Permeable Shrinking Surface Research Articles

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.

Response surface methodology on optimizing heat transfer rate for the free convection of micro-structured fluid through permeable shrinking surface

Response surface methodology on optimizing heat transfer rate for the free convection of micro-structured fluid through permeable shrinking surface

Multiple solutions of unsteady flow of CNTs nanofluid over permeable shrinking surface with effects of dissipation and slip conditions

The objective of this paper is to analyze the unsteady incompressible flow of the viscous nanofluid on a contracting surface with viscous dissipation effects. Presented and contrasted are analyses of both multi-wall carbon nanotubes (MWNTs) and single-wall carbon nanotubes (SWNTs). As the common (or base) fluids, kerosene oil and water are utilized. In the existence of first-order thermal and velocity slip conditions, mathematical modeling and analysis are performed. Using the MATLAB software’s bvp4c solver tool, numerical solutions to the governing nonlinear modeled problems were obtained. This technique is particularly effective for developing many solutions to highly nonlinear differential equations. In addition, a comparison is done between this study and previously published works. The temperature, velocity, skin friction coefficient and heat-transfer rate have been explored for various significant factors included in the problem statements. In the unsteadiness parameter regime, dual solutions can be found. As the velocity slip parameter is increased, the flow slows down. In comparison to SWCNTs kerosene, MWCNTs kerosene oil has a greater velocity curve for the nanoparticles volume fraction. Increases in volume fraction decrease skin friction, whereas increases in the unsteadiness parameter speed up the drag force. Furthermore, as the Eckert number intensity increases, so do the temperature profiles in both solutions. Finally, the stability study revealed that the initial solution is robust, whereas the breakage in the second solution in the Nusselt number shows singularity, and thus the second solution is considered unstable.

Three-dimensional unsteady radiative hybrid nanofluid flow through a porous space over a permeable shrinking surface

This study explores the heat transfer and fluid flow properties that occur within the radiative unsteady hybrid alumina-copper/water nanofluid flow through a porous space over a permeable shrinking surface in a three-dimensional domain. The fluid flow model in the form of partial differential equations is transformed into ordinary differential equations through dimensionless similarity variables. The finalized form of the model is then resolved using the finite difference method with the Lobato IIIa formula via the built-in MATLAB function known as bvp4c. Two non-unique solutions are executed; however, the second solution is not stable. The findings suggest that the effective heat transfer performance of the hybrid nanofluid can be established by increasing the porosity and suction parameters. The laminar flow phase can also be maintained by increasing the suction and porosity parameters while extensively shrinking the surface. However, a smaller magnitude of the shrinking capacity of the surface is suggested to result in a better heat transfer performance. Effective heat transfer can also be achieved by increasing the thermal radiation parameter within a specific range of smaller shrinking capacity. Overall, this study provides a vital guideline for simulating the fluid flow system and suggests strategies to optimize fluid flow and heat transfer performance.

Dual solutions for magnetic-convective-quadratic radiative MoS2 − SiO2/H2O hybrid nanofluid flow in Darcy-Fochheimer porous medium in presence of second-order slip velocity through a permeable shrinking surface: Entropy and stability analysis

ABSTRACT This investigation aims to scrutinize the flow phenomenon and thermal variations of magnetohydrodynamic hybrid nanofluid flow induced by a shrinking surface. The novelty of the work is to examine the flow and heat transport behavior with entropy production of mixed convective / hybrid nanofluid through a Darcy–Forchheimer porous medium in the presence of nonlinear quadratic thermal radiation with second-order velocity slip over a contracting surface. Nanoparticles molybdenum disulfide and silicon dioxide are coupled with the base fluid water () to construct / hybrid nanofluid. The governing set of nonlinear partial differential equations with corresponding boundary constraints is converted into a set of nonlinear ordinary differential equations using the similarities transformation before being solved numerically with the help of the default solver in the MATLAB bvp4c package. A dual solution is determined based on the emerging parameters, including a certain amount of mass suction parameter, nanoparticle volume fractions, magnetic field, Grashof number, nonlinear quadratic thermal radiation, Darcy–Forchheimer factor, and first- and second-order velocity slip factors, for the velocity, temperature, skin friction, and local Nusselt number, and they are analyzed tabularly and graphically. These results also indicate that the solution for the upper branch was stable, while it was unstable for the lower branch based on the stability analysis. Quadratic thermal radiation has been discovered to considerably impact the fluid’s temperature and the pace of heat transfer. The magnetic field resistance and Forchheimer number slow the flow of the liquid and increase its temperature. Furthermore, by combining silicon oxide with a volume percentage of molybdenum disulfide, the flow is retarded, and heat transfer is enhanced. With an increase in the nanoparticle volume fraction by , the skin friction is boosted up by almost and and local Nusselt number is decelerated by almost , for a particular upper branch over the shrinking surface due to the influences of and nanoparticles, respectively. Furthermore, quadratic thermal radiation and first-second-order velocity slip considerably enhance the entropy formation.

Numerical simulation of melting heat transfer towards stagnation point region over a permeable shrinking surface

Numerical simulation of melting heat transfer towards stagnation point region over a permeable shrinking surface

The flow of hybrid nanofluid past a permeable shrinking sheet in a Darcy–Forchheimer porous medium with second-order velocity slip

The objective of this research is to study the significance of second-order velocity slip in a Darcy–Forchheimer porous medium with the hybrid nanofluid flow toward a permeable shrinking surface. Heat generation and radiative heat flux are introduced in the energy model. Two distinct nanoparticles of aluminum oxide (Al2O3) and copper (Cu) are used to represent the hybrid nanofluid flow with water (H2O) as the base fluid. An appropriate method of similarity transformation is applied to reduce a PDE system into a model of non-linear ODEs. With the aid of a bvp4c solver in Matlab, the respective findings are graphically presented for the profiles of velocity and temperature, skin friction coefficient, and Nusselt numbers with physical parameters, such as suction, porous medium permeability, Darcy–Forchheimer number, shrinking, radiation, and nanoparticle volume fraction. The hybrid nanofluid presented a higher estimation of heat and mass transfer rates than the classic mono-nanofluid. Moreover, the parameters of Darcy–Forchheimer number and second-order velocity slip significantly expand the fluid flow. It is found that the occurrence of opposing flow (λ < 0) will generate two solutions, where the implementation of stability analysis perceived the first solution to be the most realizable.

Heat and mass transfer of a hybrid nanofluid flow with binary chemical reaction over a permeable shrinking surface

The effect of a binary chemical reaction defined by activation energy on the heat and mass transfer of a hybrid nanofluid flow over a permeable stretching surface was analyzed. The governing equations of the problem were reduced to a set of nonlinear ordinary differential equations that were solved using the nonlinear shooting method. Dual solutions were observed within an interval of the suction parameter, with all other parameters fixed. The results show that the domain of the existence of dual solutions widens with an increase in the volume fraction of copper nanoparticles, the Richardson's number, and the combined buoyancy force parameter. The opposite is observed with an increase in the volume fraction of alumina nanoparticles, stretching parameter, and temperature difference parameter. The skin friction coefficient, local Nusselt number, and Sherwood number increase with an increase in the suction parameter, volume fraction of copper nanoparticles, Richardson's number, and combined buoyancy force parameter. The mass transfer is sensitive to a low value of the dimensionless activation energy, and is greater with an increase in the fitted rate constant, temperature difference parameter, and non-dimensional reaction rate. The flow properties are greatly influenced by changes in the suction parameter, stretching parameter, and nanoparticle volume fraction.

Transient flow of Maxwell Nanofluid Over a Shrinking Surface: Numerical Solutions and Stability Analysis

This article explores the theoretical analysis for thermal and mass transport of Maxwell nanofluid along permeable shrinking surface. The thermal and concentration configuration involve heat generation/absorption and chemical reaction in the flow regime. Brownian motion and thermophoresis phenomenon are considered in the mass transport analysis. This physical configuration is translated in terms of nondimensional differential system. A numerical investigation of the governing equations is carried out with Bvp4c technique in MATLAB. Further, it has been found that shrinking and suction at porous surface leads to multiple solutions of the system. The results in terms of line graphs portray that the stronger suction at shrinking surface possess higher heat and mass transfer rate at surface. The heat transfer rate enhances by the larger values of Biot number. Further, the velocity, temperature and mass distribution indicate maximum values at stronger relaxation parameter.

Magnetohydrodynamic slip flow and heat transfer over a nonlinear shrinking surface in a heat generating fluid

In this paper, the problem of steady slip magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a nonlinear permeable shrinking surface in a heat generating fluid is studied. The transformed boundary layer equations are then solved numerically using the bvp4c function in MATLAB solver. Numerical results are obtained for various values of the magnetic parameter, the slip parameter and the suction parameter. The skin friction coefficients, the heat transfer coefficients, as well as the velocity and temperature profiles for various values of parameters are also obtained and discussed.Â

Impact of Nonlinear Thermal Radiation on the Time-Dependent Flow of Non-Newtonian Nanoliquid over a Permeable Shrinking Surface

Symmetry and fluid dynamics either advances the state-of-the-art of mathematical methods and extends the limitations of existing methodologies to new contributions in fluid. Physical scenario is modelled in terms of differential equations as mathematical models in fluid mechanics to address current challenges. In this work a physical problem to examine the unsteady flow of a third-grade non-Newtonian liquid induced through a permeable shrinking surface containing nanoliquid is considered. The model of Buongiorno is utilized comprising the thermophoresis and Brownian effects through nonlinear thermal radiation and convective condition. Based on the flow symmetry, suitable similarity transformations are employed to alter the partial differential equations into nonlinear ordinary differential equations and then these ordinary differential equations are numerically executed via three-stage Lobatto IIIa formula. The flow symmetry is discussed for interesting physical parameters and thus this work is concluded. More exactly, the impacts of pertinent constraints on the concentration, temperature and velocity profiles along together drag force, Sherwood and Nusselt numbers are explained through the aid of the tables and plots. The outcomes reveal that the dual nature of solutions is gained for a specific amount of suction and flow in the decelerating form A &lt; 0 . However, the unique result is obtained for flow in accelerating form A ≥ 0 . In addition, the non-linear parameter declines the liquid velocity and augments the concentration and temperature fields in the first result, whereas the contrary behavior is scrutinized in the second result.

Numerical study of unsteady flow and heat transfer CNT-based MHD nanofluid with variable viscosity over a permeable shrinking surface

Purpose The purpose of this paper is to present a novel model on the unsteady MHD flow of heat transfer in carbon nanotubes with variable viscosity over a shrinking surface. Design/methodology/approach The temperature-dependent viscosity makes the proposed model non-linear and coupled. Consequently, the resulting non-linear partial differential equations are first reformed into set of ordinary differential equations through appropriate transformations and boundary layer approximation and are then solved numerically by the Keller box method. Findings Graphical and numerical results are executed keeping temperature-dependent viscosity of nanofluid. It is noted that, for diverse critical points, it is found that at one side of these critical values, multiple solutions exist; on the other side, no solution exists. A comparison is also computed for the special case of existing study. The temperature and pressure profiles are also plotted for various effective parameters. Originality/value The work is original.

Stability analysis of impinging oblique stagnation-point flow over a permeable shrinking surface in a viscoelastic fluid

This study attempts to present the stability of dual solutions obtained from impinging inclined stagnation-point flow past a permeable shrinking flat plate in a viscoelastic fluid. The similarity transformation helps to simplify the complex model in the form of partial differential equations, into a system of ordinary differential equations. The bvp4c function provides the numerical solutions according to the variations in the governing parameters. The skin friction along the permeable shrinking surface is dependent on the elasticity of the fluid. A higher degree of shrinking persuades quicker flow separations. The dual solutions are apparent when the sheet is stretching/shrinking. Stability analysis reveals that the second solution is unstable and therefore, may not be practicable. The results from this study can be useful to explain and enhance the hydraulic fracturing system in the mining industry. All numerical results presented are original and new for the study of fluid flow and heat transfer of inclined stagnation-point flow towards a permeable shrinking surface in a viscoelastic fluid.

A review on slip-flow and heat transfer performance of nanofluids from a permeable shrinking surface with thermal radiation: Dual solutions

A computational study on the stagnation-point flow of an electrically conducting nanofluid over a non-linear stretching/shrinking surface with first-order slip phenomenon is carried out. Because, nanofluids are considered as one of the closest kinds to the practical application of fluid flows owing to its comprehensive properties such as the Brownian motion and thermophoresis. The simulations were performed to understand the heat and mass transfer traits in the presence of non-linear radiation. Moreover, the Rosseland approximation model is incorporated to investigate the mechanisms of radiative heat transfer performance of nanofluids. For all cases, it has been seen that the governing conservation equations of current model possesses a similarity solution. The transformed system of nonlinear ordinary differential equations, is then integrated numerically with a boundary value problem solver, bvp4c in Matlab software. The captured numerical results have been displayed graphically and some interesting features like multiple (upper and lower) solutions are found. The critical values corresponding to the suction parameter fw and the shrinking parameter λ are computed. The rising thermo-physical dimensionless parameters overseeing the flow are power-law parameter, Hartmann number, slip parameter, Eckert number, temperature ratio parameter, radiation parameter, Brownian motion and thermophoresis parameters and Lewis number. It is found that, the slip parameter has a reducing impact on the skin friction coefficient for both upper and lower branch solutions. The major outcome of the present study is that the temperature ratio parameter boosts the temperature profiles for both solutions. While the temperature profiles show a decreasing behavior for higher non-linear radiation parameter. Validation of numerical scheme is accomplished by means of benchmarking with some already reported studies, and a great correlation is illustrated.

Boundary layer flow and heat transfer past a permeable shrinking surface embedded in a porous medium with a second-order slip: A stability analysis

The fluid flow and heat transfer over a permeable shrinking sheet embedded in a porous medium with a second-order slip is studied. Using appropriate similarity variables, the governing partial differential equations are reduced to ordinary differential equations before being solved numerically by a shooting method for different values of the selected governing parameters. The numerical results reveal that two (dual) solutions are possible for a certain range of these parameters. A stability analysis is performed to determine which solution is stable and which one is not. The effects of suction and the second order slip parameters on the skin friction coefficient and the local Nusselt number as well as on the velocity and temperature profiles are plotted and discussed. It is found that applying the slip condition increases the range of solutions. Also, the skin friction coefficient is higher for the no slip condition compared to that of with slip condition.

MHD 3D flow of nanofluid in presence of convective conditions

An analysis has been carried out for the magnetohydrodynamic (MHD) flow of viscous nanofluid saturating porous medium. The flow is induced by a convectively heated permeable shrinking surface. Appropriate transformations reduce the nonlinear partial differential system to an ordinary differential system. Flow and heat transfer characteristics are computed by HAM solutions. The results of velocity, temperature and Nusselt number are analyzed for various parameters of interest. It is noted that higher nanoparticle volume fraction decreases the velocity field. Also the temperature and heat transfer rate are enhanced for larger values of Biot number.

Magnetohydrodynamic Three-Dimensional Flow of Nanofluid by a Porous Shrinking Surface

AbstractThis study investigates the steady three-dimensional flow of viscous nanofluid past a permeable shrinking surface with velocity slip and temperature jump. An incompressible fluid fills the porous space. The fluid is electrically conducting in the presence of an applied magnetic field. The governing nonlinear partial differential equations are reduced to ordinary differential equations by similarity transformations. The analytic solutions are presented in series form by the homotopy analysis method. Convergence of the obtained series solutions is explicitly discussed. The velocity and temperature profiles are shown and analyzed for different emerging parameters of interest. It is observed that by increasing the volume of copper nanoparticles, the thermal conductivity increases and the boundary layer thickness decreases. The velocity profile increases and temperature profile decreases for the larger velocity slip parameter. The temperature is a decreasing function of the thermal slip parameter. Henc...

Unsteady flow of Maxwell fluid in the presence of nanoparticles toward a permeable shrinking surface with Navier slip

A detailed study on the problem of unsteady boundary layer flow and heat transfer of an upper-convected Maxwell fluid in the presence of nanoparticles over a permeable shrinking sheet with wall mass transfer is presented. In contrast to the conventional no-slip condition at the surface, Navier’s slip condition is applied at the surface. By use of a similarity transformation, the partial differential equations are reduced to a system of ordinary differential equations which is then solved numerically with shooting technique. The numerical results pertaining to the present study indicate that dual solutions exist for negative values of the unsteadiness parameter (A). It results in from the stability analysis that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically realizable. It is also found that as the Maxwell parameter (β) and velocity slip parameter (δ) increase, the range of the unsteadiness parameter (A) for which the solution exists gradually increases. The local Nusselt number and the local Sherwood number increase with the increase in the values of Maxwell parameter (β) and velocity slip parameter (δ). Furthermore, the effects of different physical parameters on the flow, temperature and concentration profiles are shown graphically and discussed in details.

MAGNETOHYDRODYNAMIC VISCOUS FLOW OVER A SHRINKING SHEET IN A SECOND-ORDER SLIP FLOW MODEL

In this paper, we investigate a magnetohydrodynamic viscous flow over a permeable shrinking surface by means of a second-order slip flow model. We have obtained a closed form of exact solution for the Navier−Stokes equations by using the similarity variable technique. The effects of slip, suction, and magnetic parameters have been investigated in detail. The results show that there are two solution branches, namely, a lower solution branch and an upper solution branch. The behavior of velocity and shear stress profiles at different values of slip, suction, and magnetic parameters has been discussed through graphs.