Steady Boundary Layer Flow Research Articles

Dual solutions of nanaofluid forced convective flow with heat transfer and porous media past a moving surface

The paper presents a numerical study to explore the possible similarity solutions as well as dual branch solutions to study the performance evaluation of various nanoparticles associated water as the base fluid in the case of steady two-dimensional forced convection boundary layer flow through a moving flat porous plate under external magnetic fields. We considered water as a base fluid embedded with the three different types of nanoparticles namely copper (Cu), alumina (Al2O3) and titania (TiO2). The governing equations are simplified by similarity approach. The resulting equations are solved numerically and the numerical results are explored through graphs and tables and discussed in detail. The influences of problem parameters are discussed for the steady solution. The paper extends results of previous works by others authors contributing to increase the scientific knowledge on the subject. The skin friction coefficient and local Nusselt number on the plane are studied as functions of the problem parameters. The study reveals that the problem considered admits of upper and lower branch solutions for moving parameter λ, magnetic parameter M, the power law parameter n, convection heat transfer b and nanoparticle volume fraction parameter ϕ.

Dual solutions for boundary layer flow and heat transfer of biomagnetic fluid over a stretching/shrinking sheet in presence of a magnetic dipole and a prescribed heat flux

This paper analyzes the steady boundary layer flow and heat transfer of biomagnetic fluid over a stretching/shrinking sheet with prescribed surface heat flux under the influence of a magnetic dipole. The governing equations are transformed into a set of ordinary differential equations (ODEs) by using similarity transformations. Numerical results are obtained using the boundary value problem solver bvp4c of MATLAB. The effects of various physical parameters on the velocity and temperature profiles as well as skin friction coefficient are discussed. The paper shows that dual solutions exist for certain values of stretching/shrinking sheet and suction parameters. Stability analysis is performed to determine which solution is stable and physically valid. Results of the stability analysis depict that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable.

Dual solutions on boundary-layer flow over a moving surface in a flowing nanofluid with second-order slip

The steady boundary-layer flow of a nanofluid past a moving semi-infinite flat plate in a uniform free stream in the presence of second order slip is studied using a second order slip flow model. The governing PDE are transformed into non-linear ODE by using appropriate similarity transformations, which are then solved numerically using bvp4c solver for different values of selected parameters. We found that the solutions existed for dual in a certain range of velocity ratio parameter. Therefore, a stability analysis has been analyzed to show which solutions are stable. The effects of velocity ratio parameter, Lewis number, Prandtl number, Brownian motion parameter, thermopherosis parameter, mass suction, first order slip parameter, and second order slip parameter on the skin friction coefficient, heat transfer coefficient, dimensionless velocity, temperature as well as nanoparticle volume fraction profiles are figured out graphically and discussed. These results reveals that the slip parameters expand the range of the solutions obtained. The increment of slip parameters lead to decrease the skin friction coefficient while increase the heat transfer coefficient. In addition, the value of Lewis nmber, Prandtl number, Brownian motion parameter, and thermopherosis parameter are significantly affected the heat transfer coefficient. Lastly, the first solution is stable and physically relevant, while the second solution is not.

Impacts of viscous dissipation and Joule heating on hydromagnetic boundary layer flow of nanofluids over a flat surface subjected to Newtonian heating

Main concern in this analysis is to study the two-dimensional, steady boundary layer flow of viscous, incompressible, electrically conducting nanofluids past a flat plate in the presence of magnetic field with heat being transferred by Newtonian heating way. Influences of viscous dissipation and Joule heating are considered also. Nonlinear partial differential equations are reduced into nonlinear ordinary differential equations by formulating similarity transformations. Numerical solutions of transformed boundary layer equations are clarified by applying the Keller-Box method. Effects of several types of nanofluids and various specified parameters such as solid volume fraction, magnetic parameter, Brinkmann number and local Biot number on velocity and temperature fields have been plotted graphically, while values of surface shear stress and surface heat flux are presented via table. Further, comparison of obtained computational values has been made with earlier published results for non-magnetic case.

A novel hybridity model for TiO2-CuO/water hybrid nanofluid flow over a static/moving wedge or corner

In this study, we are going to investigate semi-analytically the steady laminar incompressible two-dimensional boundary layer flow of a TiO2-CuO/water hybrid nanofluid over a static/moving wedge or corner that is called Falkner-Skan problem. A novel mass-based approach to one-phase hybrid nanofluid model that suggests both first and second nanoparticles as well as base fluid masses as the vital inputs to obtain the effective thermophysical properties of our hybrid nanofluid, has been presented. Other governing parameters are moving wedge/corner parameter (λ), Falkner-Skan power law parameter (m), shape factor parameter (n) and Prandtl number (Pr). The governing partial differential equations become dimensionless with help of similarity transformation method, so that we can solve them numerically using bvp4c built-in function by MATLAB. It is worthwhile to notice that, validation results exhibit an excellent agreement with already existing reports. Besides, it is shown that both hydrodynamic and thermal boundary layer thicknesses decrease with the second nanoparticle mass as well as Falkner-Skan power law parameter. Further, we understand our hybrid nanofluid has better thermal performance relative to its mono-nanofluid and base fluid, respectively. Moreover, a comparison between various values of nanoparticle shape factor and their effect on local heat transfer rate is presented. It is proven that the platelet shape of both particles (n1 = n2 = 5.7) leads to higher local Nusselt number in comparison with other shapes including sphere, brick and cylinder. Consequently, this algorithm can be applied to analyze the thermal performance of hybrid nanofluids in other different researches.

Thermal energy statistics for Jeffery fluid flow regime: A generalized Fourier’s law outcomes

This paper is about Jeffery fluid with thermal stratification effects at a stagnation point. The thermal energy and heat transfer is studied through Cattaneo–Christov heat flux model. The flow is induced by the stretching cylinder. The homogeneous–heterogeneous chemically reactive species are taken into account. The homogeneous reaction is provided by isothermal cubic autocatalytic kinetics and the heterogeneous reaction by first order kinetics. The steady state boundary layer flow is discussed in case when both reactants and auto-catalyst have equal diffusion coefficients. The concerned mathematical problem is developed by laws of conservation of mass, momentum and energy which provides a coupled partial differential equations. The order of these equations is reduced through similarity transformation. Later on, the set of reduced coupled equations are sorted out numerically by means of Runge–Kutta Fehlberg technique with shooting algorithm. The fluid velocity is decreasing at Deborah number. The influence of thermal relaxation parameter and thermal stratification parameter on fluid temperature trend is decreasing. The numerical values for skin friction coefficient is examined and found excellent match with existing literature.

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.

MHD Flow and Heat Transfer of SiC-TiO2/DO Hybrid Nanofluid due to a Permeable Spinning Disk by a Novel Algorithm

This study intends to semi-analytically investigate the steady 3D boundary layer flow of a SiC-TiO2/DO hybrid nanofluid over a porous spinning disk subject to a constant vertical magnetic field. Here, the novel attitude to single-phase hybrid nanofluid model corresponds to considering nanoparticles and base fluid masses to compute solid equivalent volume fraction, solid equivalent density, and also solid equivalent specific heat at constant pressure. The basic PDEs are transformed into dimensionless ODEs using Von Karman similarity transformations, which are then solved numerically using bvp4c function. Results indicate that mass suction and magnetic field effects diminish all hydrodynamic and thermal boundary layer thicknesses. Finally, a significant report is presented to investigate quantities of engineering interest due to governing parameters’ effects.

Steady incompressible magnetohydrodynamics Casson boundary layer flow past a permeable vertical and exponentially shrinking sheet: A stability analysis

AbstractSteady incompressible magnetohydrodynamic mixed convection boundary layer flow of a Casson fluid on an exponentially vertical shrinking sheet using the non‐Newtonian heating equation is investigated in this paper. There are three main objectives of this study, namely, to develop a new mathematical model, to obtain multiple solutions, and to perform stability analysis. The governing partial differential equations have been changed into nonlinear ordinary differential equations. The resultant equations of boundary value problems are then converted into the equivalent initial value problems using the shooting method before they can be solved using Runge‐Kutta of order four. The numerical results are obtained and found to be in good agreement with the published literature. The results also indicate that the velocity boundary layer becomes thinner as the magnetic, slip, and Casson parameters increase. Dual solutions for temperature and velocity distributions are obtained. Furthermore, the results suggest that the presence of the force of buoyancy (opposing flow case) would cause the occurrence of dual solutions. However, based on the stability analysis, only the first solution is stable.

Soret- Dufour Effect on Mixed Convection Past a Vertical Plate in Non-Darcy Porous Medium Saturated With Buongiorno Nanofluid in the Presence of Thermal Dispersion

ABSTRACTNumerical analysis was investigated for steady two-dimensional double diffusive mixed convection boundary layer flow over a semi-infinite vertical plate embedded non-Darcy porous medium filled with nanofluid, in presence of thermal dispersion and under convective boundary conditions. The Buongiorno nanofluid model is used, while the porous medium is described by the Darcy-Forchheimer extension. The governing partial differential equations are transformed into four coupled nonlinear ordinary differential equations using an appropriate similarity transformations and the resulting system of equations is then solved numerically by the finite-difference method. Numerical results are presented to illustrate how the physical parameters affect the flow field, temperature, concentration and solid volume fraction profiles. In addition, the variation of heat, mass and nanoparticle transfer rates at the plate are exhibited graphically for different values of pertinent parameters.

Numerical thermal study on CNTs/ C2H6O2– H2O hybrid base nanofluid upon a porous stretching cylinder under impact of magnetic source

In this essay, the physical aspects of the steady laminar boundary layer flow of CNTs/(C2H6O2–H2O) hybrid base nanofluid over a porous stretching cylinder under impact of magnetic force has been explored using 4th order Runge-kutta (RKF 4) numerical method. The impact of changeable, various parameters like: Reynolds number (Re), CNTs volume fraction (ϕ), Squeeze number (S), and Magnetic parameter (M) on the thermal and flow boundary layers are exemplified quantitatively through figures. As well as, impacts of various nanoparticles are analyzed on the velocity/temperature profiles and Nusselt number. Outputs illustrate that: the parameters S, M and Re have a negative and decreasing effect on skin friction coefficient and Nusselt number, therefore have reduced surface drag force and heat transfer rate. As well as, the choice of types of nanoparticles has a significant impact on the stream function and the cooling/heating processes.

The influence of MHD and heat generation/absorption in a Newtonian flow field manifested with a Cattaneo–Christov heat flux model

The purpose of this report is to emphasize magnetohydrodnamics, heat generation/absorption and slip effects over a Newtonian fluid flow with homogeneous–heterogeneous chemical reactions induced by the rotating disk. The homogeneous reaction is provided by isothermal cubic autocatalytic kinetics and the heterogeneous reaction by first order kinetics. The concerned steady state boundary layer flow is discussed in the case when both reactants and auto-catalyst have equal diffusion coefficients. The Cattaneo–Christov approach is proposed to derive the energy equation and heat transfer phenomena. The consequential partial differential equations descend to ordinary differential equations by using similarity transformation. Further, these equations are sorted numerically using the Runge–Kutta–Fehlberg technique with a shooting scheme. The influences of arising parameters on fluid velocity, temperature and concentration are observed through graphs. Further, the numerical results for the skin friction coefficient and local Nusselt number are examined and compared with existing literature.

Numerical analysis for steady boundary layer flow of Maxwell fluid over a stretching surface embedded in a porous medium with viscous dissipation using the spectral relaxation method

In the current paper, a theoretical analysis is laid out to explore the features of flow, heat and mass transfer characteristics of Maxwell fluid over a stretching sheet, which can be embedded in a porous medium with viscous dissipation. To get the numerical solution a powerful numerical technique, spectral relaxation method, is applied for the set of transformed equations derived from the physical model of the flow. Thereafter, numerical outcomes are computed to discuss the convergence and accuracy of the proposed technique. The impacts of different flow controlling parameters, which are experienced in the problem, are resolved. All the obtained outcomes from the above numerical procedure are displayed through graphs and tables to discuss various resulting parameters. The main notable observations are an increment in surface shear stress and decrement in heat and mass transfer rates for the increase in the strength of the porous medium.

Numerical Analysis of Boundary Layer Flow Adjacent to a Thin Needle in Nanofluid with the Presence of Heat Source and Chemical Reaction

The steady boundary layer flow of a nanofluid past a thin needle under the influences of heat generation and chemical reaction is analyzed in the present work. The mathematical model has been formulated by using Buongiornos’s nanofluid model which incorporates the effect of the Brownian motion and thermophoretic diffusion. The governing coupled partial differential equations are transformed into a set of nonlinear ordinary differential equations by using appropriate similarity transformations. These equations are then computed numerically through MATLAB software using the implemented package called bvp4c. The influences of various parameters such as Brownian motion, thermophoresis, velocity ratio, needle thickness, heat generation and chemical reaction parameters on the flow, heat and mass characteristics are investigated. The physical characteristics which include the skin friction, heat and mass transfers, velocity, temperature and concentration are further elaborated with the variation of governing parameters and presented through graphs. It is observed that the multiple (dual) solutions are likely to exist when the needle moves against the direction of the fluid flow. It is also noticed that the reduction in needle thickness contributes to the enlargement of the region of the dual solutions. The determination of the stable solution has been done using a stability analysis. The results indicate that the upper branch solutions are linearly stable, while the lower branch solutions are linearly unstable. The study also revealed that the rate of heat transfer is a decreasing function of heat generation parameter, while the rate of mass transfer is an increasing function of heat generation and chemical reaction parameters.

An innovative mass-based model of aqueous zinc oxide–gold hybrid nanofluid for von Kármán’s swirling flow

In this research, we have investigated analytically the incompressible laminar steady three-dimensional boundary layer flow of an aqueous ZnO–Au hybrid nanofluid over an impermeable rotating disk with the constant radial stretching rate. The novel attitude to single-phase hybrid nanofluid model corresponds to considering nanoparticles mass as well as base fluid mass to computing the solid equivalent volume fraction, the solid equivalent density and also the solid equivalent specific heat at constant pressure. Here, other governing parameters are stretching strength parameter \((C)\), shape factor parameter \((n)\) and Prandtl number \((Pr).\) The basic nonlinear governing PDEs are transformed into a set of dimensionless nonlinear ODEs using well-known von Karman similarity transformations, which are then solved numerically using a finite difference code from MATLAB. It is worth mentioning that validation results demonstrate a good agreement with previously published reports. Results indicate that with the increase in stretching strength parameter and second nanoparticle’s mass, both dimensionless temperature distribution and thermal boundary layer thickness decrease. Moreover, when 15 g of both first and second nanoparticles is dispersed into 100 g pure water (equivalent with \(\phi = 3.33\)% as the total nanoparticles volume fraction), the heat transfer rate increases more than 40% in comparison with the regular fluid. Besides, the results demonstrate that the heat transfer rate enhances about 2.18% with nanoparticles of platelet shape \((n_{1} = n_{2} = 5.7)\) instead of spherical ones. Finally, the present new algorithm sufficiently can be used for analysis flow and heat transfer characteristics of hybrid nanofluids in various problems with great confidence.

Melting Heat Transfer and MHD Boundary Layer Flow of Eyring-Powell Nanofluid Over a Nonlinear Stretching Sheet with Slip

The steady laminar incompressible viscous magneto hydrodynamic boundary layer flow of an Eyring- Powell fluid over a nonlinear stretching flat surface in a nanofluid with slip condition and heat transfer through melting effect has been investigated numerically. The resulting nonlinear governing partial differential equations with associated boundary conditions of the problem have been formulated and transformed into a non-similar form. The resultant equations are then solved numerically using the Runge-Kutta fourth order method along with the shooting technique. The physical significance of different parameters on the velocity, temperature and nanoparticle volume fraction profiles is discussed through graphical illustrations. The impact of physical parameters on the local skin friction coefficient and rate of heat transfer is shown in tabulated form.

Analytical Solution to the Boundary Layer Slip Flow and Heat Transfer over a Flat Plate using the Switching Differential Transform Method

In this paper, the two-dimensional steady boundary layer flow and heat transfer over a flat plate with slip velocity and temperature jump conditions at the walls were analyzed. Using similarity transforms, the governing equations were reduced to a system of ordinary differential equations. Semi-analytical solutions to the resulting boundary value problem were obtained using the differential transform method (DTM). In order to cover the asymptotic boundary conditions, a method of switching curves was proposed. In this switching approach, the traditional solution to the DTM, which is valid for finite horizons, was followed by another path that was also an analytical solution to the problem. The main preference of the resulting closed form solution with respect to numerical solution is the possibility of parametric studies. The method was verified using some available numerical data, and the results showed that our proposed method had reasonable efficiency and accuracy.

Chemical reaction effect of an axisymmetric flow over radially stretched sheet

A steady boundary layer flow over a porous flat plate has been considered in the present study. Mass transfer analysis with first order chemical reaction is also considered instead of heat transfer. The plate concentration is considered in the form of power law instead of taking constant. The governing PDEs are transformed into ordinary differential equations using similarity transformation and then these ODEs are solved by employing Runge-Kutta fourth order method associated with shooting technique. A parametric study of all involving parameters is obtained by the help of graphs. The major findings are: (i) the concentration of the fluid in its boundary layer decrease with increase in heavier species, the reaction rate parameter and the power law exponent; (ii) the rate of mass transfer increases with an increase in reaction rate parameter and power-law exponent.

A Study on Non-Newtonian Transport Phenomena in Mhd Fluid Flow From a Vertical Cone With Navier Slip and Convective Heating

Abstract In the current study is to examine numerically the effects of presence of a radial magnetic field, slip and jump conditions on the steady two-dimensional free convective boundary layer flow over an external surface of a vertical cone for an electro-conductive polymer. A proper non-similarity transformation simplifies the system of partial differential equations into a system of ordinary differential equations. The collocation formula in the MATLAB software then solves the system of non-similarity equations. The finding results show that, a weak elevation in temperature is accompanied with the increase in the Carreau fluid parameter, whereas a significant acceleration in the flow is computed near the cone surface. The study is relevant to smart coating transport phenomena.

Analysis of mixed convection in water boundary layer flows over a moving vertical plate with variable viscosity and Prandtl number

PurposeThe purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.Design/methodology/approachThe nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.FindingsThe effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.Originality/valueThe present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.