Wedge Angle Parameter Research Articles

Nonsimilar modeling and numerical convective transport analysis of forced flow of radiative Carreau nanofluid with zero mass flux boundary condition

AbstractPresent research focuses on nonsimilar analysis of the flow of a non‐Newtonian Carreau nanofluid against different geometrical configurations affected by thermal radiations. The flow is induced by stretchable surface with the implementation of zero‐net mass‐flux conditions on the surface. This considered model is commonly known as Kuznetsov and Nield's proposed updated model for nanoparticles. The derived flow equations are first nondimensionalized by employing appropriate nonsimilar transformations. The transformed system is analytically tackled by employing the local nonsimilarity (LNS) approach up to the second‐truncation level in association with the numerical algorithm bvp4c. The consequences of appropriate parameters, such as the suction parameter, wedge angle parameter, Weissenberg number, Prandtl number, constant velocity parameter, temperature ratio, Brownian motion, Lewis number, thermophoresis and radiation parameters, on fluid velocity, thermal, and concentration profiles are calculated and graphed. Drag coefficient, Nusselt, and Sherwood numbers are also computed and presented in tabular form. It is observed that intensification in the suction parameter shows augmentation in the local skin friction coefficient. Enhancement in the wedge angle parameter increases both the Sherwood and Nusselt numbers. Enhancement in velocity profile of the nanofluids is noticed with the increasing estimations of suction parameter. Thermophoresis parameter enhances both thermal and concentration profiles, however increasing Lewis number leads to a decline in the concentration boundary layer. With judgment, a comparative assessment is made of the present and previous results. This research may be helpful for the researchers that are interested in studying prospective industrial and engineering nanofluid applications, notably in geophysical and geothermal systems, heat exchangers, solar water heaters, and many others.

Numerical investigation on movement of triple points on oblique detonation surfaces

A normal detonation wave in a gaseous mixture is a transient, multidimensional structure containing triple points (TPs) that collide in pairs and then propagate oppositely. However, the TPs on an oblique detonation wave (ODW) almost propagate along the same direction in most studies. In this study, the reactive Euler equations coupled with a two-step induction–reaction kinetic model are used to solve a two-dimensional wedge-induced ODW. Two novel movement patterns are observed in most cases. Results show that the TPs of the ODW can propagate upstream and even stand on the wave surface. The movement patterns of TPs include downstream, upstream, and steady according to their propagation direction relative to the wedge. We find that the ratio of the post-ODW flow speed Uτ to the transverse wave speed UT dominates the TP movement types. When the speed ratio Uτ/UT is approximately equal to 1, the TPs can stand on the wave surface. Above unity, downstream TPs form, and upstream TPs correspond to a value smaller than 1. Furthermore, the inflow Mach number has little influence on UT, while Uτ changes significantly. This is largely due to the high sensitivity of the ODW angle to the inflow. The high heat release rate benefits upstream TPs, and steady TPs form under a large wedge angle. The results are confirmed by varying the inflow Mach number, wedge angle, and chemical parameters.

Stability Analysis of Unsteady Hybrid Nanofluid Flow over the Falkner-Skan Wedge.

Numerous manufacturing processes, including the drawing of plastic films, have a major impact on mass transport. These functionalities necessitate the solution of the Falkner–Skan equation and some of its configurations when applied to various geometries and boundary conditions. Hence, the current paper discusses the impact of unsteady hybrid nanofluid flow on a moving Falkner–Skan wedge with a convective boundary condition. This problem is modeled by partial differential equations, which are then converted into ordinary (similar) differential equations using appropriate similarity transformations. The bvp4c technique in MATLAB solves these ordinary differential equations numerically. Since more than one solution is possible in this paper, stability analysis is conducted. Thus, it is found that only one stable solution is identified as reliable (physically realizable in practice). The skin friction coefficient and heat transfer rate, along with the velocity and temperature profile distributions, are examined to determine the values of several parameters. The findings reveal that dual-type nanoparticles and wedge angle parameters improve thermal efficiency. A lower value of the unsteadiness parameter reduces the efficiency of hybrid nanofluids in terms of heat transfer and skin friction coefficient, whereas increasing the Biot number of the working fluid does not affect the critical point in the current analysis.

Entropy generation on magnetohydrodynamic laminar boundary‐layer Casson CNT‐based nanofluid flow across a wedge by using the homotopy analysis method

AbstractThe purpose of the study is to scrutinize the entropy generation analysis on magnetohydrodynamic heat transfer flow from Casson single‐walled carbon nanotube on a wedge with Joule heating and viscous dissipation. Kerosene oil is considered as base fluid because of its exclusive features, advanced thermal conductivity, application, and unique behavior. Using similarity variables, the regulating equations are modified into nonlinear coupled, ordinary differential equations, which are then tackled using homotopy analysis method. Impacts of emerging parameters on entropy generation, temperature, velocity, and Bejan number distributions are discussed and shown graphically. The Nusselt number and skin‐friction coefficient values are shown in a table. The results reveal that velocity enhances due to increasing magnetic and Casson parameters. It was inspected that entropy production enhances due to increasing wedge angle and magnetic parameter and decays with Casson parameter. Also, it is examined that the Bejan number upsurges due to larger Casson and wedge angle parameters but a reverse trend can be observed with increasing values of a magnetic parameter. The present results have been endorsed by comparing with the available data in the literature, it was discovered that they are in excellent agreement.

Structural Design and Dynamic Simulation Optimization of the Triggering Device in a Pressure-Holding Controller for Deep in Situ Coring

As Earth’s shallow coal resources are gradually depleted, humans turn their mining operations to deeper regions. However, because the mechanics of deep-rock masses have not been fully established, the development of deep resources lacks theoretical guidance, and the continuity of such engineering activities is poor. The basis of deep-rock mechanics theory is to achieve deep in situ rock fidelity coring (including the maintenance of pore pressure and temperature). To achieve this goal, deep in situ pressure-holding coring technology is needed. The pressure-holding controller is the key corer component for realizing deep in situ pressure-holding and coring technology. The flap-valve-type pressure-holding controller driven by an elastic force or gravity alone is not enough to provide the initial sealing pressure for the sealing surface. Therefore, a trigger mechanism that assists the pressure-holding controller in achieving closing and initial sealing was designed. Then, the action and friction characteristics of the triggering mechanism were calculated according to the experimental dynamics simulation calculations of different closing characteristics that are affected by gravity in pressure-holding controller space. Optimization was conducted to determine the optimal values of the trigger mechanism spring stiffness, wedge angle, and other parameters. The mechanism can provide technical support for deep pressure-holding coring and improve the pressure-holding power of deep in situ rock coring.

Significance of chemical reaction with activation energy for Riga wedge flow of tangent hyperbolic nanofluid in existence of heat source

This manuscript uncovers the heat and mass transfer of an unsteady tangent hyperbolic nanofluid flow across an extensible Riga wedge under the effects of stagnation point, heat source, and activation energy. The flow computations with modified Hartmann numbers are embedded in this investigation particularly in the unsteady tangent hyperbolic liquid stream scenario. The focus pertains to augment heat conduction in the bulk liquid as heat and mass transport media. The implications of controlling parameters on non-dimensional speed, temperature, as well as concentration profiles are visually portrayed. The governing partial differential equations are modified into non-dimensional forms by reducing the number of independent factors, which are then pursued numerically utilizing the Runge-Kutta method with the shooting tool. The velocity of Newtonian fluid improves as the magnitude of wedge angle parameter βw rises, although it is marginally lower than that of tangent hyperbolic fluid, the temperature of Newtonian fluid intensifies substantially faster than that of tangent hyperbolic fluid for higher values of βw. The skin friction factor increases with alterations to the Hartmann parameter, Weissenberg factor, wedge angle parameter as well as suction parameter. The percentage increase in skin friction factor is 13.3 and 21.93 when modified Hartmann number takes input in the range 0 ≤ Mh ≤ 0.2 and unsteady parameter 0.1 ≤ A ≤ 0.5. The Schmidt number, chemical change, and wedge angle parameters are all designed to boost the Sherwood number.

Maxwell time-dependent nanofluid flow over a wedge covered with gyrotactic microorganism: an activation energy process

With progressively more sophisticated enhancements in nanotechnology and optimisation, the demand is increasing for more effective and robust heat transfer fluids with significantly greater thermal conductivities than those of traditional ones. The current article deals with the flow of Maxwell nanofluid, over a wedge with the impact of activation energy and motile microorganisms. A transformed construction is recognised to avail an ordinary differential system by exploiting appropriate similarity transformations. The controlling equations for governing flow situations are constructed and addressed using the well-known numerical shooting procedure. For numerical results, bvp4c routine built-in MATLAB software is used. The influence of all the parameters is discussed for the velocity profile, temperature, volumetric concentration profile, andconcentration profile of microorganisms. The progressive valuation of magnetic parameter, wedge angle parameter and bioconvection Rayleigh number reduce the velocity of flow. The basic values of these parameters shall be Pr = 1, Bi = EE = γ = 1.0, Nt = Nb = 0.5, Le = Ha = m = Q = 1, β = 0.1, A = 0.5, Nr = 2, λ 1 = 2, n = 1, Ω = 5, and α = π/3. The volumetric concentration of nanoparticles is boosted with higher values of melting parameter and solutal stratification Biot number.

Flow and heat transfer over a permeable moving wedge in a hybrid nanofluid with activation energy and binary chemical reaction

PurposeThe analysis of boundary layers is needed to reflect the behaviour of fluid flows in current industrial processes and to improve the efficacy of products. Hence, this study aims to analyse the flow and heat transfer performance of hybrid alumina-copper/water (Al2O3-Cu/H2O) nanofluid with the inclusion of activation energy and binary chemical reaction effect towards a moving wedge.Design/methodology/approachThe multivariable differential equations with partial derivatives are converted into a specific type of ordinary differential equations by using valid similarity transformations. The reduced mathematical model is elucidated in the MATLAB system by using the bvp4c procedure. This solution method is competent in delivering multiple solutions once appropriate assumptions are supplied.FindingsThe results of multiple control parameters have been studied, and the findings are verified to provide more than one solution. The coefficient of skin friction was discovered to be increased by adding nanoparticles volume fraction from 0% to 0.5% and 1%, by almost 1.6% and 3.2%. Besides, increasing the nanoparticles volume fraction improves heat transfer efficiency gradually. The inclusion of the activation energy factor displays a downward trend in the mass transfer rates, consequently reducing the concentration profile. In contrast, the increment of the binary reaction rate greatly facilitates the augmentation of mass transfer rates. There is a significant enhancement in the heat transfer rate, approximately 13.2%, when the suction effect dominates about 10% in the boundary layer flow. Additionally, the results revealed that as the activation energy rises, the temperature and concentration profiles rise as well. It is proved that the activation energy parameter boosts the concentration of chemical species in the boundary layer. A similar pattern emerges as the wedge angle parameter increases. The current effort aims to improve the thermal analysis process, particularly in real-world applications such as geothermal reservoirs, chemical engineering and food processing, which often encountered mass transfer phenomenon followed by chemical reactions with activation energy.Originality/valueThe present results are original and new for the study of flow and heat transfer over a permeable moving wedge in a hybrid nanofluid with activation energy and binary chemical reaction.

Analysis of boundary layer nanofluid flow over a stretching permeable wedge-shaped surface with magnetic effect

The problem of steady two-dimensional boundary layer flow of momentum, heat and mass transfer over a stretching permeable wedge-shaped surface in a nanofluid in presence of magnetic field has been studied. In this respect, the governing partial differential equations have been converted into ordinary differential equations by using the local similarity transformation. The transformed governing equations have been then solved numerically using the bvp4c in MATLAB software. The effects of the pertinent parameters, namely wedge angle parameter (β), Brownian motion (Nb), thermophoresis (Nt), magnetic parameter (M), moving wedge parameter (λ), permeability parameter (K*), Prandtl number (Pr), and Lewis number (Le) on fluid velocity, thermal and concentration within the boundary layer have been analyzed. The numerical results obtained of the skin friction coefficients, local Nusselt number and local Sherwood number, as well as the velocity, temperature and concentration profiles have been presented graphically and also in tabular form. The results indicate that the momentum boundary layer thickness increases with increasing values of wedge angle and moving wedge but reduces for magnetic and permeability effects. The heat transfer rate increases for wedge angle, moving wedge, Brownian motion but decreases for thermoporesis and magnetic effects. The mass transfer rate decreases for Brownian motion and thermoporesis effects but increases for wedge angle and moving wedge parameters. Finally, the numerical results have been compared with previously published research and found to be in good agreement.

The flow of a micropolar nanofluid past a stretched and shrinking wedge surface with absorption

This research is examining, a continuous, laminar, flow of a micropolar nanofluid through a stretched and shrinking wedge in the presence of heat generation or absorption and applied magnet field over a wedge surface. A number of governing parameters are employed to assess the results. The governing partial differential equations were transformed into ordinary differential equations which were solved numerically by using the Runge Kutta Gill and shooting methods. The steady-state velocity, temperature, and angular velocity profiles are shown graphically. The result showed the effects of nanoparticle concentration, wedge angle, suction and material parameter on velocity, temperature and angular velocity fields.

Analytical ADM study of time-dependent hydromagnetic flow of biofluid over a wedge

In this research work, we consider the two-dimensional time-dependent laminar hydromagnetic boundary-layer flow of a bio-magnetic fluid over a wedge using a micropolar fluid model with convective boundary conditions and taking into account the action of a transversely magnetic field. The partial differential equations that govern velocity, temperature and micro-rotation are transformed into nonlinear ordinary differential equations with similarity transformations. The findings are analytically analyzed afterward through the Adomian decomposition method (ADM) and numerically through the shooting technique based on Runge–Kutta–Fehlberg. In this study, we have considered the effect of the unsteadiness parameter $$K$$ , wedge angle parameter $$\beta$$ , Reynolds number Re, magnetic field parameter $$M$$ and induced magnetic field $$h$$ on the evolution of dimensionless velocity, temperature and micro-rotation of the bio-magnetic flow throughout the boundary layer. It is found that the flow separation may occur with the increase in unsteadiness parameter $$K$$ and is prevented as the wedge angle parameter $$\beta$$ rises. Also, results indicate that in the vicinity of the wedge surface, increasing K parameter leads to a reduction in fluid temperature and grows the micro-rotation of the blood corpuscles. Finally, comparisons between analytical and numerical data clearly show the effectiveness of the adopted analytical ADM technique.

Upper-convected Maxwell fluid analysis over a horizontal wedge using Cattaneo-Christov heat flux model

Boundary-layer flow of upper-convected Maxwell fluid over a wedge with suction and heat generation/absorption is presented in this paper by considering the Cattaneo-Christov heat flux model. The governed equations are transformed into a set of the ODE using similarity transformations. A third-order finite difference method for the ODE is used to find the local similarity solutions of the problems. The effects of the wedge angle parameter, viscoelastic fluid parameter, thermal relaxation time parameter, and heat generation/absorption parameter are presented in this study.

Existence of dual solutions for wedge flow of magneto-Williamson nanofluid: A revised model

This communication intends to elaborate the mechanism of heat and mass transport of an unsteady stagnation point flow of Williamson nanofluid past a wedge subject to magnetohydrodynamics (MHD), thermophoresis and Brownian motion effects. In this study, the flow equations with magnetic parameter is incorporated especially in the Williamson fluid flow case. The appropriate transformations are used to convert the governing partial differential equations into ordinary differential equation and then solved numerically by using shooting scheme with fourth order Runge-Kutta-Fehlberg method in MATLAB software. The influence of wedge angle parameter, the local Weissenberg number, unsteadiness parameter, magnetic parameter, suction parameter, the Biot number, thermophoresis and Brownian motion parameter on dimensionless velocity, temperature and nanoparticle concentration fields as well as skin friction coefficient and local Nusselt number are rigorously demonstrated and discussed. This study also elaborates the critical range of velocity ratio parameter and suction parameter, for the existence of dual branch of solutions. The obtained results show that Biot number enhances the fluid temperature and concentration. Further, the suction parameter is an increasing function of rate of heat transfer. Furthermore, the analysis suggests that the upper branch solution is stable and physically possible.

Viscous dissipation effect on Williamson nanofluid over stretching/shrinking wedge with thermal radiation and chemical reaction

This paper scrutinizes the effect of viscous dissipation on unsteady two-dimensional boundary layer flow of Williamson nanofluid over a stretching/Shrinking wedge. To express the boundary condition in concentration problem the passive control concept used. The governing PDEs are converted to ODEs by means of a similarity transformation before being solved numerically by finite difference scheme called Keller-Box method. The equations were numerically solved by using Matlab software 2013a. The characteristics of parameters such as wedge angle, unsteadiness, Williamson, slip, Brownian motion, thermophoresis, chemical reaction parameters, Prandtl number, Biot-number, Eckert number and Lewis number on velocity, concentration and temperature profiles and skin friction coefficient, Nusselt number and Sherwood number are presented in graphs and tables. The result of the study designates that the velocity profiles increased with an upsurge of wedge angle, unsteady parameter and suction parameter while it is diminished with an increase of Williamson and injection parameter. The temperature profiles upsurges with the distended Williamson parameter, Biot number and injection parameter, while it is declined for large values of wedge angle, unsteady and suction parameter. With an increase of Williamson, unsteady and suction parameter the concentration profiles upsurges, while it is decreased with an increase of wedge angle and injection parameter. The numerical results are compared with available literature and obtained a good agreement.

Mixed Bioconvective Flow Over a Wedge in Porous Media Drenched with a Nanofluid

A mathematical model is accentuated the mixed bioconvective flow on a vertical wedge in a Darcy porous medium filled with a nanofluid containing both nanoparticles and gyrotactic microorganisms. Thermophoresis and Brownian motion impacts are addressed to consolidate energy and concentration equations with passivelycontrolled boundary conditions. A mixed convective parameter for the whole regime of the mixed convective is appointed. The system of governing partial differential equations is converted into a non-similar set, which are then solved by an implicit finite difference method. By taking the impacts of the varying pertinent parameters, namely, the bioconvection nanofluids and wedge angle parameters in the entire mixed convection regime, the numerical results are analyzed graphically for the dimensionless the velocity, temperature, nanoparticle volume fraction and the density motile microorganisms profiles as well as the local Nusselt and motile microorganism numbers.

Computational study of Falkner–Skan flow of chemically reactive Cross nanofluid with heat generation/absorption

The numerical investigation of magnetohydrodynamic Falkner–Skan boundary layer flow of Cross nanofluid past a wedge in moving fluid is fundamental subject of current paper. The present work is the principal endowment in presenting the flow and heat transfer characteristics of Cross nanofluid past wedge geometry. Moreover, the consequence of heat generation/absorption and diffusion of chemically reactive species is also examined. Instead of conventional no-slip condition at the surface of wedge, Newtonian heat and mass conditions are utilized. The governing problem consisting of highly nonlinear coupled equations is numerically elucidated by the legendry shooting technique. The outcomes of analysis reveal that the wedge angle parameter resulted in boosting the fluids velocity while the temperature and concentration profiles exhibited decaying trend. Enrichment in fluid temperature and nanoparticle concentration fields is found by invoking the Newtonian heat and mass conditions. The increasing values of the heat generation or absorption parameter caused diminution of local Nusselt number. Additionally, an outstanding comparison with the results already reported in the literature is demonstrated for special case.

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The results discover that two solutions exist, up to a certain value of the stretching/shrinking and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions for copper and wedge angle parameter increase. It is also found that the hybrid nanofluid enhances the heat transfer rate compared with the regular nanofluid. The reduction of the heat transfer rate is observed with the increase in radiation parameter. The temporal stability analysis is performed to analyze the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.

The assessment of time dependent flow of Williamson fluid with radiative blood flow against a wedge

The present pagination reports both Brownian diffusion and thermophoresis aspects subject to magnetohydrodynamic Williamson fluid model. Assuming the flow is unsteady and blood is treated as Williamson fluid over a wedge with radiation. The governing equations are transformed into ordinary differential equations by using similarity variables. The numerical solutions of the transformed governing equations are obtained by using the RK 4th order method along with shooting technique solver. The effects of various physical parameters such as Hartmann number, local Weissenberg number, radiation parameter, unsteadiness parameter, Prandtl number, Lewis number, Brownian diffusion, thermophoresis, wedge angle parameter, moving wedge parameter, on velocity, temperature, concentration, skin friction, heat transfer rate and mass transfer rate have been discussed in detail. The velocity and temperature profile deprives for larger We and an opposite trend is observed for concentration. The radiation parameter is propositional to temperature and a counter behavior is observed for Pr.

Mixed Bioconvective Flow Over a Wedge in Porous Media Drenched with a Nanofluid

A mathematical model is accentuated the mixed bioconvective flow on a vertical wedge in a Darcy porous medium filled with a nanofluid containing both nanoparticles and gyrotactic microorganisms. Thermophoresis and Brownian motion impacts are addressed to consolidate energy and concentration equations with passivelycontrolled boundary conditions. A mixed convective parameter for the whole regime of the mixed convective is appointed. The system of governing partial differential equations is converted into a non-similar set, which are then solved by an implicit finite difference method. By taking the impacts of the varying pertinent parameters, namely, the bioconvection nanofluids and wedge angle parameters in the entire mixed convection regime, the numerical results are analyzed graphically for the dimensionless the velocity, temperature, nanoparticle volume fraction and the density motile microorganisms profiles as well as the local Nusselt and motile microorganism numbers.

Carreau nanofluid heat and mass transfer flow through wedge with slip conditions and nonlinear thermal radiation

In the present study, we have perceived the impact of nonlinear thermal radiation on heat transfer analysis of Carreau nanofluid flow through wedge by considering slip conditions into account. The extremely nonlinear partial differential equations are transformed into nonlinear ordinary differential equations by using suitable similarity variables, and these equations together with boundary conditions are solved by using the most extensively validated finite element method. The impact of various pertinent parameters, such as Weissenberg number, wedge angle parameter, radiation parameter, temperature ratio parameter, Prandtl number, thermophoresis parameter, Brownian motion parameter, constant velocity ratio parameter, suction parameter, temperature slip parameter, Lewis number, power law index parameter, concentration slip parameter, chemical reaction parameter and magnetic parameter, on velocity, temperature and concentration profiles is calculated and is revealed through graphs. The values of Nusselt number, Sherwood number and skin friction coefficient are also calculated and shown in tables. It is noticed that there is a remarkable intensification in the values of Nusselt number, Sherwood number and skin friction coefficient as the values of Weissenberg number rise. The temperature and concentration distributions both intensify with rising values of temperature slip parameter (ξ).