Wall Skin Friction Research Articles

Unsteady Self-similar Flow over an Impulsively Started Shrinking Sheet: Flow Augmentation with No Separation

Abstract The unsteady self-similar flow due to a permeable shrinking sheet is analyzed in this investigation. The current theoretical study is enacted in the light of correct self-similar formulation proposed by (Mehmood. A. Viscous flows: Stretching and shrinking of surfaces, Springer, 2017). For the existence of a meaningful solution the retarded boundary-layer developed due to retarded shrinking wall velocity u w x = ± x t \left( {{u_w}\left( x \right) = {{ \pm x} \over t}} \right) is supported by the sufficient mass suction introduced at the shrinking surface. Main theme of this paper is to utilize the correct mathematical formulation for the shrinking sheet flow in order to investigate the existence of dual solutions of the considered problem. By using suitable self-similar transformations, the nonlinear Navier–Stokes equations are converted to corresponding non-linear ordinary differential equations. A reliable numerical technique (shooting method) is applied to solve the resulting ODEs for the involved physical parameters. Particular to this problem, it is observed that a sufficient amount of wall suction is mandatory S < S c ; S c ≤ 0 \left( {S \lt {S_c}; {S_c} \le 0} \right) for the existence of meaningful solutions; and also the solutions are non-unique. As the magnitude of wall suction is reduced (i. e. S → S c S \to {S_c} ) the solution seizes to exist by having non-zero coefficient of wall skin-friction, reflecting the absence of any flow separation. On the other hand, a stronger flow augmentation is noted for the increasing values of the wall suction parameter S S . The results are presented through graphs as well as in tabulated form. It is noticed that dual solutions exist for sufficiently large magnitude of the suction parameter S > S c \left( { \left| S \right| \gt \left| {{S_c}} \right| } \right) .

EFFECT OF MASS AND HEAT TRANSFER IN OSCILLATORY TWO DIMENSIONAL FLOW OF A MICRO POLAR FLUID OVER AN INFINITE PERMEABLE PLATE IN A POROUS MEDIUM UNDER THE EXISTENCE OF MAGNETIC FIELD

In this paper we study the effect of Mass and Heat transfer under the existence of transverse magnetic field for an oscillating two dimensional Micro-polar fluid flow through a moving infinite permeable plate in a porous medium. Investigate the Solutions for angular momentum, governing momentum, energy and concentration equations. Study the effect of chemical reaction, permeability parameters, velocity profiles, micro rotation profiles, wall stress coefficient and skin friction coefficient by using graph.

Soret and Dufour effects on transient free convention heat and mass transfer flow in a vertical channel with ramped wall temperature and specie concentration: an analytical approach

This work investigates unsteady free convection heat and mass transfer flow in a vertical channel in the presence of Soret and Dufour effects. The bounding walls and the specie are considered to have ramped temperature and ramped concentration respectively. Perturbation method is first used to decouple the governing equations that arise from the model due to the presence of combined Soret and Dufour effects. Laplace transform technique is then used to obtain an analytical solutions for the temperature, concentration and velocity. In order to cross check the accuracy of the proposed analytical method, numerical solutions are obtained using PDEPE in MATLAB. The influences of the two effects as well as the ramped boundary conditions on the fluid flow are graphically presented and discussed. The results show that these two effects and the imposed boundary conditions affect the fluid temperature, concentration, velocity, rate of heat transfer, rate of mass transfer and wall Skin friction. Moreover, it is found that the solutions obtained by the authors Jha and Gambo correspond to the results of the present work when Soret effect is absent.

Critical values in transport phenomena for curved power-law sheet utilizing [formula omitted]/water hybrid nanoliquid: Model prediction and stability analysis

The present investigation reveals the impact of mixture of nanoparticles (Al2O3 and Cu) in basefluid and convective heating on the power-law shrinking curved surface with radius of curvature (K). The homogeneous hybrid nanoliquid (0.1% of Al2O3-Cu/water) model with theoretical and fitted (predicted) experimental correlations is transformed into coupled system of non-linear ordinary differential equations for finding possible branches of the solution. The critical values (cc,βc and χc) have been evaluated for some cases, beyond these values there is either no solution or multiple solutions exist. Two different nanofluid models (Model I and II) are compared and found to be contradictory for skin friction and Nusselt number in current physical model. Linear stability analysis for finding stable branch, is also performed through construction of eigenvalue (EV) problem. The MATLAB built-in package LinearFit.model is used for multiple regression estimation (MRE) in case of stable branch which shows that nanoparticle concentration has maximum contribution towards the heat transfer. Moreover, the wall skin friction has strong dependence on curvature parameter. As Prandtl number increases, the linearly fitted model is found to be more suitable for convective boundary case (γ = 0.5).

Thermal Radiation Effects on Casson Dusty Boundary-Layer Fluid Flow Along an Isothermal Truncated Vertical Cone

A boundary-layer analysis is presented to study the effect of intense thermal radiations on natural convection flow of Casson dusty particulate suspension past a truncated cone. Contribution of radiative heat flux in a two-phase model is reported by means of Rosseland diffusion approximation. In order to convert the governing equations into non-dimensional form, a continuous set of transformations is used and the resulting equations are integrated numerically via an implicit finite difference method. Numerical results for Casson dusty fluid flow characteristics are shown graphically under the variation of various important parameters. It is found that thermal radiation parameter, $$R_\mathrm{d}$$, and dusty fluid parameter, $$\alpha _\mathrm{d}$$, increase the magnitude of heat transfer rate. Casson rheological parameter, $$\beta $$, has also pronounced effect on the flow and it increases the rate of heat transfer and reduces wall skin friction coefficient.

Magnetohydrodynamic free convection of non-Newtonian power-law fluids over a uniformly heated horizontal plate

The MHD free convection flow of non-Newtonian power-law fluids over a horizontal plate subjected to a constant heat flux is studied. The results are presented for various values of the three influential parameters, i. e. the generalized Hart?mann number, the generalized Prandtl number, and the non-Newtonian power-law viscosity index. Increasing the Hartmann number increases the thermal boundary-layer thickness and the surface temperature and consequently decreases the wall skin friction and Nusselt number. A lower generalized Prandtl number results in a larger skin friction coefficient and higher wall temperature as well as thicker thermal boundary-layer. The viscosity index is predicted to influence the flow conditions depending on the value of generalized Hartmann number. At high generalized Prandtl number numbers, by decreasing non-Newtonian power-law index, the wall skin friction, temperature scale, and thermal boundary-layer thickness are increased and the Nusselt number is decreased, while the opposite trend is observed for low generalized Prandtl number. A general correlation for the Nusselt number is derived using the numerical results

Unsteady free convective heat transfer in third-grade fluid flow from an isothermal vertical plate: A thermodynamic analysis

The current study investigates theoretically and numerically the entropy generation in time-dependent free-convective third-grade viscoelastic fluid convection flow from a vertical plate. The nondimensional conservation equations for mass, momentum and energy are solved using a Crank–Nicolson finite difference method with suitable boundary conditions. Expressions for known values of flow-variables coefficients are also derived for the wall heat transfer and skin friction and numerically evaluated. The effect of Grashof number, Prandtl number, group parameter (product of dimensionless temperature difference and Brinkman number) and third-grade parameter on entropy heat generation is analyzed and shown graphically. Bejan line distributions are also presented for the influence of several control parameters. The computations reveal that with increasing third-grade parameter, the entropy generation decreases and Bejan number increases. Also, the comparison graph shows that contour lines for third-grade fluid vary considerably from the Newtonian fluid. The study is relevant to non-Newtonian thermal materials processing systems.

Direct numerical simulation of turbulence over resolved and modeled rough walls with irregularly distributed roughness

To simulate turbulent flow over a rough wall without resolving complicated rough geometries, a macroscopic rough wall model is developed based on spatial (plane) averaging theory. The plane-averaged drag force term, which arises through averaging the Navier–Stokes equations in a plane parallel to a rough wall, can be modeled using a plane porosity and a plane hydraulic diameter. To evaluate the developed model, direct and macroscopic model simulations for turbulence over irregularly distributed semi-spheres at Reynolds number of 300 are carried out using the D3Q27 multiple-relaxation time lattice Boltzmann method. The results show that the developed model can be used to predict rough wall skin friction. The results agree quantitatively with standard turbulence statistics such as mean velocity and Reynolds stress profiles with the fully resolved DNS data. Since velocity dispersion occurs inside the rough wall and is found to contribute to turbulence energy dissipation, which the developed model cannot account for, the developed model fails to reproduce dispersion-related turbulence energy dissipation. However, it is found that the plane-averaged drag force term can successfully recover the deficiency of dispersion-related turbulence energy dissipation.

Boundary Value Problem for a Heated Nanofluid Flow in the Presence of Magnetic Field

The aim of this paper is to introduce some new numerical results on the magneto-thermomechanical interaction between heated viscous incompressible magnetic nanofluid and a cold wall in the presence of a spatially varying magnetic field. The governing nonlinear boundary layer equations are converted into coupled nonlinear ordinary differential equations by similarity transformation. The ODE system is solvable numerically for example using higher derivative method. The investigation is focused on the influence of governing parameters corresponding to various physical conditions. Numerical results are exhibited for the dimensionless wall skin friction and for heat transfer coefficients at the wall, along to distributions of the velocity and the temperature.

Laminar natural convection of power‐law fluids over a horizontal heated flat plate

AbstractNatural convection of power‐law fluids over a horizontal flat plate with constant heat flux is studied. The stretching transformations relating the similarity forms of the boundary layer velocity, pressure, and temperature profiles are applied to the governing boundary layer equations. The resultant set of coupled ordinary differential equations are solved analytically and numerically using the integral method and the finite difference method, respectively. The results are presented for the details of the velocity and temperature fields for various values of the non‐Newtonian power‐law viscosity index (n) and the generalized Prandtl number (Pr*). At a fixed value of the viscosity index, increasing the Prandtl number increases the skin friction and wall temperature. For Pr* > 1, a lower viscosity index results in larger wall skin friction, temperature scale, and thermal boundary layer thickness, and thus lower Nusselt number. The reverse trend is observed for Pr* < 1. By using an integral solution and the numerical results, a semi‐analytical correlation for the Nusselt number is obtained, valid for and .

An enthalpy‐preserving shock‐capturing term for residual distribution schemes

SummaryIn this contribution, we investigate strategies to perform shock‐capturing computation of steady hypersonic flow fields by means of residual distribution schemes. The ultimate objective is the computation of flow solutions for which the correct upstream enthalpy value is recovered in the postshock region. To this end, the parallelism existing between the classical Bx scheme and the stabilized finite element techniques is exploited. The simple Lax‐Friedrichs dissipation term is leveraged to build two new residual distribution schemes. Upon testing on both inviscid and viscous steady problems, solutions obtained with one of the two schemes are shown to recover the correct upstream total enthalpy level in the postshock region. This last scheme provides also improved wall pressure and skin friction predictions; heat transfer predictions are, unfortunately, similar to those offered by the Bx scheme. A conjecture for explaining this behavior is exposed.

Numerical solutions for unsteady boundary layer flow of a dusty fluid past a permeable stretching/shrinking surface with particulate viscous effect

PurposeThis present aims to present the numerical study of the unsteady stretching/shrinking flow of a fluid-particle suspension in the presence of the constant suction and dust particle slip on the surface.Design/methodology/approachThe governing partial differential equations for the two phases flows of the fluid and the dust particles are reduced to the pertinent ordinary differential equations using a similarity transformation. The numerical results are obtained using the bvp4c function in the Matlab software.FindingsThe results revealed that in the decelerating shrinking flow, the wall skin friction is higher in the dusty fluid when compared to the clean fluid. In addition, the effect of the fluid-particle interaction parameter to the fluid-phase can be seen more clearly in the shrinking flow. Other non-dimensional physical parameters such as the unsteadiness parameter, the mass suction parameter, the viscosity ratio parameter, the particle slip parameter and the particle loading parameter are also considered and presented in figures. Further, the second solution is discovered in this problem and the solution expanded with higher unsteadiness and suction values. Hence, the stability analysis is performed, and it is confirmed that the second solution is unstable.Practical implicationsIn practice, the flow conditions are commonly varying with time; thus, the study of the unsteady flow is very crucial and useful. The problem of unsteady flow of a dusty fluid has a wide range of possible applications such as in the centrifugal separation of particles, sedimentation and underground disposable of radioactive waste materials.Originality/valueEven though the problem of dusty fluid has been broadly investigated, limited discoveries can be found over an unsteady shrinking flow. Indeed, this paper managed to obtain the second (dual) solutions, and stability analysis is performed. Furthermore, the authors also considered the artificial particle-phase viscosity, which is an important term to study the particle-particle and particle-wall interactions. With the addition of this term, the effects of the particle slip and suction parameters can be investigated. Very few studies in the dusty fluid embedded this parameter in their problems.

Slip and Hall Current Effects on Jeffrey Fluid Suspension Flow in a Peristaltic Hydromagnetic Blood Micropump

The magnetic properties of blood allow it to be manipulated with an electromagnetic field. Electromagnetic blood flow pumps are a robust technology which provide more elegant and sustainable performance compared with conventional medical pumps. Blood is a complex multi-phase suspension with non-Newtonian characteristics which are significant in microscale transport. Motivated by such applications, in the present article, a mathematical model is developed for magnetohydrodynamic pumping of blood in a deformable channel with peristaltic waves. A Jeffery’s viscoelastic formulation is employed for the rheology of blood. A two-phase fluid-particle (“dusty”) model is utilized to better simulate suspension characteristics (plasma and erythrocytes). Hall current and wall slip effects are incorporated to achieve more realistic representation of actual systems. A two-dimensional asymmetric channel with dissimilar peristaltic wave trains propagating along the walls is considered. The governing conservation equations for mass, fluid and particle momentum are formulated with appropriate boundary conditions. The model is simplified using long wavelength and creeping flow approximations. The model is also transformed from the fixed frame to the wave frame and rendered non-dimensional. Analytical solutions are derived. The resulting boundary value problem is solved analytically, and exact expressions are derived for the fluid velocity, particulate velocity, fluid/particle fluid and particulate volumetric flow rates, axial pressure gradient, pressure rise and skin friction distributions are evaluated in detail. Increasing Hall current parameter reduces bolus growth in the channel, particle-phase velocity and pressure difference in the augmented pumping region, whereas it increases fluid phase velocity, axial pressure gradient and pressure difference in the pumping region. Increasing the hydrodynamic slip parameter accelerates both particulate and fluid phase flow at and close to the channel walls, enhances wall skin friction, boosts pressure difference in the augmented pumping region and increases bolus magnitudes. Increasing viscoelastic parameter (stress relaxation time to retardation time ratio) decelerates the fluid phase flow, accelerates the particle-phase flow, decreases axial pressure gradient, elevates pressure difference in the augmented pumping region, and reduces pressure difference in the pumping region. Increasing drag particulate suspension parameter decelerates the particle-phase velocity, accelerates the fluid phase velocity, strongly elevates axial pressure gradient and reduces pressure difference (across one wavelength) in the augmented pumping region. Increasing particulate volume fraction density enhances bolus magnitudes in both the upper and lower zones of the channel and elevates pressure rise in the augmented pumping region.

Statistical discussions on skin frictional drag of turbulence over randomly distributed semi-spheres

The influence of dynamical effects of rough wall turbulence, namely velocity dispersion, drag force and turbulence, on rough wall skin friction coefficient is statistically discussed by performing direct numerical simulation of rough-walled open channel flows and analyzing spatial and Reynolds (double) averaged equations. Numerical calculations are conducted by the D3Q27 multiple-relaxation-time lattice Boltzmann method (MRT-LBM). For the rough surfaces, randomly distributed semi-spheres are considered. Analyzing an integrated double averaged momentum equation, a main contributor to the skin friction coefficient is found to be the turbulence contribution and a second contributor is the drag contribution, and the drag contribution particularly increases with increasing the equivalent roughness. Although the streamwise mean velocity dispersion is significantly induced by the acceleration/deceleration of the streamwise velocity due to the roughness elements, the wall-normal mean velocity dispersion is not significant. Consequently, the off-diagonal component of the dispersive covariant term is far smaller than the Reynolds shear stress and the velocity dispersion thus hardly contributes to an increase in the skin friction coefficient.

A new kind of hairpin-like vortical structure induced by cross-interaction of sinuous streaks in turbulent channel**Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LQ18A020002), the National Natural Science Foundation of China (Grant No. 41776105), and the Foundation of the Educational Committee of Zhejiang Province, China (Grant No. Y201737053).

This work is motivated by previous experimental and numerical studies which reveal that the hairpin vortex could be formed by the interaction between spanwise adjacent low-speed streaks. To prove that such an interaction mechanism is still applicable in the normal direction, two sinuous low-speed streaks with the same streamwise phase are set to be in the upper half and bottom half of a small size channel, respectively, and their evolution and interaction are investigated by direct numerical simulation. A new kind of hairpin-like vortical structure, distributed in the normal direction and straddled across both halves of the channel, is found during the cross-interaction process of the low-speed streaks. The influence of such a normal-distributed hairpin-like vortex (NHV) on the turbulent statistical regularity is also revealed. It is observed that the NHV can lead to a sudden surge of wall skin friction, but the value of the normal velocity as well as the streamwise and spanwise vorticity sharply decrease to zero in the center of the channel.

Three-Dimensional Modeling Shock-Wave Interaction with a Fin at Mach 5

The three-dimensional single-fin configuration finds application in an intake geometry where the cowl-shock wave interacts with the side-wall boundary layer. Accurate numerical simulation of such three-dimensional shock/turbulent boundary-layer interaction flows, which are characterized by the appearance of strong crossflow separation, is a challenging task. Reynolds-averaged Navier–Stokes computations using the shock-unsteadiness modified Spalart–Allmaras model is carried out at Mach of 5 at large fin angle of $$23^{\circ }$$ . The computed results using the modified model are compared to the standard Spalart–Allmaras model and validated against the experimental data. The focus of the work is to implement the modified model and to study the flow physics in detail in the complex region of swept-shock-wave turbulent boundary-layer interaction in terms of the shock structure, expansion fan, shear layer and the surface streamlines. The flow structure is correlated with the wall pressure and skin friction in detail. It is observed that the standard model predicts an initial pressure location downstream of the experiments. The modified model reduces the eddy viscosity at the shock and predicts close to the experiments. Overall, the surface pressure using modified model has predicted accurately at all the locations. The skin friction is under-predicted by both the models in the reattachment region and is attributed to the poor performance of turbulence models due to flow laminarization.

A numerical treatment for partial slip flow and heat transfer of non-Newtonian Reiner-Rivlin fluid due to rotating disk

In this article, partial slip flow of Reiner-Rivlin fluid induced by a rough rotating disk is modeled. Heat transfer is also addressed by assuming more general temperature jump condition. The constitutive relations in Reiner-Rivlin fluid lead to a coupled and strongly non-linear differential system. A convenient numerical treatment is invoked to solve the resulting similarity equations for broad ranges of non-Newtonian fluid parameter and slip coefficients. Our main interest is to predict the behaviors of fluid elasticity and wall slip coefficients on the von-Kármán flow problem. Expressions of wall skin friction and surface heat transfer are calculated and deliberated for broad parameter values. Different from radial and axial velocities, tangential velocity appears to increase as Reiner-Rivlin fluid parameter (K) increases. Reduction in surface drag coefficient, which is vital in some applications, can be accomplished by increasing the parameter K. Volumetric flow rate is also inversely proportional to the parameter K. However, heat transfer rate diminishes when parameter K enlarges. We also conclude that larger torque would be required to keep steady rotation of the disk for higher values of wall slip coefficients.

Numerical Modeling of Transpiration-Cooled Turbulent Channel Flow with Comparisons to Experimental Data

Transpiration cooling is a promising active cooling technique that provides coolant through a porous wall at a rate sufficient to maintain temperatures below a desired limit. The present study uses ANSYS® CFX to numerically investigate the influence of cooling gas injection on the temperature, velocity, and wall skin friction in the boundary layer of a subsonic turbulent hot-gas channel flow for various blowing ratios (), hot-gas temperatures (), and Mach numbers (, ). Here, a cooled permeable porous ceramic matrix composite sample with a hot-gas channel flow is simulated using a monolithic and two-domain approach. For the two-domain approach, separate solvers are used for the hot-gas and porous domains, respectively. These are applied alternatively and coupled to each other by boundary conditions imposed at the respective interface. The simulations are validated against experimental data and provide complementary insight into the effects of the cooling, which cannot be assessed from experimental measurements alone. The results show that, although a monolithic approach would be more convenient from a numerical point of view, a two-domain approach has proven to be superior in matching experimental data for this study. Furthermore, improved thermal boundary-layer profiles downstream of the porous sample are obtained by including the aft wall in the coupling process. This study adds to the limited theoretical and numerical investigations found in the literature on transpiration cooling.

Numerical solutions for gyrotactic bioconvection of dusty nanofluid along a vertical isothermal surface

The aim of the present paper is to establish the detailed numerical results for bioconvection boundary-layer flow of a two-phase dusty nanofluid. The dusty fluid contains gyrotactic microorganisms along an isothermally heated vertical wall. The physical mechanisms responsible for the slip velocity between the dusty fluid and nanoparticles, such as thermophoresis and Brownian motion, are included in this study. The influence of the dusty nanofluid on heat transfer and flow characteristics are investigated in this paper. The governing equations for two-phase model are non-dimensionalized and then solved numerically via two-point finite difference method together with the tri-diagonal solver. Results are presented graphically for wall skin friction coefficient, rate of heat transfer, velocity and temperature profiles and streamlines and isotherms. To ensure the accuracy, the computational results are compared with available data and are found in good agreement. The key observation from the present analysis is that the mass concentration parameter, Dρ, extensively promotes the rate of heat transfer, Qw, whereas, the wall skin friction coefficient, τw, is reduced by loading the dust parameters in water based dusty nanofluid.

Electrothermal transport of nanofluids via peristaltic pumping in a finite micro-channel: Effects of Joule heating and Helmholtz-Smoluchowski velocity

The present article studies theoretically the electrokinetic pumping of nanofluids with heat and mass transfer in a micro-channel under peristaltic waves, a topic of some interest in medical nano-scale electro-osmotic devices. The microchannel walls are deformable and transmit periodic waves. The Chakraborty-Roy nanofluid electrokinetic formulation is adopted in which Joule heating effects are incorporated. Soret and Dufour cross-diffusion effects are also considered. Under low Reynolds number (negligible inertial effects), long wavelength and Debye linearization approximations, the governing partial differential equations for mass, momentum, energy and solute concentration conservation are derived with appropriate boundary conditions at the micro-channel walls. The merging model features a number of important thermo-physical, electrical and nanoscale parameter, namely thermal and solutal Grashof numbers, the Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) and Joule heating to surface heat flux ratio. Closed-form solutions are derived for the solute concentration, temperature, axial velocity, averaged volumetric flow rate, pressure difference across one wavelength, and stream function distribution in the wave frame. Additionally expressions are presented for the surface shear stress function at the wall (skin friction coefficient), wall heat transfer rate (Nusselt number) and wall solute mass transfer rate (Sherwood number). The influence of selected parameters on these flow variables is studied with the aid of graphs. Bolus formation is also visualized and analyzed in detail.