Unsteady Boundary Layer Research Articles

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

Heat and mass transfer analysis in unsteady boundary layer flow of Maxwell nanofluid over a stretching sheet

This paper presents analytic study of heat and mass transfer in a two-dimensional, unsteady flow of Maxwell nanofluids over a horizontal stretching sheet. The non-linear governing equations with the relevant boundary conditions have been simplified by using similarity transformations and the resulting equations are solved by using the homotopy analysis method. The convergence and accuracy of the solutions are verified. Impacts of magnetic field, thermal radiation, heat source, surface permeability and chemical reaction on velocity, temperature and nanoparticles volume fraction profiles are examined and presented in graphical and tabular forms. The study reveals that increasing the effect of heat source maximizes the temperature profile whereas it reduces the nanoparticle volume fraction profile in the boundary layer. On the other hand, the increase in chemical reaction is found to enhance the nanoparticle concentration.
 Keywords:- Homotopy Analysis Method; Unsteady Flow; Boundary Layer Flow; Maxwell Nanofluid

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

AbstractThe present study analyzes the effect of chemical reaction on an unsteady magnetohydrodynamic boundary layer viscous fluid over a stretching surface embedded in a porous medium with a uniform transverse magnetic field. A Darcy‐Forchheimer drag force model is employed to simulate the effect of second‐order porous resistance. Dissipative heat energy based on both viscous and Joule dissipation along with a heat source/sink is considered to enhance the energy equation. Similarity analysis is imposed to transform the governing differential equations into a set of nonlinear coupled ordinary differential equations. These sets of equations are solved numerically using the Runge‐Kutta fourth‐order scheme followed by the shooting algorithm. The effects of physical parameters such as magnetic field, Prandtl number, Eckert number, Schmidt number, unsteadiness parameter, and chemical reaction parameters have been discussed on velocity, temperature, and concentration fields. Computation for the coefficient of skin friction, rate of heat and mass transfer is done and presented in a table for validation of the present outcomes.

On the Numerical Analysis of Unsteady MHD Boundary Layer Flow of Williamson Fluid Over a Stretching Sheet and Heat and Mass Transfers

A thorough and detailed investigation of an unsteady free convection boundary layer flow of an incompressible electrically conducting Williamson fluid over a stretching sheet saturated with a porous medium has been numerically carried out. The partial governing equations are transferred into a system of non-linear dimensionless ordinary differential equations by employing suitable similarity transformations. The resultant equations are then numerically solved using the spectral quasi-linearization method. Numerical solutions are obtained in terms of the velocity, temperature and concentration profiles, as well as the skin friction, heat and mass transfers. These numerical results are presented graphically and in tabular forms. From the results, it is found out that the Weissenberg number, local electric parameter, the unsteadiness parameter, the magnetic, porosity and the buoyancy parameters have significant effects on the flow properties.

Analytical and Numerical Study on Cross Diffusion Effects on Magneto-Convection of a Chemically Reacting Fluid with Suction/Injection and Convective Boundary Condition

The purpose of this paper is to investigate the Soret and Dufour effects on unsteady mixed convective boundary layer flow of a viscous fluid over a stretching surface in a porous medium in the presence of magnetic field with heat generation/absorption, chemical reaction, suction/injection and convective boundary condition. The governing time-dependent partial differential equations are transformed into non-linear ordinarydifferential equations using similarity transformations. These equations subject to the appropriate boundary conditions are solved analytically by homotopy analysis method (HAM) and numerically by Runge-Kutta fourth order method and shooting technique.The numerical solution is compared with analytical solution. The influence of the different parameters on velocity, temperature and concentration profiles are discussed in graphical as well as in tabular form. It is observed that the fluid velocity and temperature increase on increasing the buoyancy ratio parameter and heat generation/absorption parameter. Also found that the surface heat and mass transfer rates increase on increasingthe suction/injection and heat generation/absorption parameters.

Linear Stability of Momentum Boundary Layer Flow and Heat Transfer Over a Moving Wedge

Abstract This paper studies the linear stability of the unsteady boundary-layer flow and heat transfer over a moving wedge. Both mainstream flow outside the boundary layer and the wedge velocities are approximated by the power of the distance along the wedge wall. In a similar manner, the temperature of the wedge is approximated by the power of the distance that leads to a wall exponent temperature parameter. The governing boundary layer equations admit a class of self-similar solutions under these approximations. The Chebyshev collocation and shooting methods are utilized to predict the upper and lower branch solutions for various parameters. For these two solutions, the velocity, temperature profiles, wall shear-stress, and temperature gradient are entirely different and need to be assessed for their stability as to which of these solutions is practically realizable. It is shown that algebraically growing steady solutions do exist and their effects are significant in the unsteady context. The resulting eigenvalue problem determines whether or not the steady solutions are stable. There are interesting results that are linked to bypass an important class of boundary layer flow and heat transfer. The hydrodynamics behind these results are discussed in some detail.

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.

Impact of slip effects on unsteady Sisko nanoliquid heat and mass transfer characteristics over stretching sheet filled with gold nanoparticles

AbstractWe have presented a comparison between steady and unsteady magnetohydrodynamic boundary layer flow, heat transfer features of Au–kerosene‐based nanoliquid over a stretching surface by taking variable viscosity, variable thermal conductivity, and slip boundary conditions in this study. Appropriate similarity translations are engaged to reduce nonlinear partial differential equations into a set of ordinary differential equations. These equations along with boundary conditions are elucidated numerically by finite‐element technique. Influence of several pertinent parameters on velocity, temperature, and concentration scatterings, in addition to that, the values of Nusselt number, skin‐friction coefficient, and Sherwood number are scrutinized in detail and the outcomes are exhibited through plots and tables. It is perceived that the values of Nusselt number, skin‐friction coefficient, and Sherwood number intensify in both steady–unsteady cases as the values of volume fraction parameter rise.

Unsteady MHD natural convective boundary layer flow and heat transfer over a truncated cone in the presence of pressure work

Journal of Applied Mathematics and Computational Mechanics, Prace Naukowe Instytutu Matematyki i Informatyki, Politechnika Częstochowska, Scientific Research of the Institute of Mathematics and Computer Science, Czestochowa University of Technology

Unsteady Magneto hydrodynamic Boundary Layer Flow towards a Heated Porous Stretching Surface with Thermal Radiation and Heat Source/Sink Effects

Mathematical model of unsteady boundary layer flow and heat transfer is explored for analyzing the study of influence of thermal radiation on incompressible viscous electrically conducting fluid over continuous stretching surface embedded in a porous medium in the presence of heat source/sink. The scope of influencing parameters that describing phenomenon are determined and governing time dependent boundary layer equations are transformed to ordinary differential equations by using appropriate similarity transformation. Numerical computation of the problem was carried out by shooting iteration technique together with Runge-Kutta fourth order integration scheme. Effects of unsteadiness parameter, permeability parameter, magnetic parameter, thermal radiation parameter, Prandtl number and heat source/sink parameter on velocity and temperature profiles are computed and illustrated graphically, whereas local skin friction coefficient and local Nusselt number are represented numerically through tables. In nonmagnetic flow condition the result is found in concordance with earlier investigations.

Effect of Magnetic Field on the Unsteady Boundary Layer Flows Induced by an Impulsive Motion of a Plane Surface

Abstract The unsteady laminar boundary layer flow of an electrically conducting viscous fluid near an impulsively started flat plate of infinite extent is considered, with a view to examine the influence of transverse magnetic field fixed to the fluid. A new type of similarity transformation is proposed, which renews the governing partial differential equation into a linear ordinary differential equation with four physical parameters, viz. unsteadiness parameter β, magnetic parameter M, and the velocity indices (p, q). The analytic solution of this equation has been found in terms of a first kind confluent hypergeometric function for some specific parameter regimes. This solution shows the structure of a new type of boundary layer flow that includes the solution of the first Stokes problem as a special case. For non-zero values of (p, q), there is a definite range of p (either −∞ < p < 2q or 2q < p < ∞ according to β < or > 0) for which this flow problem will be valid. This analysis reveals an important relation ( p β + M 2 = q β ) $(p\beta+{M^{2}}=q\beta)$ at which separation appears inside the layer and has been detected as the separation threshold of the problem. Indeed, this relation gives us the critical value of one when the others are known. Flow separation inside the layer is delayed with an increasing value of q but cannot be completely removed whatever is the value of q (>0). The present analysis ensures that the reverse flow can be suppressed by the use of a proper amount of magnetic field M depending upon the values of p, q, and β. The obtained result provides insight into the stability of the boundary layer flows.

IMPACT OF SUCTION/INJECTION AND HEAT TRANSFER ON UNSTEADY MHD FLOW OVER A STRETCHABLE ROTATING DISK

In this article, the unsteady magnetohydrodynamic two-dimensional boundary layer flow and heat transfer over a stretchable rotating disk with mass suction/injection is investigated. Temperature-dependent physical properties and convective boundary conditions are taken into account. The governing coupled nonlinear partial differential equations are transformed into a system of ordinary differential equations by adopting the well-known similarity transformations. Further, the solutions are obtained through the semi-analytical method called an Optimal Homotopy Analysis Method (OHAM). The obtained results are discussed graphically to predict the features of the involved key parameters which are monitoring the flow model. The skin friction coefficient and Nusselt number are also examined. The validation of the present work is verified with the earlier published results and is found to be in excellent agreement. It is noticed that an increase in the viscosity parameter leads to decay in momentum boundary layer thickness, and the inverse trend is observed in the case of the temperature profile.

Generalized second-order slip for unsteady convective flow of a nanofluid: a utilization of Buongiorno’s two-component nonhomogeneous equilibrium model

AbstractThe unsteady convective boundary layer flow of a nanofluid along a permeable shrinking/stretching plate under suction and second-order slip effects has been developed. Buongiorno’s two-component nonhomogeneous equilibrium model is implemented to take the effects of Brownian motion and thermophoresis into consideration. It can be emphasized that, our two-phase nanofluid model along with slip concentration at the wall shows better physical aspects relative to taking the constant volume concentration at the wall. The similarity transformation method (STM), allows us to reducing nonlinear governing PDEs to nonlinear dimensionless ODEs, before being solved numerically by employing the Keller-box method (KBM). The graphical results portray the effects of model parameters on boundary layer behavior. Moreover, results validation has been demonstrated as the skin friction and the reduced Nusselt number. We understand shrinking plate case is a key factor affecting non-uniqueness of the solutions and the range of the shrinking parameter for which the solution exists, increases with the first order slip parameter, the absolute value of the second order slip parameter as well as the transpiration rate parameter. Besides, the second-order slip at the interface decreases the rate of heat transfer in a nanofluid. Finally, the analysis for no-slip and first-order slip boundary conditions can also be retrieved as special cases of the present model.

High sensitive flexible hot-film sensor for measurement of unsteady boundary layer flow

The detailed flow characteristics in the boundary layer are critical for physical understanding of complex flow and aerodynamic performance optimization of aircraft. In this study, high sensitive micro-electro-mechanical system flexible hot-film sensor was developed for measurement of unsteady boundary layer flow. The effects of annealing temperature and time on the temperature coefficient of resistance (TCR) were studied, the highest TCR value of 5100 ppm °C−1 was obtained after 6 h of vacuum thermal annealing treatment at 400 °C. The flow transition and separation characteristics developed on two-dimensional NACA 0012 airfoil at various Reynolds numbers and angles of attack were investigated by using flexible hot-film sensors with validation by surface pressure distribution and aerodynamic force coefficient. The accurate locations of onset, 50% intermittent and end of transition were detected successfully. The behavior of spatial progression to the leading edge of transition point was found as the Reynolds number and angle of attack increases. The hot-film sensor measurements also demonstrated the static stall of the airfoil was caused by the leading edge separation bubble.

Phase-Lags' Radial Variations Between Velocity, Shear Stress, and Pressure Gradient in Ultrahigh Frequency Pulsating Turbulent Flows

Abstract Two-dimensional numerical simulations of wall-bounded turbulent pulsating flow driven by a sinusoidal velocity through a circular smooth tube are carried out. These computations for a Womersley number α ranged from 0.7 to 2069 and a dimensionless frequency ω+ ranged from 1.2×10−5 to 33.5. The aim of this study is to calculate the phase lag inside the unsteady turbulent boundary layer and across the tube. The phase lag of the velocity and shear stress with respect to the pressure gradient is deduced. Also, the instantaneous logarithmic layer and the turbulent parameters are analyzed. It is found that capturing the phase lag near the wall depends on resolving the Stokes layer thickness δst. At ultrahigh frequencies, the centerline velocity was delayed from the pressure gradient and wall shear stress by 45 deg and 90 deg, respectively. Consequently, the velocity and shear stress lagged behind the pressure gradient by 90 deg and 280 deg at the core of the tube, respectively, and by 45 deg at the wall. Thus, the trend of the radial phase lag increases toward the tubes center for ω+>0.06, which contrasts with that at low frequencies. When a reversed flow is caused by increasing the amplitude of the imposed oscillations, the phase lag is not affected noticeably by this increment. The radial phase lag is kept constant outside the oscillatory boundary layer at high frequencies because the radial gradient of the axial velocity has vanished.

Application of hot-film anemometry to resolve the unsteady boundary layer transition of a laminar airfoil experiencing limit cycle oscillations

The unsteady boundary layer behavior of a supercritical laminar airfoil model, which undergoes limit cycle oscillations in pitch, is investigated by the application of hot-film anemometry. The data basis is a 2D flutter experiment under transonic flow conditions. The laminar airfoil model was elastically mounted with a single degree of freedom in pitch and performed self-excited limit cycle oscillations at a Mach number of {text {Ma}}=0.73 and a Reynolds number of {text {Re}}approx 2times 10^6. An analysis of the hot-film signals on the basis of the quasi-wall shear stress is carried out, with which the boundary layer state for steady and unsteady flow is resolved. An algorithm is presented which allows an automated detection of the transition position, so that a correlation between airfoil motion and transition location movement can be quantified. A sudden movement of the boundary layer transition is observed at the upper and lower reversal points of the limit cycle oscillation, while in parts of the up- and downstroke of the laminar airfoil a shock-induced transition occurs. During the limit cycle oscillation, a delayed response of the boundary layer occurs, resulting in a significant phase lag between the movement of the boundary layer transition and the motion of the laminar airfoil.

MHD FREE CONVECTION BOUNDARY LAYER FLOW OF A NANO FLUID OVER A PERMEABLE SHRINKING SHEET WITH NTH ORDER CHEMICAL REACTION

An analysis is presented to study the free convective unsteady magnatohydrodynamic boundary layer flow of a Nano fluid over a permeable shrinking sheet in the presence of nth order chemical reaction. Magnetic field of varying strength is applied normal to the sheet. The Nano fluid model under consideration includes Brownian motion, thermophoresis effects and nth order chemical reaction. The governing partial differential equations are transformed into a set of ordinary differential equations by applying the local similarity transformations and then the highly coupled nonlinear differential equations are solved by the method of lines. The effect of various controlling flow parameters on the dimensionless velocity, temperature and nanoparticle volume fraction profiles are analyzed.

Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

Prandtl number scalings for unsteady natural convection boundary-layer flow on an evenly heated vertical plate in a homogeneous Pr > 1 fluid

Scalings for the thicknesses of the thermal and velocity boundary layers, the plate temperature, and the maximum vertical velocity in a homogeneous Pr > 1 fluid are validated against numerical results for unsteady natural convection boundary-layer flow on an evenly heated vertical plate. Results have been obtained for Rayleigh number and Prandtl number and the scaling relations are shown to provide a good description of the flow for both the initial conduction dominated, one-dimensional, unsteady phase and the fully developed convection dominated, two-dimensional, steady phase of the flow. Scaling constants have been obtained for all relations.

Back Flow of the Two-dimensional Unsteady Prandtl Boundary Layer Under an Adverse Pressure Gradient

In this paper, we study the occurrence of a back-flow point of the two-dimensional unsteady Prandtl boundary layer under an adverse pressure gradient. For the two-dimensional unsteady Prandtl bound...