Dimensionless Velocity Profiles Research Articles

Varying wall temperature and thermal radiation effects on MHD boundary layer liquid flow containing gyrotactic microorganisms

Nanofluid dynamics and magnetohydrodynamics have tremendously contributed to industrial applications. The presence of nanoparticles in base fluids enhances the specific chemical and physical properties. This study intends to examine the combined impacts of magnetic field and convective boundary state on bioconvection of a Casson fluid and concentration of nanoparticles in presence of gyrotactic microorganisms over a straight extending sheet. To simplify the governing equations comprising momentums, temperature, and concentration of nanoparticles, and microorganisms, the similarity transformations are employed. Emerged system of coupled nonlinear differential equations is solved by the differential transformation method and MATHEMATICA software. The impacts of the Brownian motion parameter, thermophoresis parameter, Casson fluid parameter, radiation parameter, suction or mass flux parameter, magnetic field, Prandtl number, Lewis number, Peclet number, and bioconvection parameter on dimensionless velocity, temperature, nanoparticles concentration, and microorganisms density profile are interpreted through graphs. The present bioconvection analysis is most relevant to the study of bioproducts.

Effect of thermal radiation and MHD on hybrid Ag–TiO2/H2O nanofluid past a permeable porous medium with heat generation

The major objective of this study is to identify the behaviour of flow and heat transfer on mixed convection with the appearance of hybrid nanofluid in a porous medium, heat generation, suction/injection, thermal radiation and magnetohydrodynamics (MHD). Two distinct fluids of Ag (silver) and TiO2 (titanium dioxide) are used in this model to represent the hybrid condition and a model of non-linear ODEs is obtained by conducting a technique of similarity transformation. The findings and solutions are gained with the aid of the shooting method in Maple and the bvp4c solver in Matlab. The outcomes of dimensionless velocity and temperature profiles are exemplified quantitively through respective figures with performing parameters such as suction, mixed convection, thermal radiation and volume fraction of nanoparticle. Through our comparison analysis, the application of added hybrid nanoparticles revealed a better performance of thermal transmittance compared to the traditional mono-nanoparticle. We also identified two different branches of solutions in the occurrence of λ < 0 (opposing flow). In addition, a stability analysis was conducted throughout this research due to the existence of two levels of solutions, and the first branch is perceived to be the most solid and recognizable solution.

The Impact of Cattaneo–Christov Double Diffusion on Oldroyd-B Fluid Flow over a Stretching Sheet with Thermophoretic Particle Deposition and Relaxation Chemical Reaction

The current study focuses on the characteristics of flow, heat, and mass transfer in the context of their applications. There has been a lot of interest in the use of non-Newtonian fluids in biological and technical disciplines. Having such a substantial interest in non-Newtonian fluids, our goal is to explore the flow of Oldroyd-B liquid over a stretching sheet by considering Cattaneo–Christov double diffusion and heat source/sink. Furthermore, the relaxation chemical reaction and thermophoretic particle deposition are considered in the modelling. The equations that represent the indicated flow are changed to ordinary differential equations (ODEs) by choosing relevant similarity variables. The reduced equations are solved using the Runge–Kutta–Fehlberg fourth–fifth order technique (RKF-45) and a shooting scheme. Physical descriptions are strategized and argued using graphical representations to provide a clear understanding of the behaviour of dimensionless parameters on dimensionless velocity, concentration, and temperature profiles. The results reveal that the rising values of the rotation parameter lead to a decline in the fluid velocity. The rise in values of relaxation time parameters of temperature and concentration decreases the thermal and concentration profiles, respectively. The increase in values of the heat source/sink parameter advances the thermal profile. The rise in values of the thermophoretic and chemical reaction rate parameters declines the concentration profile.

Multiple slips and heat source effects on MHD stagnation point flow of casson fluid over a stretching sheet in the presence of chemical reaction

The numerical analysis of the steady MHD stagnation point flow of a Casson fluid flow over a stretching sheet in the presence of a heat source and the first-order chemical reaction with multiple slip boundary conditions taking into account viscous dissolution, Joule warming, and the first-order chemical response with multiple slip boundary conditions is performed. The governing flow equations are interpreted with the assistance of identity transmutations, and the condensed nonlinear coupled ordinary differential equalisations are determined applying the shooting approach. With the use of graphs, the impacts of several factors on the dimensionless velocity, temperature, and concentration profiles are demonstrated. In addition, graphical representations of the variation in skin friction coefficient for different values of the Casson fluid parameter against the Eckert number, the variation in the rate of heat transfer coefficients for various values of the Radiation specification against the Schmidt number, and the variation in the rate of mass transfer for different values of the chemical reaction specification against the Schmidt number are provided. Our findings indicate that when there is an increase in Heat source and Chemical reaction parameter always leads to degeneration in temperature profile and Chemical reaction. The Chemical reaction parameter was found to enhance the Sherwood number.

Numerical Investigation on Turbulent Flow and Heat Transfer of Helium-Xenon Gas Mixture in a Circular Tube

Gas-cooled space nuclear reactor system usually utilizes the helium-xenon gas mixture as the working fluid. Since the typical helium-xenon mixture has the Prandtl number of about 0.2, which is lower than that of water and air, the turbulent flow and heat transfer features need to be further investigated among the helium-xenon mixture and other fluids. In the current paper, numerical investigations by ANSYS Fluent are performed on helium-xenon mixture flow (HeXe40, M = 40.0 g/mol, Pr = 0.21), airflow (Pr = 0.71), and water flow (Pr = 6.99) in the circular tube. Direct numerical simulation results of liquid metal flow (Pr = 0.01) are also adopted for comparison. Results show that the dimensionless velocity profile and shear stress in the boundary layer of HeXe40 are close to those of other fluids. The empirical correlations from other fluids can also predict well the friction factor of helium-xenon mixtures. Due to the discrepancy in turbulent heat diffusivity ratio, the dimensionless radial temperature profile and turbulent heat conduction of HeXe40 significantly differ from those of other fluids. The molecular conduction region of HeXe40 develops up to y+ ≈ 30 and extends to the logarithmic region of the flow boundary layer. Moreover, the available experimental Nusselt numbers of helium-xenon mixtures are compared with several convective heat transfer correlations, in which Kays correlation is better.

Multiple Solutions for Stagnation-Point Flow of Unsteady Carreau Fluid along a Permeable Stretching/Shrinking Sheet with Non-Uniform Heat Generation

The aim of the present study was to explore the effect of a non-uniform heat source/sink on the unsteady stagnation point flow of Carreau fluid past a permeable stretching/shrinking sheet. The novelty of the flow model was enhanced with additional effects of magnetohydrodynamics, joule heating, and viscous dissipation. The nonlinear partial differential equations were converted into ordinary differential equations with the assistance of appropriate similarity relations and were then tackled by employing the Runge-Kutta-Fehlberg technique with the shooting method. The impacts of pertinent parameters on the dimensionless velocity and temperature profiles along with the friction factor and local Nusselt number were extensively discussed by means of graphical depictions and tables. The current results were compared to the previous findings under certain conditions to determine the precision and validity of the present study. The fluid flow velocity of Carreau fluid increased with the value of the magnetic parameter in the case of the first solution, and the opposite behavior was noticed for the second solution. It was seen that temperature of the Carreau fluid expanded with the higher values of unsteadiness and magnetic parameters. It was visualized from multiple branches that the local Nusselt number declined with the Eckert number parameter for both the upper and lower branch.

Topological Characteristics of Obstacles and Nonlinear Rheological Fluid Flow in Presence of Insulated Fins: A Fluid Force Reduction Study

In this work, a comprehensive study of fluid forces and thermal analysis of two-dimensional, laminar, and incompressible complex (power law, Bingham, and Herschel–Bulkley) fluid flow over a topological cross-sectional cylinder (square, hexagon, and circle) in channel have been computationally done by using finite element technique. The characteristics of nonlinear flow for varying ranges of power law index 0.4 ≤ n ≤ 1.6 , Bingham number 0 ≤ Bn ≤ 50 , Prandtl number 0.7 ≤ Pr ≤ 10 , Reynolds number 10 ≤ Re ≤ 50 , and Grashof number 1 ≤ Gr ≤ 10 have been examined. Considerable evaluation for thermal flow field in the form of dimensionless velocity profile, isotherms, drag and lift coefficients, and average Nusselt number Nu avg is done. Also, for a range of Bn , the drag forces reduction is observed for circular and hexagonal obstacles in comparison with the square cylinder. At Bn = 0 corresponding to Newtonian fluid, maximum reduction in drag force is reported.

Application of HAM to laminar boundary layer flow over a wedge with an external magnetic field

AbstractThe incompressible laminar along with injection or suction over a wedge for a boundary layer flow is studied. Falkner–Skan transformations reduce the governing partial differential equations (PDEs) to two nonlinear coupled PDEs and are solved by the homotopy analysis method (HAM). The variation of a dimensionless temperature and velocity profiles and for , , and to the nonidentical values of the parameter for injection/suction has been shown in the graph. The results hence obtained show that the flow field is determined by the existence of the applied magnetic field. The finite difference method is applied to the reduced PDEs and the velocity and temperature profiles are compared with the HAM solutions and depicted graphically. To distinguish singularities in the graph, we have applied Pade for the HAM series solution, which is depicted in graphs for all three cases. We have also estimated the radius of convergence of HAM solutions by Domb–Sykes plot for injection, no suction, and suction respectively. The important observation made by us through HAM and numerical solution is the existence of flow separation for injection, which is not shown by previous authors.

Advances in transport phenomena with nanoparticles and generalized thermal process for vertical plate

In this paper, a quantitative analysis is performed to investigate the convective flow of Maxwell fluid along with an erect heated plate via Prabhakar-like energy transport. The governing equations for this mathematical model are attained by Prabhakar fractional derivative. Laplace transform is applied to obtain the generalized results for dimensionless velocity and temperature profiles. By applying the conditions of nanofluid flow, we develop the constantly accelerated, variables accelerated, and non-uniform accelerated solution of the model, respectively. Prabhakar fractional derivative for Maxwell fluid based on generalized Fourier’s thermal flux is determined for heat transfer. For volume fraction φ and fractional parameters α, β, and γ, different structures of graphs are obtained. Furthermore, fluid temperature and velocity can be increased by enhancing the fractional parameters’ values. The comparison of nanoparticles Ag and nanoparticles Cu with water-based nanoparticles for velocity and temperature profile is also examined. The behavior of second grade and Maxwell fluid results to become a viscous fluid is justified.

Numerical simulation for heat and mass transport analysis for magnetic-nanofluids flow through stretchable convergent/divergent channels

This paper adopts a theoretical approach to explore the heat and mass transport features for MHD Jeffery–Hamel flow of viscous nanofluids through convergent/divergent channels with stretching or shrinking walls. Recently, this type of flows generated by nonparallel inclined plates with converging or diverging properties has been frequently utilized in various industrial and engineering processes, like, blood flow through arteries, different cavity flows and flow through canals. The current flow model is formulated mathematically in terms of partial differential equations (PDEs) in accordance with conservation laws under an assumption that the flow is symmetric and purely radial. In addition, heat and mass transport mechanisms are being modeled in the presence of Brownian motion and thermophoretic aspects using Buongiorno’s nanofluid model. The dimensionless variables are employed to get the non-dimensional forms of the governing PDEs. The built-in MATLAB routine bvpc4 is implemented to determine the numerical solutions for governing the nonlinear system of ordinary differential equations (ODEs). Numerical results are presented in the form of velocity, temperature and concentration plots to visualize the influence of active flow parameters. The simulated results revealed that the Reynold number has an opposite effect on dimensionless velocity profiles in the case of convergent and divergent channels. Besides, the temperature distributions enhance for higher values of Brownian motion parameter.

Symmetric and Non-Symmetric Flows of Burgers’ Fluids through Porous Media between Parallel Plates

Unidirectional unsteady flows of the incompressible Burgers’ fluids between two infinite horizontal parallel plates are analytically studied when the magnetic and porous effects are taken into consideration. The fluid motion is induced by the two plates, which move in their planes with time-dependent velocities. Exact general expressions are established both for the dimensionless velocity and shear stress fields as well as the corresponding Darcy’s resistance in the channel using the Laplace transform. If both plates move with equal velocities in the same direction, the fluid motion becomes symmetric with respect to the mid-plane between them. Otherwise, its motion is non-symmetric. To bring to light the behavior of the fluid, the dimensionless velocity profiles versus the spatial variable as well as its time evolution are presented both for the symmetric and asymmetric case. Finally, for comparison, similar graphical representations are presented together for the velocities of the incompressible Oldroyd-B and Burgers’ fluids. For large values of the time t, as expected, the behavior of the two different fluids is almost identical. The Darcy’s resistance against y is also graphically represented for the symmetric flow at different values of the time t. The influence of the magnetic field on the fluid motion is graphically revealed and discussed.

Convective flow of a fractional second grade fluid containing different nanoparticles with Prabhakar fractional derivative subject to non‐uniform velocity at the boundary

This article disputes the study of convective flow for improved nanofluid along with an erect heated plate via Prabhakar‐like energy transport. The governing equations for this mathematical model are obtained by Prabhakar fractional derivative. To attain the generalized results for dimensionless velocity profile and temperature profile, a scheme of Laplace transform is applied. By applying the conditions of nanofluid flow, we develop the constantly accelerated, variables accelerated, and non‐uniform accelerated solution of the model. Prabhakar fractional derivative for improved nanofluid based on generalized Fourier's thermal flux is determined for heat transfer. Different structures of graphs are performed for ordinary fractional parameters. As a result, it is found that temperature of Ag − H2O is higher than Cu − H2O and TiO2 − H2O nanoparticles and the reverse trend can be found for velocity. Furthermore, temperature and velocity can be enhanced by increasing the values of fractional parameters.

The Influences of Squeezed Inviscid Flow between Parallel Plates

Purpose. The main purpose of this study is to investigate the unsteady flow behavior of second-grade inviscid fluid between parallel plates. The effects on the flow are explored through modeling of continuity, momentum, and energy equations. Graphical and tabular exploration has been made to analyze the impact of several influential variables on the dimensionless temperature and velocity profiles. Three-dimensional graphs and stream lines are also mentioned. Design/Approach/Methodology. The governing equations have been metamorphosed into nonlinear ordinary differential equations by using suitable transformation which is the main focus of the study. To approach the solution of the problem numerically, we have used the numerical method such as shooting technique along with Runge–Kutta method is implemented. Findings. The graphs for the squeezing number, Prandtl number, and Eckert number are decreasing by increasing the values of these parameters. The graphs of skin friction coefficient and Nusselt number are increasing by changing the values of both parameters. Originality/Value. The significances of an unsteady squeezed flow of a nonviscous second-grade fluid between parallel plates by using boundary layer phenomenon are discussed.

Numerical study and error estimation in power-law nanofluid flow over vertical frustum of a cone

The aim of this article is to analyze the mixed convective Ostwald–de Waele power-law nanofluid flow over vertical frustum of a cone in a non-Darcy porous medium using an efficient numerical technique. The involved power-law nanofluid model utilizes water as the base fluid, and Ti-alloy (Ti6Al4V) and multi-wall carbon nanotubes (MWCNTs) as the nanoparticles. The solution of resultant non-similarity equations subjected to boundary conditions is described using the local non-similarity technique along with an efficient spectral local linearization method. The error estimation is provided to show the efficiency of above-mentioned solution procedure. A detailed explanation about the impact of nanoparticle volume fraction on the dimensionless velocity and temperature profiles along with heat transfer rate and skin friction coefficient is also provided for both the opposing and aiding flow cases. On comparison of the present results in particular cases with the relevant published data, it is assured that this method gives highly accurate outcomes for this kind of very complex fluid flow problems. The domination of dilatant nanofluid over pseudo-plastic nanofluid in both the aiding and opposing flow cases is noticed for velocity profiles, and the velocity is decreased with an increment in the nanoparticle volume fraction. Also, the variation in profiles with a streamwise coordinate $$\xi$$ shows non-similar nature of the problem. The use of Ti-alloy and MWCNTs in this work makes it very profitable in various important sectors like aerospace and medical sector.

Zero Mass Flux Dependent on Radiative Magnetohydrodynamics Carreau Nanofluid Over a Radially Surface with Temperature Jump and Slip Flow: A Hybrid Nanofluid Analysis

The present study explores the slip flow and heat transfer induced by a radially surface with MHD Carreau nanofluid. In addition, the effects of temperature jump, non-linear radiation and the dependent zero mass flux also taken into account. This study also considers the cross-diffusion effect on temperature and concentration governing profiles. Appropriate transformations are engaged in order to acquire nonlinear differential equations (ODEs) from the partial differential system, their solutions are obtained by Runge-Kutta 4th order with shooting scheme in MATLAB. The impact of pertinent flow parameters such as first and second order velocity slip parameter, temperature jump, magnetic parameter, heat source, radiation parameter, melting surface parameter, temperature ratio parameter on dimensionless velocity, temperature and concentration profiles achieved graphically as well as local skin friction, Nusselt number and Sherwood number are demonstrated in the form of Table. first order velocity slip parameter (slip1) on f′, Θ and Φ profile fields. With an increment in the velocity slip first order parameter (slip1) we have perceived a fall in the momentum boundary layer and concentration profiles and a growth in the fluid temperature field.

Velocity distribution of wall-attached jets in slotted-inlet ventilated rooms

The wall-attached jets for ventilation in spaces have been drawn considerable interest for their benefit of high ventilation efficiency and thermal sensation. In this study, the velocity distribution of a wall-attached jet under isothermal conditions in slotted-inlet ventilated spaces is investigated by experimental and numerical approaches. The wall-attached jet issues air from a slot inlet that flows down along the surface of a vertical wall, impinging on the floor attached to the vertical wall and spreading over the floor surface. The results show that the flow field of a wall-attached jet can be divided into three regions: vertical attachment region (region I), horizontal air reservoir region (region II), and jet impingement region. The correlation equations for the centerline velocity decay and velocity profiles are obtained. For the fully developed jet in region I and II, the dimensionless velocity profiles can be expressed as u0/um(y*)~(y*/b)γ and u0/um(x)~(x/b + Kh)γ, respectively, where γ is a constant related to the momentum decay rate. Over the whole range of jet flow conditions in this study, the value of γ is 1.11. Moreover, a unified exponential expression for the cross-sectional velocity profiles is proposed for both regions I and II. For the jet impingement region, the flow is complex and involves separation, reattachment, vortical flow, and pressure gradients. Large-scale vortices exist in the corner, and the vortices diminish as the jet inlet velocity increases. The current study can provide a theoretical basis for further engineering design applications of wall-attached jets for attachment ventilation.

Flakner-Skan equation flow of Newtonian fluid past a moving wedge with suction/injection

In this study, numerically analysed the Falkner-Skan equation in the two-dimensional laminar flow past a moveable wedge for a Newtonian fluid with suction/injection is investigated through Matlab environment. The boundary conditions are scrutinized and applied in this equation for different conditions. The simultaneous effect of the parameter which used to measure the pressure gradient along x-axis (β), velocity ratio between the wedge and mainstream (λ), suction and injection are inspected on the momentum boundary layer thickness or dimensionless velocity profile.

Modeling of MHD fluid flow over an unsteady stretching sheet with thermal radiation, variable fluid properties and heat flux

This work considers the problem of boundary layer laminar flow and heat transfer for MHD fluid due to an unsteady stretching sheet with extended heat flux. Both the viscosity and thermal conductivity are assumed to vary with temperature. The equations governing the proposed problem which in partial forms are reduced to a system of coupled non-linear ordinary differential equations using suitable dimensionless transformations. An effective shooting method coupled with the Runge–Kutta algorithm is used to solve the resulting system of ordinary differential equations. The influences of different governing parameters on the dimensionless velocity and temperature profiles are depicted graphically and analyzed in detail. Additionally, the current numerical results obtained via shooting method with the results have been compared with the existing published work in the literature review and good agreements were observed.

Sensitivity analysis of emerging parameters in the presence of thermal radiation on magnetohydrodynamic nanofluids via wavelets

The current article investigates magnetohydrodynamics nanofluid flow with radiation effect between two horizontal rotating plates numerically using scale-3 Haar wavelets. The rudimentary governing equations have been transformed set of nonlinear ordinary differential equations (ODEs) using similarity transformation. Then, obtained nonlinear system of ODEs is solved by wavelet collocation method. The effect of various emerging parameters such as magnetic parameter, rotation parameter, Prandtl number, Schmidt number, and Brownian motion parameter has been analysed on dimensionless velocity, temperature and concentration profiles. The result section represents the output in from of figures. Through convergence analysis of scale-3 Haar wavelets, it is concluded that error goes to zero as resolution level goes to infinity.

Comprehensive analysis of the effect of air injection on the wake development of an airfoil

The goal of this investigation is to study the effect of air injection on the wake development. As a widely commercial product, airfoil CFJ0025-131-196, is selected, and the profiles for velocity deficit, wake profiles for different attack angles, and profiles for change in the place where the velocity starts to increase are found. For the air jet velocity, the values of 0.0, 20.4, and 33.3 m s−1 are examined while angles of attack are adjusted to 0, 6, and 14°. The main flow speed is 10 m s−1. It is found that when the dimensionless distance from the trailing edge goes up, the velocity deficit has a downward trend. Furthermore, the higher jet velocity is, the smoother the velocity deficit profile becomes. In addition, in a constant dimensionless distance, increasing the angle of attack results in growing the amplitude of the dimensionless velocity profile. The results also reveal that the location at which the velocity starts to increase moves down by the increase in the air jet velocity. Having a broad knowledge about the wake development of an airfoil will help to know its performance better and find more suitable ways to enhance its performance.