scholarly journals On the Study of Viscoelastic Walters' B Fluid in Boundary Layer Flows

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Seyed Ali Madani Tonekaboni ◽  
Ramin Abkar ◽  
Reza Khoeilar
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Order Approximation ◽  
Nonlinear Differential Equations ◽  
Boundary Layer Flows ◽  
Sakiadis Flow ◽  
Stream Functions ◽  
Layer Flow ◽  
Walter’S B Fluid ◽  
Walters B Fluid

Viscoelastic Walters' B fluid flows for three problems, stagnation-point flow, Blasius flow, and Sakiadis flow, have been investigated. In each problem, Cauchy equations are changed to a nondimensional differential equations using stream functions and with assumption of boundary layer flow. The fourth-order predictor-corrector finite-difference method for solving these nonlinear differential equations has been employed. The results that have been obtained using this method are compared with the results of the last studies, and it is clarified that this method is more accurate. It is also shown that the results of last study about Sakiadis flow of Walter's B fluid are not true. In addition, the effects of order of discretization in the boundaries are investigated. Moreover, it has been discussed about the valid region of Weissenberg numbers for the second-order approximation of viscoelastic fluids in each case of study.

Comparison of Numerical Methods for Nano Boundary Layer Flow

2011 ◽  
Vol 66 (8-9) ◽  
pp. 539-542
Author(s):  
Nader Y. Abd Elazem ◽  
Abdelhalim Ebaid
Keyword(s):  
Boundary Layer ◽  
Numerical Methods ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Nonlinear Differential Equations ◽  
The Other ◽  
Chebyshev Collocation ◽  
Collocation Scheme ◽  
Layer Flow

Abstract The nonlinear differential equations describing the nano boundary layer flow is investigated in this paper utilizing Chebyshev collocation scheme. The results obtained in this research are compared with those obtained by the other published works.

scholarly journals Similarity Requirements for Mixed Convective Boundary Layer Flow over Vertical Curvilinear Porous Surfaces with Heat Generation/Absorption

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Kh. Abdul Maleque
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Three Dimensional ◽  
Heat Absorption ◽  
Boundary Layer Flows ◽  
Convective Boundary ◽  
Layer Flow ◽  
Surface Similarity ◽  
Lamé Coefficients ◽  
Flow Study

Similarity requirements for three dimensional combined forced and free convective laminar boundary layer flows over the porous inclined vertical curvilinear surfaces with buoyancy effects and heat absorption/generation effects are investigated theoretically. The potential flow in the mainstream and Gabriel lame coefficients outside of the boundary layer are the function of ξ,η. Hence, the external velocity components (Ue, Ve) and Gabriel lame coefficients h1,h2,h3 are independent of ζ. Here, h3ξ,η=1 has been set such that ζ represents actual distance measured normal to the surface. Similarity requirements for an incompressible fluid are sought on the basis of detailed analyses in order to reduce the governing partial differential equations into a set of ordinary differential equations. Finally, different possible cases are exhibited in a tabular form with the inclusion of ΔT variations for onward flow study that are helpful to the future researchers for the flow over the orthogonal curvilinear surfaces.

Boundary-Layer Flow of Walters’ B Fluid with Newtonian Heating

2015 ◽  
Vol 70 (5) ◽  
pp. 333-341 ◽  
Author(s):  
Tasawar Hayat ◽  
Anum Shafiq ◽  
Meraj Mustafa ◽  
Ahmed Alsaedi
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Newtonian Heating ◽  
Stretching Surface ◽  
Dimensionless Velocity ◽  
Layer Flow ◽  
Wall Mass ◽  
Walters B Fluid

AbstractThis work studies the flow of Walters-B fluid over a stretching surface with Newtonian heating. The governing partial differential equations are first simplified through boundary layer approximations and then reduced into ordinary differential equations by using the appropriate substitutions. The resulting problems have been solved for the series solutions by a homotopic approach. Convergence analysis is performed and appropriate values are determined by plotting the so-called ℏ-curves. Graphical results for the dimensionless velocity and temperature are presented and discussed for various physical parameters. In addition, the expressions of skin friction coefficient and the local Nusselt number are presented. The dimensionless expressions of wall shear stress and wall mass flux are analysed graphically and numerically.

Analysis of Carreau fluid flow by convectively heated disk with viscous dissipation effects

2020 ◽  
Vol 75 (10) ◽  
pp. 825-832 ◽  
Author(s):  
Rabia Malik ◽  
Hina Sadaf ◽  
Fiza Dastar
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Nonlinear Differential Equations ◽  
Two Dimensional ◽  
Tabular Form ◽  
Carreau Fluid ◽  
Heated Disk ◽  
Layer Flow ◽  
Nonlinear Velocity

AbstractThe primary motive of this study is to examine boundary layer flow of Carreau fluid over a convectively heated disk stretching with nonlinear velocity. The flow is assumed to be two dimensional. Moreover, viscous dissipation possessions are taken into description. The dominating nonlinear differential equations involving partial derivatives are changed into nonlinear differential equations involving ordinary derivatives by applying suitable transformations. Numerical outcomes for velocity and temperature are obtained from MATLAB’s built-in solver bvp4c and presented graphically and in tabular form.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

2013 ◽  
Vol 29 (3) ◽  
pp. 559-568 ◽  
Author(s):  
G. C. Shit ◽  
R. Haldar ◽  
A. Sinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Layer Flow

AbstractA non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

scholarly journals Solving the Nonlinear Boundary Layer Flow Equations with Pressure Gradient and Radiation

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 710
Author(s):  
Michalis A. Xenos ◽  
Eugenia N. Petropoulou ◽  
Anastasios Siokis ◽  
U. S. Mahabaleshwar
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Pressure Gradient ◽  
Boundary Layer Flow ◽  
Mathematical Formulation ◽  
Dimensionless Temperature ◽  
Partial Differential ◽  
Analytical Results ◽  
Layer Flow

The physical problem under consideration is the boundary layer problem of an incompressible, laminar flow, taking place over a flat plate in the presence of a pressure gradient and radiation. For the mathematical formulation of the problem, the partial differential equations of continuity, energy, and momentum are taken into consideration with the boundary layer simplifications. Using the dimensionless Falkner–Skan transformation, a nonlinear, nonhomogeneous, coupled system of partial differential equations (PDEs) is obtained, which is solved via the homotopy analysis method. The obtained analytical solution describes radiation and pressure gradient effects on the boundary layer flow. These analytical results reveal that the adverse or favorable pressure gradient influences the dimensionless velocity and the dimensionless temperature of the boundary layer. An adverse pressure gradient causes significant changes on the dimensionless wall shear parameter and the dimensionless wall heat-transfer parameter. Thermal radiation influences the thermal boundary layer. The analytical results are in very good agreement with the corresponding numerical ones obtained using a modification of the Keller’s-box method.

A Theory for Fine Particle Deposition in Two-Dimensional Boundary Layer Flows and Application to Gas Turbines

1982 ◽  
Vol 104 (1) ◽  
pp. 69-76 ◽  
Author(s):  
M. Mengu¨turk ◽  
E. F. Sverdrup
Keyword(s):  
Boundary Layer ◽  
Gas Turbines ◽  
Particle Deposition ◽  
Fine Particles ◽  
Magnitude Estimate ◽  
Two Dimensional ◽  
Boundary Layer Flows ◽  
Order Of Magnitude ◽  
Dimensional Boundary ◽  
Layer Flow

A theory is presented to predict deposition rates of fine particles in two-dimensional compressible boundary layer flows. The mathematical model developed accounts for diffusion due to both molecular and turbulent fluctuations in the boundary layer flow. Particle inertia is taken into account in establishing the condition on particle flux near the surface. Gravitational settling and thermophoresis are not considered. The model assumes that the fraction of particles sticking upon arrival at the surface is known, and thus, treats it as a given parameter. The theory is compared with a number of pipe and cascade experiments, and a reasonable agreement is obtained. A detailed application of the model to a turbine is also presented. Various regimes of particle transport are identified, and the range of validity of the model is discussed. An order of magnitude estimate is obtained for the time the turbine stage can be operated without requiring cleaning.

Mixed Convection Boundary Layer Flow Near the Lower Stagnation Point of a Cylinder Embedded in a Porous Medium Using a Thermal Nonequilibrium Model

2016 ◽  
Vol 138 (8) ◽  
Author(s):  
Haliza Rosali ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Boundary Layer Flow ◽  
Thermal Conductivity Ratio ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Layer Flow

The present paper analyzes the problem of two-dimensional mixed convection boundary layer flow near the lower stagnation point of a cylinder embedded in a porous medium. It is assumed that the Darcy's law holds and that the solid and fluid phases of the medium are not in thermal equilibrium. Using an appropriate similarity transformation, the governing system of partial differential equations are transformed into a system of ordinary differential equations, before being solved numerically by a finite-difference method. We investigate the dependence of the Nusselt number on the solid–fluid parameters, thermal conductivity ratio and the mixed convection parameter. The results indicate that dual solutions exist for buoyancy opposing flow, while for the assisting flow, the solution is unique.

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