Partial Differential Equations of Boundary Layer of Conventional Fluid’s Natural Convection

2018 ◽  
pp. 33-43
Author(s):  
De-Yi Shang ◽  
Liang-Cai Zhong
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential

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.

scholarly journals On the Multidomain Bivariate Spectral Local Linearisation Method for Solving Systems of Nonsimilar Boundary Layer Partial Differential Equations

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Vusi Mpendulo Magagula
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Large Time ◽  
Nonlinear Partial Differential Equations ◽  
Computation Time ◽  
General System ◽  
Partial Differential ◽  
Boundary Layer Equations ◽  
Grid Points

In this work, a novel approach for solving systems of nonsimilar boundary layer equations over a large time domain is presented. The method is a multidomain bivariate spectral local linearisation method (MD-BSLLM), Legendre-Gauss-Lobatto grid points, a local linearisation technique, and the spectral collocation method to approximate functions defined as bivariate Lagrange interpolation. The method is developed for a general system of n nonlinear partial differential equations. The use of the MD-BSLLM is demonstrated by solving a system of nonlinear partial differential equations that describe a class of nonsimilar boundary layer equations. Numerical experiments are conducted to show applicability and accuracy of the method. Grid independence tests establish the accuracy, convergence, and validity of the method. The solution for the limiting case is used to validate the accuracy of the MD-BSLLM. The proposed numerical method performs better than some existing numerical methods for solving a class of nonsimilar boundary layer equations over large time domains since it converges faster and uses few grid points to achieve accurate results. The proposed method uses minimal computation time and its accuracy does not deteriorate with an increase in time.

Solution methodology of convection boundary layer problems using Adomian decomposition method

2012 ◽  
Vol 227 (7) ◽  
pp. 1554-1565
Author(s):  
MJ Javanmardi ◽  
K Jafarpur ◽  
M Mahzoon
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Convection Boundary Layer ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Convection Boundary ◽  
Boundary Layer Problems

Adomian decomposition method has been applied to some convection boundary layer problems. It is shown that the method is excellent in solving nonlinear partial differential equations. Comparison of the results so obtained and those from conventional methods proves the technique to be powerful and to give nearly exact solutions. Since most physical problems are governed by nonlinear ordinary or partial differential equations, application of this method may be advised to simplify the method of solution.

scholarly journals Effects of Joule Heating and Viscous Dissipation on Magnetohydrodynamic Boundary Layer Flow of Jeffrey Nanofluid over a Vertically Stretching Cylinder

Coatings ◽  
2021 ◽  
Vol 11 (3) ◽  
pp. 353
Author(s):  
Haroon Ur Rasheed ◽  
Abdou AL-Zubaidi ◽  
Saeed Islam ◽  
Salman Saleem ◽  
Zeeshan Khan ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Formulation ◽  
Skin Friction Coefficient ◽  
Deborah Number ◽  
Radiation Absorption ◽  
Partial Differential ◽  
System Parameters ◽  
Jeffrey Nanofluid

This article investigates unsteady magnetohydrodynamic (MHD) mixed convective and thermally radiative Jeffrey nanofluid flow in view of a vertical stretchable cylinder with radiation absorption and heat; the reservoir was addressed. The mathematical formulation of Jeffrey nanofluid is established based on the theory of boundary layer approximations pioneered by Prandtl. The governing model expressions in partial differential equations (PDEs) form was transformed into dimensionless form via similarity transformation technique. The set of nonlinear nondimensional partial differential equations are solved with the help of the homotopic analysis method. For the purpose of accuracy, the optimizing system parameters, convergence, and stability analysis of the analytical algorithm (CSA) were performed graphically. The velocity, temperature, and concentration flow are studied and shown graphically with the effect of system parameters such as Grashof number, Hartman number, Prandtl number, thermal radiation, Schmidt number, Eckert number, Deborah number, Brownian parameter, heat source parameter, thermophoresis parameter, and stretching parameter. Moreover, the consequence of system parameters on skin friction coefficient, Nusselt number, and Sherwood number is also examined graphically and discussed.

Numerical simulation of a phase transition problem with natural convection using hybrid FEM/EFGM technique

2015 ◽  
Vol 25 (3) ◽  
pp. 570-592 ◽  
Author(s):  
Sonam Singh ◽  
Rama Bhargava
Keyword(s):  
Phase Transition ◽  
Natural Convection ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Physical Problem ◽  
Computational Time ◽  
Partial Differential ◽  
Content Type ◽  
Transition Problem ◽  
Phase Transition Problem

Purpose – The purpose of this paper is to study the flow and heat transfer characteristics of a phase transition, melting problem. In this problem, phase transition between solid and liquid takes place within a square enclosure in the presence of natural convection. Design/methodology/approach – The physical problem, described with non-linear partial differential equations, is simulated using a hybrid finite element and element free Galerkin method (FEM/EFGM) approach. In energy conservation equation, the fixed-domain, effective heat capacity method is used to take into account the latent heat of phase change. The governing partial differential equations are solved with a meshfree, EFGM near the phase transition front while in the region away from the front with uniform nodal distribution; problem is simulated with traditional FEM. Findings – A sensitivity analysis of characteristic dimensionless numbers Rayleigh number (Ra), Prandtl number (Pr), Stefan number (ste) is presented in order to investigate their impact on thermal and flow fields. Typically computational times of EFGM are higher than that of FEM. Therefore, by using EFGM only in that portion of physical problem where phase transition occurs, the hybrid FEM/EFGM strategy employed in present paper could reduce the computational time of EFGM while still retaining its accuracy. Also, the consistent performance of the results obtained with this hybrid approach is validated with those already available in literature for some special cases. Originality/value – The hybrid methodology adopted in this paper, is quite new for solving such type of phase transition problem.

scholarly journals Heat transfer analysis in the time-dependent axisymmetric stagnation point flow over a lubricated surface

2018 ◽  
Vol 22 (6 Part A) ◽  
pp. 2483-2492 ◽  
Author(s):  
Khalid Mahmood ◽  
Muhammad Sajid ◽  
Nasir Ali ◽  
Tariq Javed
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Time Dependent ◽  
Surface Shear Stress ◽  
Partial Differential ◽  
Surface Shear ◽  
Flow And Heat Transfer

In this paper time-dependent, 2-D, axisymmetric flow and heat transfer of a viscous incompressible fluid impinging orthogonally on a disc is examined. The disc is lubricated with a thin layer of power-law fluid of variable thickness. It is assumed that surface temperature of the disc is time-dependent. Continuity of velocity and shear stress at the interface layer between the fluid and the lubricant has been imposed to obtain the solution of the governing partial differential equations. The set of partial differential equations is reduced into ordinary differential equations by suitable transformations and are solved numerically by using Keller-Box method. Solutions are presented in the form of graphs and tables in order to examine the influence of pertinent parameters on the flow and heat transfer characteristics. An increase in lubrication results in the reduction of surface shear stress and consequently viscous boundary layer becomes thin. However, the thermal boundary layer thickness increases by increasing lubrication. It is further observed that surface shear stress and heat transfer rate at the wall enhance due to unsteadiness. The results for the steady case are deduced from the present solutions and are found in good agreement with the existing results in the literature.

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