Momentum Boundary Layer Equations Research Articles

Dynamics of Unsteady Flow of Chemically Reactive Upper-Convected Maxwell Fluid with Temperature-Dependent Viscosity: Keller Box Analysis

The heat and mass transfer characteristics of unsteady flow of incompressible chemically reactive upper-convected Maxwell fluid along a stretching surface in the presence of temperature-dependent viscosity has been studied. The theoretical analysis on heat and mass transfer over a stretching sheet is investigated for numerical analysis. With the use of stream function formulation, the governing boundary layer equations of momentum, energy, and concentration are reduced to a set of linked ordinary differential equations. The nonlinear ordinary differential equations are then solved numerically by using the Keller Box method. The physical behavior of governing parameters on velocity, temperature, and concentration profiles and the local skin friction coefficient and heat and mass transfer rates are graphed and tabulated. The physical impact of Maxwell parameter β, unsteadiness parameter M, Schmidt number Sc, Prandtl number Pr, reaction rate parameter γ, and variable viscosity parameter ε on the heat and mass transfer has been examined along the stretching surface numerically. The novelty of the present work is to examine the importance of destructive reaction and contractive reaction on the dynamics of upper-convected Maxwell fluid flow in the presence of temperature-dependent viscosity effects. It is observed an interesting behavior of temperature distribution and concentration profile is noted for lower value of viscosity parameter ε in the presence of chemical reaction. It is also found that skin friction and the rate of heat transfer are decreased by increasing the variable viscosity parameter ε .

The MHD Newtonian hybrid nanofluid flow and mass transfer analysis due to super-linear stretching sheet embedded in porous medium

The steady magnetohydrodynamics (MHD) incompressible hybrid nanofluid flow and mass transfer due to porous stretching surface with quadratic velocity is investigated in the presence of mass transpiration and chemical reaction. The basic laminar boundary layer equations for momentum and mass transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The mass equation in the presence of chemical reaction is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation. The mass transfer is analyzed for two different boundary conditions of concentration field that are prescribed surface concentration (PSC) and prescribed mass flux (PMF). The asymptotic solution of concentration filed for large Schmidt number is analyzed using Wentzel-Kramer-Brillouin (WKB) method. The parameters influence the flow are suction/injection, superlinear stretching parameter, porosity, magnetic parameter, hybrid nanofluid terms, Brinkman ratio and the effect of these are analysed using graphs.

Numerical Analysis of Mixed Convection Flow Past a Symmetric Cylinder with Viscous Dissipation in Viscoelastic Nanofluid

Research on the nanofluid becomes trending amongst researchers especially in the industrial and engineering field due to its important and extensive applications. Therefore, the present study aims to investigate numerically the impact of viscous dissipation conducted by sodium carboxymethyl cellulose (CMC-water) nanofluid containing copper nanoparticles at room temperature with convective boundary conditions (CBC). The Tiwari and Das model was selected in this study and the transformed boundary layer equations for momentum and energy subject to the appropriate boundary conditions were numerically solved by employing numerical scheme, namely the Keller-box method. The results were analysed in detail and presented graphically for the velocity, temperature, skin friction coefficient as well as the heat transfer coefficient. The obtained results indicated that there was no significant effect for velocity and temperature profiles when values of Eckert number increased. However, it is significant for skin friction and heat transfer coefficient profiles. In the meantime, the thermal conductivity of the fluid may increase by increasing the concentration of nanofluid.

Inquiry of MHD bioconvective non-newtonian nanofluid flow over a moving wedge using HPM

In this present article, the influence of MHD flow of a non-Newtonian Casson nanoliquid conveying gyrotactic microorganisms over a moving wedge with thermal radiation, thermophoresis and Brownian motion are reported. The basis boundary layer equations of momentum, energy, nanoparticle concentration and density of motile microorganisms, which are nonlinear PDE’s, are transformed into a nonlinear ODE’s through a set of similarity variables. The renovated equations are solved analytically using the Homotopy Perturbation Method (HPM). The analytical results are validated with the numerical results using shooting method also compared with available literature as a limiting case. The impact of salient parameters of the Casson nanoliquid are illustrated with several graphs and tables.

Response of a turbulent boundary layer to rapid freestream acceleration

In a wide range of fluid machinery, a turbulent boundary layer can be exposed to rapid transients of the freestream conditions. A simplified model of the boundary layer response would provide valuable guidance in understanding these situations in multiple engineering applications. To this end, a turbulent boundary flow, subject to freestream acceleration, was explored through high-fidelity simulations and Reynolds-averaged Navier–Stokes calculations. Test cases were considered in which the flow over a flat plate accelerated from Mach 0.3 up to 0.6 over two time scales, 10 ms and 25 ms. Based on data from the calculations, the integral boundary layer momentum equation was simplified to propose a new reduced-order model capable of computing the evolution of the boundary layer under external flow transients. Given the initial boundary layer height, and the temporal evolution of the freestream pressure, velocity, and density, the model predicts the transient development of the boundary layer. With the transient boundary layer profile known, the temporal history of the skin friction and heat transfer can be predicted, taking advantage of standard shear stress correlations and the Reynolds analogy.

Impact of generalized Fourier’s law and Fick’s law for MHD flow of Ag‒H2O and TiO2‒H2O nanomaterials

Purpose The purpose of this paper is to investigate the effect of inclined magnetic field, variable viscosity and Cattaneo–Christov heat and mass flux theories on the steady MHD free convective boundary layer flow of viscous, incompressible and electrically conducting water-driven silver and titanium-oxide nanofluids over a vertical stretching sheet. Design/methodology/approach The boundary layer equations of momentum, energy and nanoparticle concentration are partial differential equations in nature, which are reduced to nonlinear ordinary differential equations by means of similarity transformations. The resulting nonlinear equations are solved analytically by means of optimal homotopy analysis method. Findings Assessments with numerical results are performed and are found to be in an excellent agreement. Numerical results of the skin friction factor, the local Nusselt number and the local Sherwood number are obtained through tables. The effects of various physical parameters on the velocity, temperature and nanoparticles fraction are incorporated through graphs. The study analyzes the efficiency of heat transfer of nanofluids in cooling plants and rubber sheets. Originality/value No research works have been conducted to evaluate the effects of various physical phenomena on the copper and titanium nanofluids flow.

Analysis of a Chemically Reactive Mhd Flow With Heat and Mass Transfer Over a Permeable Surface

This paper investigates a chemically reactive Magnetohydrodynamics fluid flow with heat and mass transfer over a permeable surface taking into consideration the buoyancy force, injection/suction, heat source/sink and thermal radiation. The governing momentum, energy and concentration balance equations are transformed into a set of ordinary differential equations by method of similarity transformation and solved numerically by Runge- Kutta method based on Shooting technique. The influence of various pertinent parameters on the velocity, temperature, concentration fields are discussed graphically. Comparison of this work with previously published works on special cases of the problem was carried out and the results are in excellent agreement. Results also show that the thermo physical parameters in the momentum boundary layer equations increase the skin friction coefficient but decrease the momentum boundary layer. Fluid suction/injection and Prandtl number increase the rate of heat transfer. The order of chemical reaction is quite significant and there is a faster rate of mass transfer when the reaction rate and Schmidt number are increased.

Boundary layer flow of nanofluids to analyse the heat absorption/generation over a stretching sheet with variable suction/injection in the presence of viscous dissipation

ABSTRACT In this investigation, the heat and mass transfer characteristics in boundary layer flow about a stretching sheet in a porous medium filled with TiO2 – water and Al2O3 – water-based nanofluids, in the presence of internal heat generation or absorption and viscous dissipation with variable suction or injection effects is numerically studied. The similarity transformations are used to transform the governing boundary layer equations for momentum, energy and species transfer into a set of non-linear ordinary differential equations which are solved numerically by Keller-box method. The obtained numerical results are validated against results computed by using MATLAB bvp4c routine, and excellent agreement is observed. The impact of various pertinent parameters on velocity, temperature and concentration as well as the friction factor coefficient, local heat and mass transfer rates are derived and discussed through graphs and tables for TiO2 and Al2O3 water-based nanofluids. The present study reveals that an increase in Eckert number (Ec) and heat generation/absorption parameter (Q) significantly decreases local heat transfer rate.

Mixed Convection Flow of Viscoelastic Nanofluid Past a Horizontal Circular Cylinder with Viscous Dissipation

The purpose of this study was to examine the effect of viscous dissipation on mixed convection flow of viscoelastic nanofluid past a horizontal circular cylinder. Carboxymethyl cellulose solution (CMC) is chosen as the base fluid and copper as a nanoparticle with the Prandtl number Pr = 6.2. The transformed boundary layer equations for momentum and temperature subject to the appropriate boundary conditions are solved numerically by using Keller-box method. The influenced of the dimensionless parameters such as Eckert number, mixed convection parameter, nanoparticles volume fraction and viscoelastic parameter on the flow and heat transfer characteristics is analyzed in detail and presented graphically. The results come out with the velocity profiles are increased while the temperature profiles are decreased by increasing the values of nanoparticles volume fraction and viscoelastic parameter, respectively. The graph shows that, increasing Eckert number the skin friction is also increases. The values of skin friction are increased by increasing mixed convection parameter, but the values of Nusselt number produce an opposite behavior. The present study has many applications especially in heat exchangers technology and oceanography. Therefore, in future, it is hoping to study the viscoelastic nanofluid flow past a different geometric such as sphere and cylindrical cone.

Hydromagnetic Flow of Heat and Mass Transfer in a Nano Williamson Fluid Past a Vertical Plate With Thermal and Momentum Slip Effects: Numerical Study

Abstract In this article, the study of heat, momentum and mass (species) transfer in an electro-conductive polymer on the external surface of a vertical plate. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The non-dimensional, transformed boundary layer equations for momentum and energy are solved with the second order accurate implicit Keller box finite difference method under appropriate boundary conditions. The influence of Weissenberg number, magnetic body force parameter, thermal slip parameter, hydrodynamic slip parameter, stream wise variable and Prandtl number on thermo fluid characteristics are presented graphically and discussed. A weak elevation in temperature accompanies increasing Weissenberg number whereas a significant acceleration in the flow is computed near the plate surface. Rate of heat transfer is reduced with increases the Weissenberg number. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace, smart coating transport phenomena and other industries.

Extended integral wall-model for large-eddy simulations of compressible wall-bounded turbulent flows

Wall-modeling is required to make large-eddy simulations of high-Reynolds number wall-bounded turbulent flows feasible in terms of computational cost. Here, an extension of the integral wall-model for large-eddy simulations (iWMLESs) for incompressible flows developed by Yang et al. [“Integral wall model for large eddy simulations of wall-bounded turbulent flows,” Phys. Fluids 27(2), 025112 (2015)] to compressible and isothermal flows is proposed and assessed. The iWMLES approach is analogous to the von Kármán-Pohlhausen integral method for laminar flows: the velocity profile is parameterized, and unknown coefficients are determined by matching boundary conditions obeying the integral boundary layer momentum equation. It allows non-equilibrium effects such as pressure gradient and convection to be included at a computing cost similar to analytical wall-models. To take into account density variations and temperature gradients, the temperature profile is also parameterized and the integral compressible boundary layer energy equation is considered. Parameterized profiles are based on the usual logarithmic wall functions with corrective terms to extend their range of validity. Instead of solving a set of differential equations as wall-models based on the thin boundary layer equation approach, a simple linear system is solved. The proposed wall-model is implemented in a finite-volume cell-centered structured grid solver and assessed on adiabatic and isothermal plane channel flows at several friction Reynolds and Mach numbers. For low Mach number cases, mean profiles, wall fluxes, and turbulent fluctuations are in agreement with those of Direct Numerical Simulation (DNS). For supersonic flows, the results are in good agreement with the DNS data, especially the mean velocity quantities and the wall friction, while standard analytical wall-models show their limits.

Unsteady MHD flow and heat transfer of fractional Maxwell viscoelastic nanofluid with Cattaneo heat flux and different particle shapes

The paper aims to investigate the unsteady natural convection flow and heat transfer of fractional Maxwell viscoelastic nanofluid in magnetic field over a vertical plate. The effect of nanoparticle shape is first introduced to the study of fractional Maxwell viscoelastic nanofluid. Fractional shear stress and Cattaneo heat flux model are applied to construct the governing boundary layer equations of momentum and energy, which are solved numerically. The quantities of physical interest are graphically presented and discussed in detail. It is found that particle shape and fractional derivative parameters have profound influence on the flow and heat transfer.

Effect of thermal radiation on boundary layer flow and heat transfer of dusty fluid over an unsteady stretching sheet

The aim of this paper is to study the boundary layer flow and heat transfer analysis of an unsteady viscous dusty fluid over a porous stretching surface. Momentum Boundary layer equation considers the effect of transverse magnetic field whereas thermal Boundary layer equation considers the effect of thermal radiation. The governing partial Differential equations are reduced to coupled non-linear ordinary differential equations using similarity transformation. Numerical solutions of these equations are obtained with the help of RKF-45 method. The solution is found to be dependent on different governing parameters. Some important findings reported in this work reveal that the effect of radiation has significant impact in controlling the rate of heat transfer in the boundary layer region.Keywords: Unsteady flow and heat transfer; Boundary layer flow; Stretching porous Surface; Dusty fluid; Thermal radiation; Numerical solution

FREE CONVECTION HEAT AND MASS TRANSFER OF A NANOFLUID PAST A HORIZONTAL CYLINDER EMBEDDED IN A NON-DARCY POROUS MEDIUM

In the present paper, we analyzed the laminar boundary layer flow and heat transfer from a horizontal cylinder in a nanofluid-saturated non-Darcy porous medium in the presence of thermal radiation. This is the first paper presenting non-similar solutions for such a regime.The boundary layer conservation equations,which are parabolic in nature,are normalized into non-similar form and then solved computationally with an efficient, implicit, stable Keller-box finite difference scheme. Non-Darcy effects are simulated via a second-order Forchheimer drag force term in the momentum boundary layer equation. The model used for the nanofluid incorporates the effects of Brownian motion, buoyancy ratio, and thermophoresis. A non-similarity solution is presented that depends on the Brownian motion number (Nb), buoyancy ratio (Nr), thermophoresis number (Nt), Forchheimer parameter (Λ), and radiation parameter (F). Velocity is reduced with increasing Forchheimer parameter, whereas temperature and nanoparticle concentration are both enhanced.The model finds applications in energy systems and thermal enhancement of industrial flow processes

Numerical exploration of thermal radiation and Biot number effects on the flow of a non‐Newtonian MHD Williamson fluid over a vertical convective surface

AbstractA theoretical and computational study of the magnetohydrodynamic flow and free convection heat transfer in an electroconductive polymer on the external surface of a vertical plate under radial magnetic field is presented. The Biot number effects are considered at the vertical plate surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The nondimensional, transformed boundary layer equations for momentum and energy are solved with the second‐order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream‐wise variable, and Prandtl number on thermo fluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number, whereas a significant acceleration in the flow is computed near the vertical plate surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction and Nusselt number are both reduced with increasing magnetic field effect. The model is relevant to the simulation of magnetic polymer materials processing.

Analytical solution in parametric form for the two-dimensional liquid jet of a power-law fluid

The two-dimensional liquid jet of a power-law fluid is considered. The problem is formulated in terms of the components of fluid velocity which satisfy the continuity equation and the momentum boundary layer equation for a power-law fluid. The multiplier method is used to investigate the conservation laws for the system of partial differential equations and a conserved vector and the corresponding conserved quantity for the two-dimensional liquid jet is derived. The Lie point symmetries of the system of partial differential equations are calculated. A linear combination of the Lie point symmetries is associated with the conserved vector for the liquid jet to obtain the associated Lie point symmetry which is used to generate the invariant solution. An analytical solution in parametric form for the liquid jet is derived. It is found that a solution for the liquid jet exists only for 1/2<n<∞ where n is the power law exponent. The profile of the free surface and the thickness of the liquid jet are compared for a shear thinning fluid with 1/2<n<1, a Newtonian fluid with n=1 and a shear thickening fluid with 1<n<∞.

Hydromagnetic Flow and Heat Transfer in a Williamson Non-Newtonian Fluid from a Horizontal Circular Cylinder with Newtonian Heating

A theoretical and computational study of the magneto hydrodynamic flow and free convection heat transfer in an electro-conductive polymer on the external surface of a horizontal circular cylinder under radial magnetic field is presented. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. Newtonian heating is incorporated via appropriate boundary conditions as this represents better actual thermal materials processing operations. The non-dimensional, transformed boundary layer equations for momentum and energy are solved with the second order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream wise variable and Prandtl number on thermofluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number whereas a significant acceleration in the flow is computed near the cylinder surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction is increased whereas Nusselt number is reduced with greater stream wise coordinate. The study is relevant to smart coating transport phenomena.

Thermal radiation and MHD effects on boundary layer flow of micropolar nanofluid past a stretching sheet with non-uniform heat source/sink

In this paper, the study of electrically conducting micropolar nanofluids flow over a stretching sheet influencing by thermal radiation and non-uniform heat source/sink in presence of transverse magnetic field investigated numerically and simulated with RungeKutta-Fehlberg method with shooting techniques. Governing nonlinear boundary layer equations for momentum, energy and continuity equations are transformed into a system of nonlinear ordinary coupled differential equations by using similarity transformations. Influences of nanoparticle concentration and different emerging parameters on flow profiles are presented graphically coupled with comprehensive discussions for four types of metallic or nonmetallic nanoparticles, namely silver (Ag), copper (Cu), alumina (Al2O3) and titanium dioxide (TiO2) in water based micropolar fluid in order to show some interesting phenomena. Effect of different parameters on skin friction coefficient, couple stress and local Nusselt number are also discussed.

Natural convection on heat transfer flow of non-newtonian second grade fluid over horizontal circular cylinder with thermal radiation

This article numerically studies for multi-physical transport of an optically-dense, free convective incompressible non-Newtonian second grade fluid past an isothermal, impermeable horizontal circular cylinder. The governing boundary layer equations for momentum and energy transport, which are parabolic in nature, have been reduced to non-similarity non-linear conservation equations using appropriate transformations and then solved numerically by employing with most validated, efficient implicit finite difference method with Keller box scheme. The numerical code is validated with previously existing results and found to be very good agreement. The results are reported graphically and in tabular form for various physical parameters; Deborah number, Prandtl number and thermal radiation on flow velocity and temperature profiles. Furthermore, the effects of these parameters on non dimensional wall shear stress (skin friction) and surface heat transfer rate (Nusselt number) are also investigated. Increasing the Deborah number reduces velocity profile, skin friction and Nusselt number where as it enhances the temperature profile. Increasing Prandtl number decelerates the flow velocity, temperature and skin friction but Nusselt number enhances considerably. Increase in radiation parameter retards the flow velocity, temperature profiles and skin friction. But Nusselt number enhances markedly with increase in radiation parameter. Applications of the model arise in polymer processing in chemical engineering, metallurgical material processing.

Heat and mass transfer characteristics of nanofluid over horizontal circular cylinder

Abstract In this work, the impact of Brownian motion and thermophoresis on heat and mass transfer flow over a horizontal circular cylinder embedded in porous media filled with nanofluid is numerically examined. The transformed boundary layer equations for momentum, temperature and concentration subject to the appropriate boundary conditions are solved numerically by using an optimized, efficient and extensively validated Finite element method. The influence of the non-dimensional parameters such as the buoyancy ratio parameter (Nr), mixed convention parameter (Ra), thermophoresis parameter (Nt), Brownian motion parameter (Nb), tangential coordinate (ξ) and the Lewis parameter (Le) on velocity, temperature and concentration evolutions in the boundary layer region is analyzed in detail and the results are shown graphically. The local Nusselt number and the local Sherwood number are also investigated for various values of these non-dimensional parameters and the results are shown in tabular form. The comparison of present results with existing results shows good agreement.