Non-dimensional Skin Friction Research Articles

Magnetohydrodynamic (MHD) Convective Flow in a Porous Medium in the Presence Variable Pressure and Injection/Suction

This article investigates MHD convective flow with variable pressure and injection/suction in a porous medium. The governing equations are modeled using partial differential equations (PDEs) in dimensional form. The PDEs describes the unsteady flow of an incompressible electrically conducting fluid are expressed for the momentum, energy and concentration of the fluid flow. Also, the PDEs were transformed to non-dimensional form using some dimensional variables. Perturbation method was used to obtain the solutions for the velocity, temperature and concentration. The non-dimensional Skin friction, Nusselt number and Sherwood number were obtained. Effects of physical parameters associated with the present study was examined and discussed. It was observed that the concentration, temperature and velocity of the fluid rises with increase in injection parameter and an opposite trend was observed when suction parameter became significant. It is found that the temperature of the fluid reduces as the Prandtl number increase. However, an opposite trend is seen for heat source/sink.

Numerical analysis of significance of multiple shape factors in Casson hybrid nanofluid flow over a rotating disk

The goal of this paper is to identify the consequences of Darcy–Forchheimer flow (DFF) on electromagnetohydrodynamic flow of graphene oxide–iron oxide hybrid nanofluid over a rotating disk in a porous medium with viscous dissipation. The set of obtained ordinary differential equations had been solved with the corresponding boundary conditions using a numerical method called fourth-order Runge–Kutta method along with the shooting technique. The impact of the pertinent parameters on the dimensionless flow and temperature field profiles is shown using graphs. Also the nondimensional skin friction factor is stated in tabular form. The results state that as there is an increase in the value of porosity parameter, the velocity profile then diminishes. As shown in the outcomes, we accomplish that in this modeling, platelets have higher influence than the blade, brick, and cylinder. Due to nanoparticles, graphene oxide–iron oxide nanocomposite exhibits anti-microbial capabilities. These studies suggest that graphene oxide–iron oxide nanocomposite may be used to remove natural solvents and water filter.

Finite element Soret Dufour effects on an unsteady MHD heat and mass transfer flow past an accelerated inclined vertical plate

AbstractThe present study is focused on the Soret and Dufour effects on magnetohydrodynamics unsteady fluid flow over an accelerated inclined vertical plate with thermal radiation and heat source. Solution of the nondimensional governing differential equations are worked out by the efficient Galerkin finite element method. The influence of several relevant flow parameters on velocity, temperature, and concentration distributions, as well as the numerical results, are studied and graphically displayed. The nondimensional skin friction and the rate of heat and mass transfer parameters are presented in the Tables 1‐3 below. Raising the Soret number results in growing concentrations, but the converse is true for the Schmidt number. Skin friction reduces when Soret and Dufour numbers increase. The present simulations apply to the processing of magnetic materials in the chemical and metallurgical industries.

Chemical reaction and radiation effects on unsteady MHD free convection flow in a porous medium past an infinite inclined isothermal plate

The effect of chemical reaction on unsteady magentohydrodynamic (MHD) free convection flow in a porous medium past an infinite inclined plate has been investigated. Laplace transform technique is the method to solve the solutions for velocity, temperature and concentration fields. The analytical expressions for non-dimensional skin friction, Nusselt number and Sherwood number has been presented. The influence of various embedded parameter on velocity, temperature and concentration such as chemical reaction parameter, magnetic field and radiation has been discussed in detail. The effects of involved parameters have been discussed and the numerical results are presented graphically.

A Simplified Finite Difference Method (SFDM) for EMHD Powell–Eyring Nanofluid Flow Featuring Variable Thickness Surface and Variable Fluid Characteristics

We study constant and variable fluid properties together to investigate their effect on MHD Powell–Eyring nanofluid flow with thermal radiation and heat generation over a variable thickness sheet. The similarity variables assist in having ordinary differential equations acquired from partial differential equations (PDEs). A novel numerical procedure, the simplified finite difference method (SFDM), is developed to calculate the physical solution. The SFDM described here is simple, efficient, and accurate. To highlight its accuracy, results of the SFDM are compared with the literature. The results obtained from the SFDM are compared with the published results from the literature. This gives a good agreed solution with each other. The velocity, temperature, and concentration distributions, when drawn at the same time for constant and variable physical features, are observed to be affected against incremental values of the flow variables. Furthermore, the impact of contributing flow variables on the skin friction coefficient (drag on the wall) and local Nusselt (heat transfer rate on the wall) and Sherwood numbers (mass transfer on the wall) is illustrated by data distributed in tables. The nondimensional skin friction coefficient experiences higher values for constant flow regimes especially in comparison with changing flow features.

Radiation and Diffusion Thermo Effects of Visco-Elastic Fluid Past a Porous Surface in the Presence of Magnetic Field and Chemical Reaction with Heat Source

An analysis of two dimensional free convective hydro-magnetic flow of an electrically conducting visco-elastic fluid past a vertical porous surface has been studied in the presence of magnetic field and chemical reaction of first order with heat source. Simultaneously effects of heat and mass transfer are also studied in combination of the physics of diffusion thermo (Dufour effect) and suction at the plate is assumed to be constant. The equations governing are solved by perturbation technique. Analytical expressions for velocity, temperature and concentration fields, non-dimensional skin friction coefficient and Nusselt number are obtained. The results are analyzed graphically for various values of visco-elastic parameter along with a combination of other flow parameters involved in the solution.

Heat and mass transfer with viscous dissipation in horizontal channel partially occupied by porous medium in the presence of oscillatory suction

This paper deals with unsteady oscillatory flow of viscous incompressible fluid with heat & mass transfer in a horizontal channel partially occupied by porous medium following the Darcy-Brinkman model. The interior territory of the channel consists of two regions; one of them is filled with porous material and second is clear fluid. At the porous medium fluid interface, interfacial coupling conditions for the fluid velocity, temperature and concentration were used to derive the analytical solution. The effects of pertinent physical fluid parameter like porosity, viscosity ratio, density ratio etc. on velocity, temperature and concentration distribution are considered and demonstrated through graphs. Also, the non-dimensional Skin-friction coefficient, Nusselt number and Sherwood number have been calculated and reported in tabular form.

Boundary layer flow and heat transfer analysis on Cu-water nanofluid flow over a stretching cylinder with slip

Investigation of heat transfer effect on Cu-water nanofluid flow past a stretching cylinder is focused in the recent article. The numerical method of nonlinear known as RKF 4–5th has been taken into account along with shooting process to obtain the solution of required ODEs with supplementary boundary conditions. The influence of thermal radiation parameter on non-dimensional skin friction and Nusselt number along with convection parameter, solid particle volume fraction and heat generation/absorption parameter are represented in the tabular and graphical way. The volume fraction of nanofluid is considered as 0–6% with an increment of 2%. The thermal radiation parameter lies in the domain of [0.3,5]. Moreover, the values of porosity parameter (λ) and heat generation/absorption parameter (Q) are varied as 0.5⩽λ⩽2.5 and -2⩽Q⩽2, respectively. The data of authors declared that augmentation is perceived in temperature curves with the volume fraction of solid particles; moreover, momentum boundary layer depreciates with boost in volume fraction parameter of copper (Cu) particles. The obtained data are distinguished with earlier study and admirable agreement has been noted.

Unsteady MHD Free Convective Flow of a Visco-Elastic Fluid Past an Infinite Vertical Porous Moving Plate with Variable Temperature and Concentration

The present study considers the effect unsteady MHD free convective flow of a viscoelastic incompressible electrically conducting fluid past a moving vertical plate through a porous medium with time dependent oscillatory permeability and suction in presence of a uniform transverse magnetic field and heat source and chemical reaction along with heat and mass transfer are reported. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The governing equations of the fluid flow, heat and mass transfer are solved by applying multi parameter perturbation technique. Comparison with previously published work have been conducted and the results are found to be in concordance with the previous study. A parametric study is performed on the influence of the visco-elastic fluid parameter, the magnetic field parameter, the permeability parameter, on the fluid velocity. The expressions for transient velocity, temperature, species concentration and non-dimensional skin friction at the plate are illustrated through tables to observe the visco-elastic effect in combination of other flow parameters involved in the solution.

Visco-Elastic MHD Free Convective Flow through Porous Media in Presence of Radiation and Chemical Reaction 2 1 with Heat and Mass Transfer

An analysis of visco-elastic free convective transient MHD flow over a vertical porous plate through porous media in presence of radiation and chemical reaction with heat and mass transfer is presented. A transverse variable suction velocity is applied on the porous plate. The equations governing the fluid flow, heat and mass transfer are solved by applying multiple perturbation technique. The expressions for transient velocity, temperature, species concentration and non-dimensional skin friction at the plate are obtained and the expressions for transient velocity and non-dimensional skin friction at the plate are illustrated graphically to observe the visco-elastic effect in combination of other flow parameters involved in the solution.

MHD double diffusion flow by free convection past an infinite inclined plate with ramped wall temperature in a porous medium

The combined effects of heat and mass transfer on unsteady magnetohydrodynamic (MHD) free convection flow in a porous medium past an infinite inclined plate with ramped wall temperature have been investigated. The closed form analytical solutions have been obtained for the velocity, temperature and concentration fields by using Laplace transforms method. The analytical expressions for non-dimensional skin-friction, Nusselt number and Sherwood number have been computed. The effects of the embedded flow parameters such as inclination angle, radiation parameter, magnetic field parameter, and Grashof number on flow fields are shown graphically. It is found that increasing the inclination angle and radiation parameters, the fluid velocity along an inclined plate will be decreased.

An Exact Solution of Unsteady MHD Free Convection Flow of a Radiating Gas Past an Infinite Inclined Isothermal Plate

The effect of thermal radiation on unsteady magnetohydrodynamic free convection flow of an optically thin gray gas past an infinite inclined plate with constant temperature has been investigated. The governing coupled partial differential equations are solved analytically using the Laplace transform technique. The dimensionless velocity and temperature profiles are shown in graphs and the numerical values of the non-dimensional skin-friction and Nusselt number are presented in tables. The influence of the system parameters such asPrandtl number, inclination angle, magnetic field parameter, Grashof number, radiation parameter and time on flow fields have been discussed in detail. The results indicate that the inclination angle, magnetic field parameter and radiation parameter effects were to decrease the fluid velocity along an inclined plate.

Effects of Hall Current and Mass Transfer on the Unsteady Magnetohydrodynamic Flow in a Porous Channel

The combined effects of Hall current and mass transfer on the unsteady magnetohydrodynamic (MHD) flow of a viscous fluid passing through a porous channel have been investigated. The flow in the fluid has been induced due to external pressure gradient. The closed form analytical solutions have been obtained for the velocity, temperature and concentration fields. The analytical expressions for non-dimensional Skin-friction, Nusselt number and Sherwood number have been computed. The influence of various embedded flow parameters have been analyzed through graphs. The solutions obtained show that the influence of Hall parameter and mass transfer phenomenon give some interesting results. It is found that the Hall parameter have an increasing effect on the fluid velocity and approaches to the steady state as the time parameter is increased. The fluid concentration is increased for larger values of Peclet and Schmidt numbers whereas decreased with increase in Soret number and time parameter.

Steady mixed convection boundary layer flow over a vertical flat plate in a porous medium filled with water at 4°C: case of variable wall temperature

The problem of steady mixed convection boundary layer flow over a vertical impermeable flat plate in a porous medium saturated with water at 4°C (maximum density) when the temperature of the plate varies as xm and the velocity outside boundary layer varies as x2 m, where x measures the distance from the leading edge of the plate and m is a constant is studied. Both cases of the assisting and the opposing flows are considered. The plate is aligned parallel to a free stream velocity U∞ oriented in the upward or downward direction, while the ambient temperature is T∞ = Tm (temperature at maximum density). The mathematical models for this problem are formulated, analyzed and simplified, and further transformed into non-dimensional form using non-dimensional variables. Next, the system of governing partial differential equations is transformed into a system of ordinary differential equations using the similarity variables. The resulting system of ordinary differential equations is solved numerically using a finite-difference method known as the Keller-box scheme. Numerical results for the non-dimensional skin friction or shear stress, wall heat transfer, as well as the temperature profiles are obtained and discussed for different values of the mixed convection parameter λ and the power index m. All the numerical solutions are presented in the form of tables and figures. The results show that solutions are possible for large values of λ and m for the case of assisting flow. Dual solutions occurred for the case of opposing flow with limited admissible values of λ and m. In addition, separation of boundary layers occurred for opposing flow, and separation is delayed for the case of water at 4°C (maximum density) compared to water at normal temperature.

Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface

The mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent fluid is analyzed using similarity solution technique. Wall temperature and stretching velocity are assumed to have specific exponential function forms. The influence of buoyancy along with viscous dissipation on the convective transport in the boundary layer region is analyzed in both aiding and opposing flow situations. The flow is governed by the mixed convection parameter Gr/Re2. The velocity and temperature inside the boundary layer are observed to be influenced by the parameters like Prandtl number Pr, Gebhart number Gb. Significant changes are observed in non-dimensional skin friction and heat transfer coefficients due to viscous dissipation in the medium. The flow and temperature distributions inside the boundary layer are analyzed and the results for non-dimensional skin friction and heat transfer coefficients are discussed through computer generated plots.

Suspended-sediment reference concentration under waves: field observations and critical analysis of two predictive models

Two commonly adopted but fundamentally different approaches for predicting time-averaged suspended-sediment reference concentration ( C̄ REF) under waves are tested against field measurements and compared with each other. The first model relates C̄ REF to the cube of the non-dimensional skin friction, whereas the second model adopts a more complex function of excess skin friction incorporating the empirical constant γ 0. The dataset is from the zone of wave shoaling seaward of an open-coast surfzone and includes measurements of waves, currents, suspended sediment and bedforms. Estimates of C̄ REF are derived from acoustic backscatter data, and the seabed and suspension process are described from video footage. When waves were energetic, the bed was deformed into large hummocks; during less energetic conditions, the bed was rippled. The time-averaged concentration profiles over the ripples were consistent with settling flux balanced by pure gradient diffusion and a sediment diffusivity that is constant with elevation above the bed. C̄ REF in that case is shown to apply at z=0, where z is the elevation above the bed. Over the hummocks, there was a sheet flow at the base of the suspension and C̄ REF is shown to apply at z=1 cm. The concentration profiles over the hummocks implied sediment diffusivity that varied linearly with elevation within ∼10 cm of the bed and constant sediment diffusivity above that level. For both rippled and hummocky beds, γ 0 derived from the field data was found to be sensitive to the value assumed for critical stress for initiation of sediment motion, which could explain the range of values reported in the literature for γ 0. γ 0 was also found to vary in a complex way with skin friction, which suggests that the reference-concentration model based on excess skin friction is not correctly formulated. Nevertheless, two functions for γ 0 (one applying to rippled beds and the other to hummocky beds) were contrived to make the model fit the data. The model based on non-dimensional skin friction was found to be a good predictor of C̄ REF when a correction was made for flow contraction over ripples. The correction was not required for the hummocky bed, where sediment was being entrained in a thin sheet flow layer. The model based on non-dimensional skin friction correctly portrayed the relationship between flow and sediment response without contrivance and therefore should be the favoured approach in predicting reference concentration.

Magnetohydrodynamic boundary-layer flow for a non-Newtonian fluid past a wedge

The flow of a power law fluid past a symmetrical wedge is studied in the neighbourhood of the stagnation point when an external magnetic field is applied. The nonlinear equation of motion is transformed to a similarity differential equation which is solved using the method of successive approximations. The analytical solutions found by this method yield numerical values in good agreement with tabulated calculations obtained before via numerical methods for electrically nonconducting fluids. Analytical expressions are derived for both the velocity profile and the local non-dimensional skin friction coefficient. Also the three thicknesses of displacement, momentum and kinetic energy are given in closed forms.

Asymptotic boundary-layer over a slender body of revolution in axial compressible flow

The singular perturbation method developed by S. Kaplun is used to solve the thick, compressible laminar boundary layer over a slender body of revolution. The transverse curvature effect is included and is found to be characterized by a dimensionless parameter, which is essentially a function of the ratio of the thickness of the boundary layer to the radius of the body of revolution. An asymptotic series solution is developed for the region where the thickness of the boundary layer is large compared with the radius of the slender body. The nondimensional skin-friction parameter \(2ir rGTw)/(cosa. Ueve)} is calculated as a function of the thickness parameter. Interpolations are then made with another known series solution, developed by Probstein and Elliott, which is valid where the boundary layer is thin compared with the radius of the slender body. Thus, interpolation is made to cover the range where the thickness of boundary layer is in the same order as the body radius. From these interpolations, good agreement is obtained between both series for the cone and cylinder. The asymptotic series solution also indicates that the skin friction and heat-transfer rate increase with the Mach number and fall off very slowly in the reciprocal-logarithmic manner with the thickness parameter.