Governing Equations and Boundary Conditions of Mass Transfer

2002 ◽  
Keyword(s):  
Mass Transfer ◽  
Boundary Conditions ◽  
Governing Equations

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

2017 ◽  
Vol 6 (10) ◽  
pp. 116
Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Transfer Flow

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

The effect of radiation on free convective flow and mass transfer past a vertical isothermal cone surface with chemical reaction in the presence of a transverse magnetic field

2004 ◽  
Vol 82 (6) ◽  
pp. 447-458 ◽  
Author(s):  
A A Afify
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Boundary Conditions ◽  
Chemical Reaction ◽  
Transverse Magnetic Field ◽  
Convective Flow ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Free Convective Flow ◽  
Cone Surface

The effects of radiation and chemical reactions, in the presence of a transverse magnetic field, on free convective flow and mass transfer of an optically dense viscous, incompressible, and electrically conducting fluid past a vertical isothermal cone surface are investigated. The nonlinear boundary-layer equations with the boundary conditions are transferred by a similarity transformation into a system of nonlinear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth-order Runge–Kutta scheme with the shooting method. Numerical results for the skin-friction coefficient, the local Nusselt number, the local Sherwood number are given; as well, the velocity, temperature, and concentration profiles are presented for a Prandtl number of 0.7, the chemical-reaction parameter, the order of the reaction, the radiation parameter, the Schmidt number, the magnetic parameter, and the surface temperature parameter. PACS No.: 47.70.Fw

Analysis of Heat and Mass Transfer Between a Desiccant-Air System in a Packed Tower

1987 ◽  
Vol 109 (2) ◽  
pp. 89-93 ◽  
Author(s):  
P. Gandhidasan ◽  
M. Rifat Ullah ◽  
C. F. Kettleborough
Keyword(s):  
Mass Transfer ◽  
Gas Phase ◽  
Heat And Mass Transfer ◽  
Packing Material ◽  
Mass Transfer Resistance ◽  
Liquid Desiccant ◽  
Governing Equations ◽  
Packed Tower ◽  
Transfer Resistance ◽  
Steady State Model

Heat and mass transfer analysis between a desiccant-air contact system in a packed tower has been studied in application to air dehumidification employing liquid desiccant, namely calcium chloride. Ceramic 2 in. Raschig rings are used as the packing material. To predict the tower performance, a steady-state model which considers the heat and mass transfer resistances of the gas phase and the mass transfer resistance of the liquid phase is developed. The governing equations are solved on a digital computer to simulate the performance of the tower. The various parameters such as the effect of liquid concentration and temperature, air temperature and humidity and the rates of flow of air and liquid affecting the tower performance have been discussed.

Application of Generalized Differential Quadrature Method to the Bending of Thick Laminated Plates with Various Boundary Conditions

2006 ◽  
Vol 5-6 ◽  
pp. 407-414 ◽  
Author(s):  
Mohammad Mohammadi Aghdam ◽  
M.R.N. Farahani ◽  
M. Dashty ◽  
S.M. Rezaei Niya
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Simple Procedure ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Differential Quadrature ◽  
Governing Equations ◽  
First Order ◽  
Various Boundary Conditions ◽  
Generalized Differential

Bending analysis of thick laminated rectangular plates with various boundary conditions is presented using Generalized Differential Quadrature (GDQ) method. Based on the Reissner first order shear deformation theory, the governing equations include a system of eight first order partial differential equations in terms of unknown displacements, forces and moments. Presence of all plate variables in the governing equations provide a simple procedure to satisfy different boundary condition during application of GDQ method to obtain accurate results with relatively small number of grid points even for plates with free edges .Illustrative examples including various combinations of clamped, simply supported and free boundary condition are given to demonstrate the accuracy and convergence of the presented GDQ technique. Results are compared with other analytical and finite element predictions and show reasonably good agreement.

Physical statement of the problem for a numerical model of soil freezing and heaving taking into account heat and mass transfer

2021 ◽  
pp. 244-256
Author(s):  
Виктор Григорьевич Чеверев ◽  
Евгений Викторович Сафронов ◽  
Алексей Александрович Коротков ◽  
Александр Сергеевич Чернятин
Keyword(s):  
Finite Element Method ◽  
Mass Transfer ◽  
Finite Element ◽  
Numerical Model ◽  
Boundary Conditions ◽  
Heat And Mass Transfer ◽  
Soil Freezing ◽  
The Finite Element Method ◽  
Freezing Front ◽  
Element Method

Существуют два основных подхода решения задачи тепломассопереноса при численном моделировании промерзания грунтов: 1) решение методом конечных разностей с учетом граничных условий (границей, например, является фронт промерзания); 2) решение методом конечных элементов без учета границ модели. Оба подхода имеют существенные недостатки, что оставляет проблему решения задачи для численной модели промерзания грунтов острой и актуальной. В данной работе представлена физическая постановка промерзания, которая позволяет создать численную модель, базирующуюся на решении методом конечных элементов, но при этом отражающую ход фронта промерзания - то есть модель, в которой объединены оба подхода к решению задачи промерзания грунтов. Для подтверждения корректности модели был проделан ряд экспериментов по физическому моделированию промерзания модельного грунта и выполнен сравнительный анализ полученных экспериментальных данных и результатов расчетов на базе представленной численной модели с такими же граничными условиями, как в экспериментах. There are two basic approaches to solving the problem of heat and mass transfer in the numerical modeling of soil freezing: 1) using the finite difference method taking into account boundary conditions (the boundary, for example, is the freezing front); 2) using the finite element method without consideration of model boundaries. Both approaches have significant drawbacks, which leaves the issue of solving the problem for the numerical model of soil freezing acute and up-to-date. This article provides the physical setting of freezing that allows us to create a numerical model based on the solution by the finite element method, but at the same time reflecting the route of the freezing front, i.e. the model that combines both approaches to solving the problem of soil freezing. In order to confirm the correctness of the model, a number of experiments on physical modeling of model soil freezing have been performed, and a comparative analysis of the experimental data obtained and the calculation results based on the provided numerical model with the same boundary conditions as in the experiments was performed.

Transient Free Convection Mass Transfer of Second-grade Fluid Flow with Wall Transpiration

CFD Letters ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 35-52
Author(s):  
Mohamad Alif Ismail ◽  
Mohamad Hidayad Ahmad Kamal ◽  
Lim Yeou Jiann ◽  
Anati Ali ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Schmidt Number ◽  
Second Grade ◽  
Concentration Profiles ◽  
Governing Equations ◽  
Second Grade Fluid ◽  
Wall Suction ◽  
Viscoelastic Parameter ◽  
Grade Fluid ◽  
Wall Injection

The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.

Investigation of heat transfer in irregular porous cavity subjected to various boundary conditions

2019 ◽  
Vol 29 (1) ◽  
pp. 418-447 ◽  
Author(s):  
Irfan Anjum Badruddin
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Outer Boundary ◽  
Governing Equations ◽  
Content Type ◽  
Porous Cavity ◽  
Various Boundary Conditions ◽  
Heating Source ◽  
Transfer Behavior ◽  
Vertical Walls

Purpose The purpose of this paper is to investigate the heat transfer in an arbitrary cavity filled with porous medium. The geometry of the cavity is such that an isothermal heating source is placed centrally at the bottom of the cavity. The height and width of the heating source is varied to analyses its effect on the heat transfer characteristics. The investigation is carried out for three different cases of outer boundary conditions such as two outside vertical walls being maintained at cold temperature To, two vertical and top horizontal surface being heated to. To and the third case with top surface kept at To but other surfaces being adiabatic. Design/methodology/approach Finite element method is used to solve the governing equations. Findings It is observed that the cavity exhibits unique heat transfer behavior as compared to regular cavity. The cases of boundary conditions are found to affect the heat transfer rate in the porous cavity. Originality/value This is original work representing the heat transfer in irregular porous cavity with various boundary conditions. This work is neither being published nor under review in any other journal.

scholarly journals Visualization Techniques of Differentially Heated Lid-Driven Square Cavity

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Vekamulla Narayana
Keyword(s):  
Flow Field ◽  
Boundary Conditions ◽  
Computational Cost ◽  
Field Synergy ◽  
Governing Equations ◽  
Square Cavity ◽  
Field Synergy Principle ◽  
Visualization Techniques

In the present study, an attempt is made to explore the flow field inside the differentially heated lid-driven square cavity. The governing equations along with boundary conditions are solved numerically. The simulated results (100 ≤ Re ≤ 1000 and 0.001 ≤ Ri ≤ 10) are validated with previous results in the literature. The convection differencing schemes, namely, UPWIND, QUICK, SUPERBEE, and SFCD, are discussed and are used to simulate the flow using the MPI code. It is observed that the computational cost for all the differencing schemes get reduced tremendously when the MPI code is implemented. Plots demonstrate the influences of Re and Ri in terms of the contours of the fluid streamlines, isotherms, energy streamlines, and field synergy principle.

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