Parallel Free Stream Research Articles

Prediction model based on artificial neural network and bivariate spectral quasi-linearization method for compressible turbulent boundary-layer flow over a smooth flat surface

The compressible two-dimensional turbulent flow solutions at an arbitrary point in time and space by incorporating the mass, momentum, and energy conservation equations over a smooth flat surface and parallel free stream with unfavorable pressure gradient are studied. The Falkner–Skan transformation is applied to the turbulent boundary-layer equations and related boundary conditions, and the resulting nonlinear coupled system of partial differential equations is solved by the bivariate spectral quasi-linearization method. Moreover, to predict the thermal distribution of the flow, an artificial neural network model has been developed with the Nusselt number as target values. Several plots have been depicted, it is evaluated that the mean squared error value is 6.41 × 10−7, the overall coefficient of determination (R) is 0.997 52, and the average error rate is 0.68% for the said model, indicating the attainment of high accuracy for estimation.

Flow and heat transfer analysis of a special third grade fluid over a stretchable surface in a parallel free stream

This paper aims to investigate a boundary layer flow with heat and mass transfer of a special third grade fluid over a stretchable surface in a parallel free stream. Using the similarity variables generated by the Lie group analysis, the governing nonlinear partial differential equations (PDEs) are transformed into a system of nonlinear ordinary differential equations (ODEs). The transformed equations are then solved numerically using the shooting technique. In addition, an attempt is made to carry the asymptotic solution behavior for large stretching and suction parameters, and the asymptotic results of skin friction coefficient are then compared with the direct numerical solutions, which shows a good agreement. It is observed that the similarity equations exhibit dual solutions in a certain range of shrinking strength. These two solution branches show different behavior on the skin friction coefficient, local Nusselt number, Sherwood number, velocity, and temperature profiles. Thus, emphasis has been given to carrying out a stability analysis to determine the physically reliable solution. The stability analysis shows that the upper branch solution is stable. It is observed that the suction parameter increases the range of dual solutions and the magnitude of the critical point from where the dual solutions bifurcate; however, the non-Newtonian parameter shows the opposite behavior. The momentum, thermal and concentration boundary layer thicknesses in the upper branch solution are lower than the lower branch solution.

The quadratic convective flow of Williamson nanofluid with multiple diffusions

The present work will characterize the heat and mass transport phenomena in the nonlinear combined convective Williamson nanoliquid flow along with the moving plate in a continuously moving parallel free stream. The nonlinear thermal radiation and diffusions of chemical species such as liquid Nitrogen and liquid Ammonia are also considered in this analysis. The physical problem is modelled mathematically as a set of nonlinear coupled partial differential equations with suitable boundary conditions. The governing equations are expressed in the dimensionless form by utilizing non-similar transformations. Further, we employ the Quasilinearization technique and implicit finite difference scheme for numerical computation. The results are discussed with the aid of graphs and tables. The drag coefficient, rates of heat and mass transports are pronounced more for higher values of nonlinear convection, while reverse behaviour can be observed for the Williamson parameter. Moreover, the mass transfer rate for liquid Ammonia is approximately 22% more than that of liquid Nitrogen. So obtained numerical results in this analysis are compared with previously published works and achieved an excellent agreement.

Boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving flat plate in Darcy porous medium with a parallel free-stream: Multiple solutions and stability analysis

Boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving flat plate in Darcy porous medium with a parallel free-stream: Multiple solutions and stability analysis

Effects of MHD and porosity on entropy generation in two incompressible Newtonian fluids over a thin needle in a parallel free stream

This article is devoted to studying Magnetohydrodynamic (MHD)'s combined effect and porosity on the entropy generation in two incompressible Newtonian fluids over a thin needle moving in a parallel stream. Two Newtonian fluids (air and water) are taken into consideration in this study. The viscous dissipation term is involved in the energy equation. The assumption is that the free stream velocity is in the direction of the positive x-axis—(axial direction). The thin needle moves in the same or opposite direction of free stream velocity. The reduced similar governing equations are solved numerically with the help of shooting and the fourth-order Runge–Kutta method. The expressions for dimensionless volumetric entropy generation rate and Bejan number are obtained through using similarity transformations. The effects of the magnetic parameter, porosity parameter, Eckert number, Bejan number, irreversibility parameter, Nusselt number, and skin friction are discussed graphically in detail for and taken as Newtonian fluids. The results are compared with published work and are found in excellent agreement.

Melting Heat Transfer and Radiation Effects on Jeffrey Fluid Flow over a Continuously Moving Surface with a Parallel Free Stream

This article is proposed to address the melting heat transfer of a Jeffrey fluid in Blasius and Sakiadis flow caused due to a moving surface. Thermal radiation and a constant free stream are considered in this mathematical model. The non-linear coupled dimensionless equations from the governing equations are attained by employing appropriate similarity transformations. The resulting dimensionless equations are solved by implementing RKF method. The impact of sundry emerging parameters on different flow fields are interpreted with the help of figures and tables. For augmented values of Deborah number, the velocity profile diminishes in the case of Blasius flow and the reverse behavior in the Sakiadis flow is observed. Moreover, the velocity of non-Newtonian liquid in case of Blasius flow is superior to that of the Sakiadis flow. The present work is demonstrated by matching with the computational results in the literature and found to be outstanding agreement.

Thermodynamic Analysis of Entropy Generation Minimization in Thermally Dissipating Flow Over a Thin Needle Moving in a Parallel Free Stream of Two Newtonian Fluids.

This article is devoted to study sustainability of entropy generation in an incompressible thermal flow of Newtonian fluids over a thin needle that is moving in a parallel stream. Two types of Newtonian fluids (water and air) are considered in this work. The energy dissipation term is included in the energy equation. Here, it is presumed that u∞ (the free stream velocity) is in the positive axial direction (x-axis) and the motion of the thin needle is in the opposite or similar direction as the free stream velocity. The reduced self-similar governing equations are solved numerically with the aid of the shooting technique with the fourth-order-Runge-Kutta method. Using similarity transformations, it is possible to obtain the expression for dimensionless form of the volumetric entropy generation rate and the Bejan number. The effects of Prandtl number, Eckert number and dimensionless temperature parameter are discussed graphically in details for water and air taken as Newtonian fluids.

Analytical and Numerical Investigation of Fe3O4–Water Nanofluid Flow over a Moveable Plane in a Parallel Stream with High Suction

In the current framework, a model is constituted to explore the impacts of high suction and partial slip on Fe3O4–water nanoliquid flow over a porous moveable surface in a parallel free stream. The mechanisms of heat transfer are also modeled in the existence of Newtonian heating effect. The obtaining PDEs are transformed into a non-linear ODE system employing appropriate boundary conditions to diverse physical parameters. The governing ODE system is solved using a singular perturbation technique that results in an analytical asymptotic solution as a function of the physical parameters. The obtained solution allows us to carry out an analytical parametric study to investigate the impact of the physical parameters on the nonlinear attitude of the system. The precision of the proposed method is verified by comparisons between the numerical and analytical results. The results confirm that the proposed technique yields a good approximation to the solution as well as the solution calculation has no CPU time-consuming or round off error. Numerical solutions are computed and clarified in graphs for the model embedded parameters. Moreover, profiles of the skin friction coefficient and the heat transfer rate are also portrayed and deliberated. The data manifests that both solid volume fraction and slip impact significantly alter the flow profiles. Moreover, an upward trend in temperature is anticipated for enhancing Newtonian heating strength. Additionally, it was found that both the nanofluid velocity and temperature distributions are decelerated when the solid volume fraction and suction parameters increase. Furthermore, a rise in slip parameter causes an increment in velocity profiles, and a rise in Biot number causes an increment in the temperature profiles.

Finite element analysis of magnetohydrodynamic flow over flat surface moving in parallel free stream with viscous dissipation and Joule heating

PurposeThe purpose of this paper is to investigate two-dimensional viscous incompressible magnetohydrodynamic boundary layer flow and heat transfer of an electrically conducting fluid over a continuous moving flat surface considering the viscous dissipation and Joule heating.Design/methodology/approachSuitable similarity variables are introduced to reduce the governing nonlinear boundary layer partial differential equations to ordinary differential equations. A numerical solution of the resulting two-point boundary value problem is carried out by using the finite element method with the help of Gauss elimination technique.FindingsA comparison of obtained results is made with the previous work under the limiting cases. Behavior of flow and thermal fields against various governing parameters like mass transfer parameter, moving flat surface parameter, magnetic parameter, Prandtl number and Eckert number are analyzed and demonstrated graphically. Moreover, shear stress and heat flux at the moving surface for various values of the physical parameters are presented numerically in tabular form and discussed in detail.Originality/valueThe work is relatively original, as very little work has been reported on magnetohydrodynamic flow and heat transfer over a continuous moving flat surface. Viscous dissipation and Joule heating are neglected in most of the previous studies. The numerical method applied to solve governing equations is finite element method which is new and efficient.

Consequences of convection-radiation interaction for magnetite-water nanofluid flow due to a moving plate

Present paper examines the boundary-layer flow of magnetic nanofluid over a radiative plate moving in a uniform parallel free stream. Water is considered as the base fluid which is being filled with magnetite-Fe3O4 nanoparticles. Energy balance equation is formulated with non-linear radiation heat flux. Mathematical analysis is carried out through the famous Tiwari and Das model. Similarity approach is utilized to construct self-similar form of the governing differential system. Numerical computations are made through standard shooting method. Ferrofluid velocity is predicted to enhance upon increasing the nanoparticle volume fraction which contradicts with the available literature for non-magnetic nanofluids. It is found that Fe3O4-water ferrofluid has superior heat transfer coefficient than pure water. Results reveal that consideration of magnetic nanoparticles in water leads to better absorption of incident solar radiations. The well-known Blasius and Sakiadis flows are also explicitly analyzed from the present model.

Boundary layer flow over a moving plate in a flowing fluid considering non-linear radiations

Purpose – The purpose of this paper is to consider a laminar two-dimensional incompressible flow of an electrically conducting fluid over a moving flat plate with a parallel free stream. Design/methodology/approach – The governing equations are first reduced into self-similar forms and then solved for the numerical solutions by shooting method. Findings – The results are compared with the available studies is some special cases and found in excellent agreement. It is noticed that an increase in the magnetic field strength leads to a decrease in the momentum boundary layer thickness and enhancement in the rate of heat transfer from the plate. It is also observed that temperature and heat transfer from the plate increase when radiation effect is strengthened. Originality/value – A recently proposed idea of nonlinear radiative heat transfer with Joule heating and viscous dissipation effects is analyzed.

Dufour and radiation effect on MHD boundary layer flow past a wedge through porous medium with heat source and chemical reaction

Magnetohydrodynamics (MHD) boundary layer flow past a wedge with the influence of thermal radiation, heat generation and chemical reaction has been analyzed in the present study. This model used for the momentum, temperature and concentration fields. The principal governing equations is based on the velocity in a nanofluid and with a parallel free stream velocity and surface temperature and concentration. The governing nonlinear boundary layer equations for momentum, thermal energy and concentration are transformed to a system of nonlinear ordinary coupled differential equations by using suitable similarity transformation with fitting boundary conditions. The transmuted model is shown to be controlled by a number of thermo-physical parameters, viz. the magnetic parameter, buoyancy parameter, radiation conduction parameter, heat generation parameter, Porosity parameter, Dufour number, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, chemical reaction parameter and pressure gradient parameter. Numerical elucidations are obtained with the legendary Nactsheim-Swigert shooting technique together with RungeKutta six order iteration schemes.

Mixed convection flow due to a moving vertical plate parallel to free stream under the influence of Newtonian heating and thermal radiation

The steady mixed convection flow from a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of thermal radiation as well as Newtonian heating effects. The governing boundary layer equations are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in conjunction with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter ( ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity ( ) and the radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skinfriction coefficient ( ) and surface temperature ( ) are also presented. The results show that the streamwise co-ordinate  significantly influences the flow and thermal fields which indicate the importance of non-similar solutions. Also, it is observed that the increase of mixed convection parameter causes the increase in the magnitude of velocity profile about 65% for lower Prandtl number fluids (Pr=0.7), while it decreases in the temperature profile about 30%. Present results are compared with previously published work and are found to be in excellent agreement.

MHD boundary layer radiative, heat generating and chemical reacting flow past a wedge moving in a nanofluid.

The present study analyzed numerically magneto-hydrodynamics (MHD) laminar boundary layer flow past a wedge with the influence of thermal radiation, heat generation and chemical reaction. This model used for the momentum, temperature and concentration fields. The principal governing equations is based on the velocity u w(x) in a nanofluid and with a parallel free stream velocity u e(x) and surface temperature and concentration. Similarity transformations are used to transform the governing nonlinear boundary layer equations for momentum, thermal energy and concentration to a system of nonlinear ordinary coupled differential equations with fitting boundary conditions. The transmuted model is shown to be controlled by a number of thermo-physical parameters, viz. the magnetic parameter, thermal convective parameter, mass convective parameter, radiation-conduction parameter, heat generation parameter, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, chemical reaction parameter and pressure gradient parameter. Numerical elucidations are obtained with the legendary Nactsheim-Swigert shooting technique together with Runge–Kutta six order iteration schemes. Comparisons with previously published work are accomplished and proven an excellent agreement.

Flow and heat transfer of Powell–Eyring fluid over a shrinking surface in a parallel free stream

The present work extends the recently published paper by Jalil et al. (2013) [12] on the boundary layer flow and heat transfer of Powell–Eyring fluid over a permeable surface in a parallel free stream that is moving out of the origin to the case when the surface is moving into the origin (shrinking surface). The governing boundary layer equations are transformed to self similar nonlinear ordinary differential equations using similarity transformations. Numerical results of the resulting equations are obtained using the function bvp4c from Matlab for different values of the governing parameters. Dual solutions are found for negative values of the moving parameter λ. A stability analysis has been also performed to show that the first (upper branch) solutions are stable and physically realizable, while the second (lower branch) solutions are not stable and, therefore, not physically possible. We notice that these flow characteristics have not been presented by Jalil et al. (2013) [12]. The results are new and original.

Effects of Hall Current on MHD Boundary Layer Second-Order Viscoelastic Fluid Flow Induced by a Continuous Surface with Heat Transfer

Effects of Hall current on heat transfer and magnetohydrodynamic (MHD) boundary layer flow induced by a continuous surface in a parallel free stream of a second-order viscoelastic fluid are studied for uniform suction/injection by taking viscous dissipation into account. Complex nonsimilar solutions to the stream function and temperature are developed by means of an elegant technique, known as homotopy analysis method (HAM). Convergence of the solutions is ensured with the help of -curves. Graphical and tabular results for the effects of Hall current reveal that it has a significant influence on: complex velocity, complex temperature, magnitude of the shear stress at the surface, magnitude of the rate of heat transfer at the surface and on boundary layer thickness.

Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.

Self similar solutions for the flow and heat transfer of Powell-Eyring fluid over a moving surface in a parallel free stream

This paper deals with the boundary layer flow and heat transfer of Powell-Eyring fluid over a continuously moving permeable surface in a parallel free stream. The governing boundary layer equations are transformed to self similar nonlinear ordinary differential equations using scaling group of transformations. Numerical results of the resulting equations are obtained using the Keller-box method. The effects of various governing parameters on the flow field are discussed and analyzed. A comparison is made with the existing literature.

Unsteady thermal radiation mixed convection flow from a moving vertical plate in a parallel free stream: Effect of Newtonian heating

An unsteady mixed convection flow over a moving vertical plate in a parallel free stream is considered to investigate the combined effects of buoyancy force and thermal diffusion in presence of Newtonian heating in which heat transfer rate from the surface is proportional to the local temperature and thermal radiation effects. It is assumed that the unsteadiness is caused by the time dependent free stream velocity as well as by the moving plate velocity. The governing boundary layer equations with boundary conditions are transformed into a non-dimensional form by a group of non-similar transformations. The resulting system of coupled non-linear partial differential equations is solved by an implicit finite difference scheme in combination with the quasi-linearization technique. Computations are performed and representative set is displayed graphically to illustrate the influence of the mixed convection parameter (λ), Prandtl number (Pr), the ratio of free stream velocity to the composite reference velocity (ɛ), stream wise co ordinate (ξ) and thermal radiation parameter (R) on the velocity and temperature profiles. The numerical results for the local skin-friction coefficient (ReL1/2Cf) and wall temperature (GW(ξ,0)) are also presented. The numerical results are presented in graphs revealing some interesting features of flow and heat transfer phenomena in this study. Present results are also compared with previously published works and are found to be in excellent agreement.

MHD boundary layer flow due to a moving wedge in a parallel stream with the induced magnetic field

The present analysis considers the steady magnetohydrodynamic (MHD) laminar boundary layer flow of an incompressible electrically conducting fluid caused by a continuous moving wedge in a parallel free stream with a variable induced magnetic field parallel to the wedge walls outside the boundary layer. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations in the form of a two-point boundary value problem (BVP) and then solved numerically using a finite difference scheme known as the Keller box method. Numerical results are obtained for the velocity profiles and the skin friction coefficient for various values of the moving parameter λ, the wedge parameter β, the reciprocal magnetic Prandtl number α and the magnetic parameter S. Results indicate that when the wedge and the fluid move in the opposite directions, multiple solutions exist up to a critical value of the moving parameter λ, whose value depends on the values of S and β. MSC: 34B15, 76D10.