scholarly journals MODEL MATEMATIKA ALIRAN KONVEKSI BEBAS FLUIDA VISKOELASTIK YANG MELEWATI SILINDER ELIPTIK DENGAN PENGARUH MAGNETOHYDRODYNAMICS (MHD)

WAHANA ◽  
2018 ◽  
Vol 70 (1) ◽  
pp. 1-6
Author(s):  
Annisa Dwi Sulistyaningtyas
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Magnetic Force ◽  
Energy Equation ◽  
Elliptic Cylinder ◽  
Momentum Equation ◽  
Convection Flow ◽  
Free Convection Flow ◽  
The Mathematical Model ◽  
Fluid Characteristics

In fluid case, the mathematical model is the basic for translating a problem into a mathematical language using an equation or function. The governing equation is developed from continuity equation, momentum equation, and energy equation. Fluid characteristics are viscous and elastic result in boundary layer on the surface of elliptic cylinder. Dimensional equations are transformed into non-dimensional form and then classified into the similarity equations using boundary layer theory with influence of magnetic force. The results of this research is mathematical model of free convection flow in viscoelastic fluid passing through the elliptic cylinder with magnetohydrodinamics (MHD). For variation of magnetohydrodinamics (MHD) parameter, velocity and temperature increase when the parameter increases.

Asymptotic Model of Free Convection Flow on a Vertical Surface in Porous Media with Newtonian Heating

2015 ◽  
Vol 756 ◽  
pp. 469-475
Author(s):  
Anna A. Bocharova ◽  
Irina V. Plaksina ◽  
Andrey A. Obushnyy
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Free Convection ◽  
Vertical Surface ◽  
Momentum Equation ◽  
Convection Flow ◽  
Asymptotic Model ◽  
Free Convection Flow ◽  
Energy Equations ◽  
The Mathematical Model

The mathematical model based on system of momentum and energy equations for free convection flow along a vertical surface in porous media under boundary conditions of the third sort is solved analytically using the method of matched asymptotic expansions. The region of validity for boundary layer model and expansions for stream function and temperature with parameter of perturbations were defined. The dependence of characteristic flow from governing dimensionless parameters and was analyzed numerically. The influence of viscous and convective terms of momentum equation in the proposed mathematical model significantly increases the rate of heat transfer on plate in porous media in comparison with Darsy flow model.

scholarly journals Computational Study of the Coupled Mechanism of Thermophoretic Transportation and Mixed Convection Flow around the Surface of a Sphere

Molecules ◽  
2020 ◽  
Vol 25 (11) ◽  
pp. 2694
Author(s):  
Amir Abbas ◽  
Muhammad Ashraf ◽  
Yu-Ming Chu ◽  
Saqib Zia ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mixed Convection ◽  
Computational Study ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Partial Differential ◽  
Primitive Form ◽  
The Mathematical Model

The main goal of the current work was to study the coupled mechanism of thermophoretic transportation and mixed convection flow around the surface of the sphere. To analyze the characteristics of heat and fluid flow in the presence of thermophoretic transportation, a mathematical model in terms of non-linear coupled partial differential equations obeying the laws of conservation was formulated. Moreover, the mathematical model of the proposed phenomena was approximated by implementing the finite difference scheme and boundary value problem of fourth order code BVP4C built-in scheme. The novelty point of this paper is that the primitive variable formulation is introduced to transform the system of partial differential equations into a primitive form to make the line of the algorithm smooth. Secondly, the term thermophoretic transportation in the mass equation is introduced in the mass equation and thus the effect of thermophoretic transportation can be calculated at different positions of the sphere. Basically, in this study, some favorite positions around the sphere were located, where the velocity field, temperature distribution, mass concentration, skin friction, and rate of heat transfer can be calculated simultaneously without any separation in flow around the surface of the sphere.

scholarly journals NUMERICAL MODEL OF CURRENT AND SEDIMENT TRANSPORT IN THE WAVE BOUNDARY LAYER

2011 ◽  
Vol 1 (32) ◽  
pp. 5
Author(s):  
Yuliang Zhu ◽  
Jing Ma ◽  
Hao Wang
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Eddy Viscosity ◽  
Sediment Concentration ◽  
Wave Boundary Layer ◽  
Time Invariant ◽  
Wave Boundary ◽  
The Mathematical Model ◽  
The Relationship ◽  
Turbulent Wave

Mathematical model is one of the means to study of turbulent wave boundary layer. The paper analysis of the existing model, adopt a more reasonable boundary condition to establish a improved mathematical model of 1DV turbulent wave boundary layer using k-ε model. The paper recommends brief flow simulation and mainly introduced the simulation of the sediment concentration. The paper use the eddy-viscosity value which calculation by the mathematical model and the model of You Zaijin on time-invariant eddy-viscosity into the relationship about sediment diffusion coefficient and eddy-viscosity to calculate the sediment concentration. The calculation results turns out the way that use the eddy-viscosity value which calculation by the mathematical model into the relationship can obtain better timely sediment concentration value. When use the model simulates the time-invariant sediment concentration, the two ways have not many distinctions. It means the way that that use the eddy-viscosity value which calculation by the mathematical model into the relationship is feasible.

Instability in Boundary-Layer Free Convection along an inclined Plate

1972 ◽  
Vol 1 (4) ◽  
pp. 197-204 ◽  
Author(s):  
J.B. Lee ◽  
G.S.H. Lock
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Plane Surface ◽  
Convection Flow ◽  
Neutral Stability ◽  
Inclined Plate ◽  
Free Convection Flow ◽  
Roll Vortices ◽  
The Stability ◽  
Rayleigh Numbers

This paper gives theoretical consideration to the problem of the stability of laminar, boundary-layer, free-convection flow of air along a long, inclined plane surface heated isothermally. The analysis considers two forms of small disturbance: a two-dimensional wave disturbance, and a set of longitudinal roll vortices. Development of the appropriate disturbance equations is followed by their numerical solution. The effect of inclination on the neutral stability curves for both disturbance forms is presented graphically along with a comparison of the critical Rayleigh numbers obtained from both disturbance forms.

SELF-SIMILAR PROBLEMS FOR MODELING THE SURFACE CHEMICAL REACTIONS WITH THE GRAVITATION

1998 ◽  
Vol 3 (1) ◽  
pp. 25-32
Author(s):  
Jânis Cepîtis ◽  
Harijs Kalis
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Chemical Reactions ◽  
Glass Fibre ◽  
Surface Chemical ◽  
Self Similar ◽  
Surface Chemical Reactions ◽  
The Mathematical Model

The mathematical model of a chemical reaction which takes place on the surface of the uniformly moving vertically imbedded glass fibre material is considered. The effect of gravitation is taken into account. Boussinesq's and boundary layer fittings allow to derive boundary value problems for self‐similar systems of ordinary differential equations.

scholarly journals A Thematic Review on Mathematical Model for Convective Boundary Layer Flow

2021 ◽  
Vol 86 (2) ◽  
pp. 107-125
Author(s):  
Siti Farah Haryatie Mohd Kanafiah ◽  
Abdul Rahman Mohd Kasim ◽  
Syazwani Zokri ◽  
Nur Syamilah Arifin
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Boundary Condition ◽  
Fluid Flow ◽  
Convective Boundary Layer ◽  
Review Paper ◽  
Convective Boundary ◽  
Flow Problems ◽  
Thematic Review ◽  
The Mathematical Model

Convection refers to the heat transfer that occurs between moving fluid and surface at a different temperature. Nowadays, there has been a great deal of interest in the convective boundary layer fluid flow problems. Despite its popularity, the review paper discussing the mathematical model for various fluid types regarding various geometry and boundary conditions has been observed to fall short. This review paper adopts a thematic review based on the mathematical model captured in published fluid flow problems from 2015 until 2020. The articles were analysed using thematic analysis ATLAS.ti 8 software. Using keyword search and filtering criteria from Scopus and Web of Science (WOS) databases, 198 peer-reviewed journal articles were identified. However, after the exclusion and inclusion processes, only 50 articles were reviewed as final articles. The thematic review of these articles has further identified 120 initial codes characterising the mathematical model, grouped into 7 clusters: Viscoelastic, Williamson, Casson, Brinkman, Jeffrey, Nanofluid and hybrid Nanofluid. The report from the code-to-document in ATLAS.ti 8 found that the boundary condition, geometry and method were highlighted in the literature. The outcomes of this study will benefit the future research direction to identify the gap for future studies, specifically in extending the mathematical model for fluid flow problems as well as choosing the suitable geometry and boundary condition.

scholarly journals Combined effects of viscous dissipation and temperature dependent thermal conductivity on MHD free convection flow with conduction and joule heating along a vertical flat plate

2010 ◽  
Vol 6 (1) ◽  
pp. 30-40 ◽  
Author(s):  
R. Nasrin ◽  
M. A. Alim
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Convection Flow ◽  
Combined Effects ◽  
Temperature Dependent ◽  
Free Convection Flow ◽  
Temperature Dependent Thermal Conductivity ◽  
Vertical Flat Plate

Combined effects of viscous dissipation and temperature dependent thermal conductivity on MHD free convection flow with heat conduction and Joule heating along a vertical flat plate have been described in the present work. The governing boundary layer equations with associated boundary conditions for this phenomenon are converted to non-dimensional form using a suitable transformation. The resulting non-linear partial differential equations are then solved using the implicit finite difference method with Keller-box scheme. The numerical results in terms of the skin friction coefficient, the surface temperature, the velocity and the temperature profiles over the whole boundary layer are shown graphically for different values of the Prandtl number Pr, the magnetic parameter M, the thermal conductivity variation parameter γ, viscous dissipation parameter N and the Joule heating parameter J. Numerical results of the local skin friction co-efficient and the surface temperature profile for different values of N are presented in tabular form.Keywords: Joule heating; MHD; conduction; temperature dependent thermal conductivity; viscous dissipation;natural convection.DOI: 10.3329/jname.v5i2.2648Journal of Naval Architecture and Marine Engineering 6(1)(2009) 30-40 

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