic field is inclined at an angle of than at . Additionally, it is observed that passive control of nanoparticles results in better rates of heat and mass transmissions, against varied values of the fluid parameter with . The validation of the envisioned model is also a part of this exploration.

Multiple slips on Darcy–Forchheimer unsteady flow manifested with Cattaneo–Christov heat flux over a stretching sheet

This primary goal of this analysis is to investigate how several slips affect the flow, heat, and mass performance of Darcy–Forchheimer unstable behavior beyond a stretching sheet using a numerical analysis of the Soret effect. The novel constitutive model Cattaneo–Christov is illustrated to analyze the features of thermal relaxation time. The Cattaneo–Christov method is used to predict heat and mass transport. A surface that slanders and has varying thicknesses propels the flow. Through the use of local similarity transformations, the governing nonlinear partial differential equations reduce to the coupled ordinary differential equations and include the momentum, energy, and concentration equations. The altered ODEs are calculated numerically using the Runge–Kutta Fehlberg scheme and an efficient shooting procedure. The physical properties of the temperature, concentration, and fluid velocity profiles are shown visually and shed light on the change of several governing parameters. For example, in comparison to the classical Fourier’s heat model, our result suggests that the Cattaneo–Christov heat flux constitution has lower temperature and thermal boundary layer thickness. In the meantime, a high wall thickness parameter greatly upgrades the rate of heat transfer, and thermal relaxation has the opposite effect. Discussion is held regarding the effects of various miscellaneous variables on temperature, concentration, and velocity.

On the Darcy–Forchheimer flow of carbon nanotubes nanofluid across a stretching surface for the impact of heat source/sink and Ohmic heating

This research leads to carrying out the productivity and the efficiency of the carbon nanotubes (CNTs) that have extensive applications in solar collectors. Due to the superior thermal as well as electrical properties, the use of CNTs has an important contribution to the nanotechnology revolution. Therefore, owing to the aforementioned vital points, this investigation intended to put forth the thermophysical properties of both single and multi-walled CNT nanofluids past a stretching surface. Additionally, an electrically conducting nanofluid flow phenomenon enriches due to the inclusion of dissipation (Ohmic heating) and external heat source/sink. The dimensional form of the three-dimensional fluid flow phenomena is transformed to a non-dimensional form with the use of similarity transformation and further numerical procedure is implemented to solve the nonlinear governing equations. The substantial significance of the characterizing parameters is presented briefly via figures and the comparative analysis with the earlier investigation is deployed through the table. However, the main findings of this study are as follows: A significant attenuation in the shear rate is marked for the enhanced inertial drag but it augments for the augmented values of the magnetization; further, particle concentrations of both the CNTs favor accelerating the fluid momentum as well as temperature distribution.

Multieffect bioconvective transport of oxytactic microorganisms with thermal radiation, Lorentz force, heat source, and chemical reaction over a flexible cylinder

AbstractThe multieffect bioconvective heat transfer in porous media is essential for many technological applications. However, the literature governing practical applications is very scarce. The bioconvective transport of magnetohydrodynamic cross nanofluid carrying oxytactic microorganisms across a flexible cylinder with velocity slip, viscous dissipation, thermal radiation, and chemical reaction with a heat source in Darcy–Forchheimer porous medium is predicted in this piece of work. The random movement and thermophoresis processes are revealed by the Buongiorno model. Using a suitable similarity transformation and boundary layer approximation, the simplified model equations are converted into coupled highly nonlinear ordinary differential equations (ODEs). The resulting ODEs are dealt with numerically utilizing the BVP4C and the shooting method with predetermined thermal radiation, heat source, chemical reaction, and so forth parameters. The velocity field is inversely influenced by the Forchheimer number and porosity parameter. The Sherwood number is significantly influenced by chemical reactions. For heat source parameter (S) and increasing radiation parameter (Rd), the Nusselt number increases and convection is shown for the value of Rd near about 3. Overall, this study will help researchers in science and engineering to understand the intricate and multieffective dynamic system and industrial applications like microbiology, and biodynamical systems, biological tissues, biofilms, soil, or filter media.