Wall Thickness Parameter Research Articles

Unsteady Magnetohydrodynamic Stagnation Point Flow of a Nanofluid over a Slendering Stretching Sheet Using Buongiorno’s Model

This paper aimed to model and analyze the unsteady hydromagnetic boundary layer stagnation point nanofluid flow over a non-linear stretching surface through porous medium with variable wall thickness. The effects of radiation, dissipation, and slip velocity are taken into account. The formulation of the problem is made through Buongiorno’s model, which involves the aspects of thermophoresis and Brownian motion. The set of governing non-linear Ordinary Differential Equations (ODE’s) are solved numerically by using boundary value problem default solver in MATLAB bvp4c package. The impact of different flow quantities on fluid velocity, temperature, and nanoparticle concentration are analyzed and examined through graphs. The physical parameters like friction factor coefficient , rates of heat transfer , and nanoparticle friction are derived and presented through tables. It is found that the wall thickness parameter depreciates the nanofluid velocity for and accelerates when . Also, the unsteadiness parameter shows a significant effect on the stagnation point flow.

Impacts of variable thermal conductivity on stagnation point boundary layer flow past a Riga plate with variable thickness using generalized Fourier’s law

Abstract This article explores the problem of two-dimensional, laminar, steady and boundary layer stagnation point slip flow over a Riga plate. The incompressible upper-convected Maxwell fluid has been considered as a rheological fluid model. The heat transfer characteristics are investigated with generalized Fourier’s law. The fluid thermal conductivity is assumed to be temperature dependent in this study. A system of partial differential equations governing the flow of an upper-convected Maxwell fluid, heat and mass transfer using generalized Fourier’s law is developed. The main objective of the article is to inspect the impacts of pertinent physical parameters such as the stretching ratio parameter ( 0 ⩽ A ⩽ 0.3 ) , Deborah number ( 0 ⩽ β ⩽ 0.6 ) , thermal relaxation parameter ( 0 ⩽ γ ⩽ 0.5 ) , wall thickness parameter ( 0.1 ⩽ α ⩽ 3.5 ) , slip parameter ( 0 ⩽ R ⩽ 1.5 ) , thermal conductivity parameter ( 0.1 ⩽ δ ⩽ 1.0 ) and modified Hartmann number ( 0 ⩽ Q ⩽ 3 ) on the velocity and temperature profiles. Suitable local similarity transformations have been used to get a system of non-linear ODEs from the governing PDEs. The numerical solutions for the dimensionless velocity and temperature distributions have been achieved by employing an effective numerical method called the shooting method. It is seen that the velocity profile shows the reduction in the velocity for the higher values of viscoelastic parameter and the thermal relaxation parameter. In addition, to enhance the reliability at the maximum level of the obtained numerical results by shooting method, a MATLAB built-in solver bvp4c has also been utilized.

Study of an MHD Flow of the Carreau Fluid Flow Over a Stretching Sheet with a Variable Thickness by Using an Implicit Finite Difference Scheme

The present analysis deals with a two-dimensional MHD flow of the Carreau fluid over a stretching sheet with a variable thickness. The governing partial differential equations are converted into an ordinary differential equation by using the similarity approach. The solution of the differential equation is calculated by using the Keller box method. The solution is studied for different values of the Hartmann number, Weissenberg number, wall thickness parameter, and power-law index. The skin friction coefficient is calculated. The present results are compared with available relevant data.

MHD mixed convection heat transfer over a non-linear slender elastic sheet with variable fluid properties

Abstract An analysis is presented for mixed convection and heat transfer in a viscous electrically conducting fluid flow at an impermeable stretching vertical sheet with variable thickness. The nonlinear equations that describe the fluid flow, and heat transfer processes have been solved using the Keller-box method. A limited parametric study is undertaken to determine the sensitivity and changes in the flow and temperature fields with respect to variations in the buoyancy parameter, the temperature dependent viscosity and thermal conductivity parameters, the plate velocity power index, and the Prandtl number which are presented in graphical and tabulated formats. To validate the results, comparisons are made with the available results in the literature for some special cases and the results are found to be in good agreement. The effects of embedded parameters on the dimensionless velocity profiles and temperature are examined through graphs. The variation of Local Nusselt number is also analysed. One of the important findings of our study is that the velocity distribution at a point near the plate decreases as the wall thickness parameter increases and hence the thickness of the boundary layer becomes thinner when m < 1. Further, the effect of the magnetic field is to reduce the fluid velocity and to increase the temperature field.

MHD Carreau fluid slip flow over a porous stretching sheet with viscous dissipation and variable thermal conductivity

The aim of this article is to investigate MHD Carreau fluid slip flow with viscous dissipation and heat transfer by taking the effect of thermal radiation over a stretching sheet embedded in a porous medium with variable thickness and variable thermal conductivity. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The constitutive equations of Carreau fluid are modeled in the form of partial differential equations (PDEs). Concerning boundary conditions available, the PDEs are converted to ordinary differential equations (ODEs) by means of similarity transformation. The homotopy analysis method (HAM) is used for solution of the system of nonlinear problems. The effects of various parameters such as Weissenberg number mathit{We}^{2}, magnetic parameter M^{2}, power law index n, porosity parameter D, wall thickness parameter α, power index parameter m, slip parameter λ, thermal conductivity parameter ε, radiation parameter R and Prandtl number on velocity and temperature profiles are analyzed and studied graphically.

Melting heat transfer in the MHD flow of a third-grade fluid over a variable-thickness surface

The present study addresses the magnetohydrodynamic (MHD) flow of a third-grade fluid over a nonlinear stretched surface with variable thickness. The heat transfer phenomenon is discussed through melting. The system of nonlinear ordinary differential equations is attained by considering proper transformations. Convergent series solutions of velocity and temperature are developed. Fluid flow, temperature, skin friction coefficient and Nusselt number are examined through graphs for different parameters. It is noted that velocity and temperature decrease with decreasing the wall thickness parameter. It is also revealed that the temperature distribution enhances for increasing values of the Prandtl number. Here the velocity field reduces for increasing values of the melting parameter.

MHD stagnation point flow accounting variable thickness and slip conditions

This communication addresses the second-order velocity and thermal slip features in magnetohydrodynamic (MHD) stagnation point flow past a stretching sheet with variable thickness. Energy expression in presence of dissipation and thermal radiation are examined. A comparative study with first-order velocity and thermal slip condition is analyzed. Analytical solutions of the resulting systems are obtained by homotopy analysis method. Plots for important variables in the flow quantities are made and discussed. It is observed that velocity of fluid increases for higher estimation of velocity power index while it decreases for wall thickness parameter. Surface drag force and heat transfer rate are decreased for larger wall thickness and Prandtl number. Present computations are consistent with those of existing studies in limiting sense.

Magnetohydrodynamic (MHD) nonlinear convective flow of Walters-B nanofluid over a nonlinear stretching sheet with variable thickness

Mathematical analysis for magnetohydrodynamic (MHD) nonlinear convective flow of Walter-B nanofluid over a nonlinear stretching sheet with variable thickness is introduced. Heat transfer phenomenon is based through involvement of nonlinear thermal radiation and heat generation/absorption. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Boundary layer approximation is applied to partial differential equations. Governing equations are then converted into ordinary differential equations by invoking appropriate variables. The transformed expressions are explored through homotopic algorithm. Plots for velocity, temperature and concentration fields are presented and their behavior is deliberated for several sets of values of governing variables. Skin friction coefficient and local Nusselt number are inspected through numerical values. It is concluded that viscoelasticity reduces the velocity field while reverse situation is observed due to wall thickness parameter. Thermal field and heat transfer rate are enhanced for temperature ratio parameter. Moreover effect of Brownian motion and thermophoresis parameter are quite reverse for the concentration field.

Effect of homogeneous–heterogeneous reactions in stagnation point flow of third grade fluid past a variable thickness stretching sheet

Present work addresses the stagnation point flow of third grade fluid past a variable thicked stretching sheet. Homogeneous and heterogeneous reactions are considered. Impact of thermal radiation and variable wall temperature is studied here. System of nonlinear ordinary differential equations is obtained by suitable transformations. Convergence of series solutions is achieved. Fluid flow, temperature and concentration field are deliberated through graphs for different parameters. It is seen that velocity and temperature fields increase for higher shape parameter. Increasing values of homogeneous parameter decline the concentration profile. Velocity profile enhances when wall thickness parameter and ratio of free stream velocity and stretching velocity are increased.

Double Diffusive Flows over a Stretching Sheet of Variable Thickness with or without Surface Mass Transfer

AbstractThis paper presents a numerical investigation of the steady two‐dimensional mixed convection flow along a vertical semi‐infinite stretching sheet of variable thickness. The effect of double diffusion on velocity, thermal and concentration fields in presence of power‐law temperature and concentration distributions at wall along with surface mass transfer is considered. The nonlinear coupled partial differential equations governing the flow, thermal and concentration fields are first transformed into a nondimensional set of coupled nonlinear partial differential equations and solved numerically using an implicit finite‐difference scheme in combination with the Newton's linearization technique to obtain nonsimilar solutions at each stream‐wise location. Numerical results are presented to discuss the effects of various physical parameters on the velocity, temperature, and concentration fields. Furthermore, the numerical results for the local skin friction coefficient, local Nusselt number, and local Sherwood number are also reported. For a fixed buoyancy force, the skin friction coefficient and Nusselt number increase with Prandtl number. The increase in the Prandtl number causes about a 30% reduction in the thickness of the thermal boundary layer. The wall thickness parameter enhances the thickness of the momentum boundary layer and the velocity overshoot is observed up to 20% for wall thickness parameter . In contrast, the increase of power‐law index parameter m from to reduces approximately 10% to 25% the momentum and thermal boundary layer thicknesses depending on the values of other parameters

Numerical modeling of Carreau fluid due to variable thicked surface

Present analysis deals with the study of two dimensional MHD flow of Carreau fluid over a variable stretching sheet. The governing system partial differential equation (PDE) is reduced into ordinary differential equation (ODE) by using similarity approach. The solution of the differential equation is calculated by using a moderate and well-known numerical technique namely Keller box method. Intricate parameters, namely Hartmann number, Weissenberg number, wall thickness parameter and power law index are utilized to control the motion of fluid. Skin friction coefficient is calculated in order to examine the flow behavior near the surface of the sheet. A comparison has been made with the previous published work in order to check the accuracy of the technique. Conclusion is drawn on the basis of entire study and it is found that velocity profile reduces for large values of Hartmann number, wall thickness parameter and stretching index.

Heat generation and solar radiation effects on Carreau nanofluid over a stretching sheet with variable thickness: Using coefficients improved by Cash and Carp

Present work examines the effects of chemical reactive species and solar radiation on Carreau nanofluid induced by a stretching sheet with variable thickness. Heat generation effects are taken for exothermic reaction. In the boundary layer region, nanoparticles provides enhancement in the heat transfer phenomena. In the literature, most of the researchers used Runge Kutta Fehlberg method, but our main concentration here is to find the solution by improved form of Fehlberg method (Cash and Carp). The velocity, temperature and concentration profiles are plotted for different governing parameter, namely, wall thickness parameter, magnetic parameter, thermal conductivity parameter, chemical reaction parameter, Schmidt number and Prandtl number. It is found that the velocity profile increases by increasing Weissenberg numberWe, Hartmann number M and wall thickness parameter n. Moreover, temperature profile enhances by increasing heat generation parameter γ and radiative heat flux parameter R. The accuracy of the present method is checked with previously published work and excellent agreement is noticed.

Effects of Viscous Dissipation and Double Stratification on MHD Casson Fluid Flow over a Surface with Variable Thickness: Boundary Layer Analysis

In this article, the motion of two-dimensional Casson fluid flows with temperature dependent plastic dynamic viscosity together with double (i.e. thermal and solutal) stratification in the presence of Lorentz force is investigated. The case where the viscosity of the fluid tends to take energy away from the motion (kinetic energy) and transform it into internal energy is considered. The nonlinear governing equations and their associated boundary conditions are transformed and non-dimensionalized using similarity variables which are thereafter solved numerically using the shooting method together with the Runge-Kutta technique. The effects of the magnetic field parameter, temperature dependent viscosity parameter, Casson parameter, Eckert number, velocity power index, pressure gradient parameter and wall thickness parameter on the velocity, temperature, and concentration profiles are showed graphically and discussed. Substantial increase in temperature distribution is certain with an increase in the magnitude of Eckert number. Local skin friction coefficient decreases with an increase in pressure gradient parameter.

Computational analysis for velocity slip and diffusion species with carbon nanotubes

This article addresses a computational study for carbon nanotubes with diffusion species. Mathematical analysis and modeling are formulated in the presence of slip effect, Darcy porous medium and chemical species. Diffusion coefficients are accounted as equal amount. Optimal Homotopy Analysis Method (OHAM) is implemented in taking care for convergence control parameters. Residual errors and its graphs are plotted for CNTs nanofluids. The current data is compared with the previous published work. The results are found in favorable agreement. Physically interesting parameters are highlighted. The velocity is dominated for MWCNT than SWCNT. The velocity profile increases for power index when m>1 while opposite trend is observed for power index when m<1. Permeability parameter and volume fraction reduce the skin friction coefficient and reverse trend is noticed for slip parameter and wall thickness parameter. Opposite behavior is noticed for concentration profile at surface for homogenous-heterogeneous reactions parameters.

Domain Walls and Matter-Antimatter Domains in the Early Universe

We suggest a scenario of spontaneous (or dynamical) C and CP violation according to which it is possible to generate domains of matter and antimatter separated by cosmologically large distances. Such C ( CP ) violation existed only in the early universe and later it disappeared with the only trace of generated matter and antimatter domains. So this scenario does not suffer from the problem of domain walls. According to this scenario the width of the domain wall should grow exponentially to prevent annihilation at the domain boundaries. Though there is a classical result obtained by Basu and Vilenkin that the width of the wall tends to the one of the stationary solution (constant physical width). That is why we considered thick domain walls in a de Sitter universe following paper by Basu and Vilenkin. However, we were interested not only in stationary solutions found therein, but also investigated the general case of domain wall evolution with time. When the wall thickness parameter, δ 0 , is smaller than H−1/2 where H is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for δ0>H−1/2 We have calculated numerically the rate of the wall expansion in this case and have found that the width of the wall grows exponentially fast for δ0≫H−1 An explanation for the critical value δ0c=H−1/2 is also proposed.

On Cattaneo–Christov heat flux model for Carreau fluid flow over a slendering sheet

The underlying intentions of this article are to investigate the impact of non-Fourier heat flux model on the stagnation-point flow of non-Newtonian Carreau fluid. In this study, the innovative Cattaneo–Christov constitutive model is introduced to study the characteristics of thermal relaxation time. The flow is impelled by a slendering surface which is of the variable thickness. In the model, the physical mechanism responsible for homogeneous–heterogeneous reactions are further taken into account. Also, the diffusion coefficients of the reactant and auto catalyst are considered to be equal. The governing non-linear partial differential equations consisting of the momentum, energy and concentration equations are reduced to the coupled ordinary differential equations by means of local similarity transformations. The transformed ODEs are tackled numerically by employing an effective shooting algorithm along with the Runge–Kutta Fehlberg scheme. The physical characteristics of the fluid velocity, temperature and concentration profiles are illuminated with the variation of numerous governing factors and are presented graphically. For instance, our result indicates that the temperature and thermal boundary layer thickness are lower in case of Cattaneo–Christov heat flux model when compared to classical Fourier’s heat model. Meanwhile, the rate of heat transfer is significantly improved by a high wall thickness parameter and an opposite influence is found due to the thermal relaxation parameter. We further noticed that a higher value of homogeneous and heterogeneous reaction parameter corresponds to a deceleration in the concentration field and it shows an inverse relation for the Schmidt number. A correlation with accessible results for specific cases is found with fabulous consent.

MHD flow of Powell-Eyring nanofluid over a non-linear stretching sheet with variable thickness

This research explores the magnetohydrodynamic (MHD) boundary layer flow of Powell-Eyring nanofluid past a non-linear stretching sheet of variable thickness. An electrically conducting fluid is considered under the characteristics of magnetic field applied transverse to the sheet. The mathematical expressions are accomplished via boundary layer access, Brownian motion and thermophoresis phenomena. The flow analysis is subjected to a recently established conditions requiring zero nanoparticles mass flux. Adequate transformations are implemented for the reduction of partial differential systems to the ordinary differential systems. Series solutions for the governing nonlinear flow of momentum, temperature and nanoparticles concentration have been executed. Physical interpretation of numerous parameters is assigned by graphical illustrations and tabular values. Moreover the numerical data of drag coefficient and local heat transfer rate are executed and discussed. It is investigated that higher wall thickness parameter results in the reduction of velocity distribution. Effects of thermophoresis parameter on temperature and concentration profiles are qualitatively similar. Both the temperature and concentration profiles are enhanced for higher values of thermophoresis parameter.

Effects of Variable Fluid Properties on MHD Flow and Heat Transfer over a Stretching Sheet with Variable Thickness

AbstractThe influence of temperature-dependent fluid properties on flow and heat transfer of an electrically conducting fluid over a stretching sheet with variable thickness in the presence of a transverse magnetic field is analyzed. Using similarity transformations, the governing coupled non-linear partial differential equations (momentum and energy equations) are transformed into a system of coupled non-linear ordinary differential equations and are solved numerically by Keller-box method. For increasing values of the wall thickness parameter, the analysis reveals quite interesting flow and heat transfer patterns. The effects of the temperature dependent viscosity, the wall velocity power index, the thermal conductivity, the wall temperature parameter and the Prandtl number on the flow and temperature fields are presented. The obtained numerical results are compared with the available results in the literature for some special cases and are found to be in excellent agreement. The skin friction and the wall temperature gradient are presented for different values of the physical parameters and the salient features are analyzed.

Evolution of thick domain walls in de Sitter universe

We consider thick domain walls in a de Sitter universe following paper by Basu and Vilenkin. However, we are interested not only in stationary solutions found therein, but also investigate the general case of domain wall evolution with time. When the wall thickness parameter, δ0, is smaller than H−1/√2, where H is the Hubble parameter in de Sitter space-time, then the stationary solutions exist, and initial field configurations tend with time to the stationary ones. However, there are no stationary solutions for δ0 ⩾ H−1/√2. We have calculated numerically the rate of the wall expansion in this case and have found that the width of the wall grows exponentially fast for δ0 ≫ H−1. An explanation for the critical value δ0c = H−1/√2 is also proposed.

MHD 2D flow of Williamson nanofluid over a nonlinear variable thicked surface with melting heat transfer

This article aimed to model and analyze the effectiveness of magnetic nanoparticles and melting heat transfer in the stretched flow. Considered nonlinear nanofluid model consists of Brownian motion and thermophoresis mechanisms. Flow formulation is developed using rheological expressions of Williamson fluid. Thickness of nonlinear stretching surface is variable. Dimensional nonlinear systems are solved for the convergent series solutions. Impacts of various pertinent parameters on the non-dimensional velocity, temperature, concentration, skin friction, local Nusselt and Sherwood numbers are analyzed in detail. It is anticipated that impact of melting heat transfer parameter on velocity and temperature is opposite. Moreover it is also observed that magnetic parameter retards the flow. Larger wall thickness parameter reduces temperature and skin friction coefficient. However reverse behavior is noted for Nusselt number.