Local Skin Friction Research Articles

The Space-Time Coupled Fractional Cattaneo-Friedrich Maxwell Model with Caputo Derivatives.

In the current article, we have thoroughly investigated the collective impact of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid (Cattaneo–Friedrich Maxwell-CFM model) over a permeable surface embedded in a porous medium. Here we have utilized the Caputo time-fractional derivatives and mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s and Fick’s laws) are being used to fractionalize the presented model. The effects of radiative heat flux, Ohmic dissipation, and internal absorption are presented through generalized Fourier’s law while Fick’s law or mass transfer equation offers the effects of first order chemically reactive species. The finite element method and finite difference method are being utilized to numerically solve the nonlinear coupled differential equations. It is established, through compression of numerical and analytical solutions, that the presented model is convergent. Further, error analysis of the subject model is also carried out. Moreover, for better illustration of results, we have also offered a graphical and tabular presentation of impacts of the parameters of interest on velocity, temperature, concentration profile, local skin friction coefficient, and heat and mass transfer. It is evident from the obtained results that velocity near and away from the surface increases with the enhancement of fractional derivative parameter whereas an opposite trend is observed in the case of temperature. Furthermore, it is noticed that temperature shows a decreasing behavior for the value {Lambda }_{theta }<2 and {Lambda }_{phi }<2, on the other hand entirely opposite trend is witnessed for {Lambda }_{theta }ge 3 and {Lambda }_{phi }ge 3. From an engineering perspective, we have acquired comprehensive outcomes such that the heat transfer offers an increasing trend in the case of TR and thermal fractional parameter beta_{1} . Additionally, the chemical reaction parameter and Sc significantly contribute towards the mass transfer rate. Since, in literature, one cannot refer to such results with non-integer Caputo fractional derivatives thus the results obtained through the current assessment hold significance for future research avenues. Moreover, the numerical inferences of the subject study may contribute to an advanced thermal processing method in the food industry to swiftly increase the temperature for cooking or sterilization drives.

EFFECT OF ALIGNED MAGNETIC FIELD AND INCLINED OUTER VELOCITY IN CASSON FLUID FLOW OVER A STRETCHING SHEET WITH HEAT SOURCE

The purpose of this study was to assess the effect of the inclined outer velocity on heat and flow transportation in boundary layer Casson fluid over a stretching sheet. The flow is adopted to have non-orthogonal magnetic field with heat generation in the uniform manner on stretching surface. It has been taken that in both the directions along the x-axis, the sheet is stretched. By applying similarity transformations, the governing equations representing the heat and flow transportation are converted to ordinary differential equations. Runge-Kutta Fehlberg approach was adopted to solve numerically the moulded differential equations with the help of shooting technique. The flow is also governed by the heat source parameter, Casson fluid parameter, magnetic parameter, Prandtl number, aligned angle of magnetic field and the impinging angle parameter. The results revealed that velocity decreases with an increase in Casson fluid parameter, magnetic parameter and aligned angle of magnetic field for the case of outer velocity parameter less than one while velocity increases for the case of outer velocity parameter greater than one because of the inverted boundary layer formation for velocity profile in second case. Also, the fluid temperature increases (for the case of outer velocity parameter less than one) and temperature decreases (for the case of outer velocity parameter greater than one) with an increase in Casson fluid parameter, impinging angle parameter and aligned angle parameter. The results indicate that outer velocity and aligned magnetic field has a significant impact on fluid temperature and velocity. The behaviour of emerging fluid parameters on fluid temperature and velocity are depicted graphically and their effect on local Nusselt number (〖Nu〗_x ) and skin friction coefficient (C_f ) are represented by tables. The finding of this study may serve as to control the rate of heat transportation and fluid velocity in many manufacturing processes and industrial applications to make the desired quality of final product. Acceptance of the extant technique used in current study is correlated with the existing outcomes in the literature.

Numerical analysis on the three-dimensional flow and heat transfer of multiple nanofluids past a Riga plate

This examination is passed on to decide the properties of three-dimensional flow of H 2 O/NaC 6 H 9 O 7 base liquid with F e 3 O 4 /Al 2 O 3 nanoparticles confined by a Riga plate. Mathematical model is detailed as PDEs and afterward transmuted into ODEs with the assistance of similarity transformations. The subsequent system is numerically dealt with the aid of the Runge-Kutta procedure bolstered by shooting technique. Highlights of the flow field and thermal field are exemplified quantitatively through plots. Results for the local skin friction coefficient and local Nusselt number are registered and examined tabularly. It is induced that the modified Hartmann number and stretching ratio parameter ameliorate the velocity profile. Additionally, it is likewise explained that H 2 O − Al 2 O 3 nanofluid has high skin friction values and the rate of heat transfer of NaC 6 H 9 O 7 − Al 2 O 3 nanofluid is more desirable.

Heat and Mass Transfer of Hydrodynamic Boundary Layer Flow along a Flat Plate with the Influence of Variable Temperature and Viscous Dissipation

This paper elucidates heat together with mass transfer through a flat plate and variable temperature as well as dissipative effects. The flow assumptions resulted to steady flow equations which were simplified with appropriate similarity variables. The simplified equations were numerically solved and results are presented both in graphs and tabular form. Effects of physical quantities of interest were presented graphically. The local skin friction is observed to increase because of increase in Schmidt number. Also, increase in Prandtl number is found to boast the local Nusselt number. The behaviour of increase in Prandtl number is found to be unstable within the boundary layer regime while increase in Eckert number produces heat energy within the fluid layers. Finally, the validation of the present problem is done by comparing with previous works and was in perfect agreement.

Mathematical modelling of Transient Free Convection MHD Flow Past a Vertical Plate with Periodic Temperature Using Homotopy Perturbation Method

A mathematical model is used to study the effect of the magnetic field on the temporary free convection flow of the electrically conductive fluid past the vertical plate under periodic temperature. The governing momentum and energy equations are solved analytically using the homotopy perturbation method. An approximate analytical solution using Homotopy perturbation method and Laplace transform is carried out for temperature profile in case of constant plate temperature. The results are obtained the analytical and limiting case results ones, and a good agreement is achieved. The effect of different physical parameters on transient velocity and temperature, such as Grashof number, magnetic parameter, Prandtl number and temperature frequency, is examined. Also, the local Skin-friction and local Nusselt number coefficients are obtained and analyzed.

Influence of magnetic field and radiation on heat and mass transfer flow of nano fluid over an inclined vertical plate embedded in porous medium

We have analyzed MHDboundary layer flow, heat and mass transfer analysis of nanofluid over an inclined vertical plate saturated by porous medium with thermal radiation, and heat generation/absorption. Suitable similarity variables are introduced to convert non-linear partial differential equations into ordinary differential equations and these equations together with associated boundary conditions are solved numerically by using versatile, extensively validated, variational Finite element method. The impact of various pertinent parameters on hydrodynamic, thermal and concentration boundary layers are examined in detail and the results are shown graphically. Furthermore, the impact of these parameters on local skin friction coefficient, rate of heat transfer andrate of mass transferis also investigated. The results are compared with the works published previously and found to be excellent agreement.

Magnetohydrodynamics boundary layer flow of micropolar fluid over an exponentially shrinking sheet with thermal radiation: Triple solutions and stability analysis

The flow of electrically conducting micropolar fluid past an exponentially permeable shrinking sheet in the presence of a magnetic field and thermal radiation is studied. Similarity transformations are applied to the governing partial differential equations to form ordinary differential equations. The solution for the resultant equations, subject to boundary conditions, is then computed numerically using the bvp4c solver in MATLAB. The effects of several parameters on the local skin friction coefficient, couple stress, Nusselt number, velocity, microrotation and temperature of the fluid are analysed. Because the numerical computations for this problem result in triple solutions, stability analysis is carried out to ascertain the stability and significance of these solutions. The first solution is revealed to be stable, hence more physically meaningful than the other solutions. Meanwhile, it is found that the increase in magnetic and thermal radiation parameters reduces the fluid temperature.

Bioconvection aspects in non-Newtonian three-dimensional Carreau nanofluid flow with Cattaneo–Christov model and activation energy

In this article, a mathematical model is envisaged to scrutinize the aspect of swimming motile microorganisms for a steady 3D convectional flow of Carreau nanofluid towards a bidirectional stretching surface. Various researchers in the past years are collaborating in the nanotechnology field due to their improvement in heat capacity, chemotherapy for cancer, microelectronics, cooling of energy storage devices, cooling of nuclear system, air conditioning, and nanochips, etc. The novel concept of activation energy and double stratification effects is considered to analyze the flow problem. Thermal relaxation time and concentration relaxation time properties are both determined by implementing Cattaneo–Christov heat and mass flux in the energy and mass equation. Suitable similarity approximations are utilized to convert governing PDEs into dimensionless ODEs. Numerical solutions are determined to utilize collocation finite difference technique and 3-stages Lobatto-IIIa formula. The obtained ODE’s are resolved numerically by engaged built-in function bvp4c solver in computational software MATLAB. The behavior of various emerging parameters and local skin friction coefficients, local Nusselt numbers, local Sherwood number, motile microorganisms’ number, velocity profiles, temperature profile, concentration profile and microorganism concentration is elaborated with the help of graph and tables. Carreau fluid model is a particular category of established non-Newtonian fluid that exemplifies shear thinning $$ n<1 $$ , shear thickening $$ n>1 $$ at high shearing rates. It is examined that the influence of the mixed convection parameter against temperature distribution both the temperature field of the shear-thinning/thickening liquids is reduced.

Magnetohydrodnamics nanofluid flow of shaped nanoparticles over a porous stretching wall and slip effect

AbstractIn this study, we analyze the magnetohydrodynamic flow of magnetite‐engine oil nanofluid in the presence of nonidentical shaped nanoparticles subject to the porous medium and velocity slip effect. Energy analysis is carried out with the Ohmic heating and thermal radiation impacts. The system of partial differential equations are transformed into the system of ordinary differential equations using similarity variable. The Hamilton–Crosser model is used. The exact solutions for the momentum and heat transport analysis are found. The impact of various emerging parameters on the velocity and temperature profiles are analyzed by graphs. Furthermore, the local skin friction and heat transfer rate are examined graphically. It is examined that the velocity field increases with an increment in the magnitude of ϕ and L. An increase in the value of Hartman number enhancing the temperature profile.

Joule heating, activation energy and modified diffusion analysis for 3D slip flow of tangent hyperbolic nanofluid with gyrotactic microorganisms

Current communication aims to examine the novel thermal consequences of thermal radiation, Joule heating and activation energy in bioconvection flow of tangent hyperbolic nanofluid. The flow is developed by a three-dimensional (3D) extending surface in presence of porous space. The heat and mass transfer inspection in non-Newtonian fluid flow is inspected in laws of modified flux relations. The Brownian movement and thermophoresis diffusions are also accounted for current analysis. The governing formulated frameworks are simplified by appropriate similarity transformations. A familiar shooting scheme for obtaining the numerical outcomes to the nonlinear system is carried out. The graphical results are obtained with the aid of shooting technique. Flow of fluid, thermal field, concentration of species and microorganism’s field are conducted for tangent hyperbolic fluid. Furthermore, the significance of various noteworthy variables on velocity field, thermal field, solutal field of nanomaterials, microorganisms’ profile, local skin friction coefficients, local heat flux rate, local Sherwood number and local microorganisms density number is scrutinized in graphical and tabular structure. The importance of current model is in the field of nanotechnology and bioengineering.

Study of the MHD Flow of Casson Nanofluid in the Presence of Oxides Nanoparticles Based C2H6O2/H2O Under Constant Heat Flux Boundary Condition

In this study, a numerical investigation of free convection in magneto-hydrodynamic (MHD) Casson nanofluid flow with heat transfer over a stretching sheet and with constant heat flux boundary condition is done. A magnetic field is considered normal to the stretching sheet. Two types of nanoparticles with various conductivities, such as iron oxide and graphene oxide are suspended in ethylene glycol/water-based Casson nanofluid. An implicit finite difference scheme known as Keller-box method has been employed in order to solve the set of nonlinear partial differential equations resulted from the governing equations, namely continuity, momentum, and energy equations. The effects of the MHD Casson nanofluids parameters on the physical properties such that local skin friction coefficient, local Nusselt number, velocity, and temperature have been displayed and discussed. The study has revealed that ethylene glycol has higher velocity and less temperature than water with different values of nanoparticle volume fraction, magnetic, and Casson parameters with the existence of Fe3O4/GO nanoparticles. Comparisons with previous studies show that the proposed method is in good agreement with other results.

Features of 3D magneto-convective nonlinear radiative Williamson nanofluid flow with activation energy, multiple slips and Hall effect

In this article, the impacts of Hall current and Arrhenius activation energy on three-dimensional hydromagnetic Williamson nanofluid flow past a slendering stretching sheet in the presence of multiple slips, viscous dissipation, Joule heating and binary chemical reaction is analyzed. The presence of nonlinear thermal radiation and nonlinear mixed convection is also taken into consideration. The dimensional governing equations are transformed into non-dimensional ordinary differential equations by using some suitable similarity transformation. The resulting coupled and highly nonlinear boundary value problem is then solved numerically by shooting technique based on Runge-Kutta-Fehlberg method. The behaviors of concentration, temperature and velocity distributions w.r.t. the various controlling parameters are illustrated graphically. However, the numerical values of local skin-friction coefficients, local heat and mass transfer rates are explained and presented in tabular form. Furthermore, a result validation is performed to check the accuracy and correctness of the obtained results by comparing the results with previously published results for some limited case of the present problem and an excellent agreement is found between the results.

Heat and Mass Transfer in Stagnation Point Flow of Maxwell Nanofluid Towards a Vertical Stretching Sheet with Effect of Induced Magnetic Field

This paper presents a mathematical model analysis of heat and mass transfer in a two-dimensional flow of electrically conducting, thermally radiative, and chemically reactive Maxwell nanofluid towards a vertical stretching and permeable sheet embedded in a porous medium. Boundary layer approximation and suitable transformations are used to reduce the governing differential equations convenient for computation. Eventually, the transformed nonlinear differential equations along with the corresponding boundary conditions are solved in the framework of optimal homotopy analysis method. The effects of induced magnetic field, buoyancy force, viscous dissipation, heat source, Joule heating, and convective boundary condition are analyzed in detail. The rates of heat, mass, and momentum transfer with respect to the relevant parameters are also examined in terms of the local Nusselt number, Sherwood number, and skin friction coefficients, respectively. Among the many results of the study, it is shown that the induced magnetic field, flow velocity, and temperature profiles are increasing functions of the Maxwell parameter. The results of the present study are also in a close agreement with previously published results under common assumptions.

Onset of shear-layer instability at the interface of parallel Couette flows

A non-planar or a bilateral mixing-layer is studied by means of a series of direct numerical simulations (DNSs). This mixing-layer forms at the interface of two co-current plane Couette flows of different Reynolds numbers. The current DNS study determined the conditions for the onset of shear-layer instability at the interface. The influence of different Reynolds number (of the co-current plane Couette flows) and their Reynolds number ratio on the mixing-layer is studied. A critical Reynolds number of about 500 (or more particularly one of the co-current plane Couette flows must be turbulent) and a Reynolds number ratio greater than 2 is required for the genesis of this bilateral shear-layer instability. Independent of the Reynolds number and the Reynolds number ratio, the temporal evolution of the shear-layer instability followed the same pattern. In addition, the oscillation frequency of the instability was found to increase with increasing Reynolds number and increasing Reynolds number ratio. Further, influence of instability on the local skin friction and the two-point correlation is elaborated on.

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

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

The skin-friction coefficient of a turbulent boundary layer modified by a large-eddy break-up device

A computational study based on well-resolved large-eddy simulations is performed to study the skin friction modification by a large-eddy breakup device (LEBU) in a zero-pressure-gradient turbulent boundary layer. The LEBU was modeled using an immersed boundary method. It is observed that the presence of the device leads to the generation of wake vortices, which propagate downstream from the LEBU and toward the wall. A skin friction decomposition procedure is utilized to study different physical mechanisms of the observed skin friction reduction. From the skin friction decomposition, it is found that the skin friction reduction can be characterized by three universal regions of different changes for the skin friction contributions. The first region is predominantly associated with the formation of the wake vortices and the reduction of Reynolds shear stress. In the second region, the mean streamwise velocity fields show that a region of velocity deficit formed downstream of the LEBU propagates toward the wall and leads to turbulence reduction due to wake wall interactions, which also induces a local maximum skin friction reduction. In the third region, the dissipation of wake vortices leads to the regeneration of Reynolds shear stress. A quadrant analysis of the Reynolds shear stress contribution reveals that the LEBU increases the Q2 and Q4 contributions and attenuates the Q1 and Q3 contributions in the first region, followed by an onset of Reynolds shear stress further downstream.

Analysis of Forced Convection Boundary Layer Flow and Heat Transfer Past a Semi-Infinite Static and Moving Flat Plate Using Nanofluids-by Haar Wavelets

The paper presents, the steady state two-dimensional forced convection boundary layer flow of heat transfer past a semi-infinite static flat plate (Blasius problem) and moving flat plate (Sakiadis problem) in the water based nanofluid with various nanoparticles. The self-similar solution exists for the boundary layer equations and using suitable similarity variables, the governing equations have been converted into coupled nonlinear ordinary differential equations (NODEs) with an infinite domain. The governing problems over an infinite interval were solved using semi-numerical technique which makes the use of power of Haar wavelets coupled with collocation method. The solutions obtained using wavelet methods have been confirmed to be more accurate as compared to other previously published results. The several physical interesting results of the problem are concentrated and verified through numerical schemes. Three different types of nonmetallic or metallic nanoparticles such as alumina (Al2O3), copper (Cu) and titania (TiO2) in the base fluid of water with Prandtl number Pr = 6.2, to study the effect of solid volume fraction parameter Φ of the nanofluids. The effect of local skin friction coefficients, Nusselt number, velocity and temperature profiles are plotted for various values of nanoparticle volume fractions and for different nanoparticles are analyzed in detail, the numerical results are presented in terms of Tables. It predicts that, the solid volume fraction affects the fluid flow and heat transfer characteristics.

Mathematical Analysis of Radiating Viscoelastic Unsteady MHD Fluid Flow through an Absorbent Media between Upstanding Equidistant plates with Joule Heating Impact

Focus of the present study is to explore Joule heating effect on incompressible, radiating, electrically conducting viscoelastic unsteady magnetohydrodynamic fluid and heat transfer through an absorbent media between upstanding equidistant plates with constant suction and slip condition. Lorentz force and Joule heating is discussed by momentum and energy equation respectively. Electric conductivity and the electromagnetic force both are in very small case in fluid flow. A consistent magnetic field is taking to perpendicular to the plane of the plates. The oscillatory time-dependent coupled equations (non-linear) are simplified to provide result for the fluid velocity and heat transfer by using structured perturbation execution. It has been noticed that velocity and heat transfer rise due to rise in Grashof number, Eckert number, heat source parameter or slip parameter while decrease as permeability parameter, radiation parameter or wavelength rises. As Hartmann number rises the fluid velocity diminishes, while opposite behaviour is noted in case of heat transfer effect. The velocity and heat transfer impact of the fluid rise with cross flow Reynolds parameter or frequency of the oscillation. Numerical outcomes for the motion and heat transpose effect profiles for multiples physical numbers also the local skin friction coefficient and spot Nusselt number are argued numerically, presented graphically along with.

Thermal Slip Flow of a Three-Dimensional Casson Fluid Embedded in a Porous Medium with Internal Heat Generation

Present assessment is considered to analysis flow as well as heat characteristics of steady, thermal slip flow of three-dimensional Casson fluid embedded in a porous medium with internal heat generation. Geometry of the present analysis is linearly stretched surface. Later, all the PDEs corresponding to the study are altered to set of nonlinear equations ODEs by means of appropriate similarity transformations. An efficient numerical scheme of spectral relaxation method (SRM) is applied to solve the nonlinear ordinary system. Variations of Nusselt number, temperature, velocity, and local skin friction coefficient with fluid parameters exhibited by graphs and tables. Spectral relaxation method gives an exact convergence to the nonlinear boundary value problems compare with general methods. In this study, to improve the precision and accuracy of the SRM successive over-relaxation (SOR) strategy is utilized. Proposed method as well as outcomes is checked with the comparison. A sensible connection is acquired between the current outcomes and accessible outcomes in writing. Some of the observations are skin friction coefficient raises and velocities decreases by the magnetic field strength. Skin friction and Local Nusselt number at the surface is more pronounced for non-Newtonian case than that of Newtonian case.

Thermal radiation, chemical reaction, Hall and ion slip effects on MHD oscillatory rotating flow of micro-polar liquid

The thermal radiation, chemical reaction, Hall and ion slip impacts on double-diffusive unsteady MHD natural convective rotating flow of micro-polar fluid past a semi-infinite vertical moving porous plate under the influence of uniform transverse magnetic field with convective boundary conditions have been investigated. The entire system is assumed to fluctuate in time with invariant frequency, therefore, the solutions of the boundary layer be of the oscillatory style. The non-dimensional governing equations are solved analytically through perturbation method and discussed computationally with references to pertinent parameters. It is observed that the velocity and micro-rotation profiles increases with an increase in Hall and ion slip parameters but reverse effects are found with an increasing in viscosity ratio and chemical reaction parameter. The thermal radiation parameter is to increase the temperature profiles but reverse effect is observed with an increasing in frequency of oscillations. Further, the concentration is decreased with increase in the Schmidt number and, it is increased with increase in the chemical reaction parameter. For engineering curiosity, the local skin friction and couple stress coefficients, rate of heat and mass transfer in terms of Nusselt number and Sherwood number are obtained analytically and discussed numerically. Although it is originated that, the local Nusselt number and local Sherwood number remains constant with varying all pertinent parameters. The heat and mass transfer on MHD flows through porous media with the chemical reaction arise in many transport processes both naturally and artificially in many branches of science and engineering applications. This phenomenon plays an important role in the chemical industry, power and cooling industry for drying, chemical vapour deposition on surfaces, cooling of nuclear reactors, and petroleum industries. The Hall and ion slip effects are used in many situations in bio-medical engineering and aero-space engineering.