?Chessboard? difference method of solving a system of differential equations of heat and mass transfer

1976 ◽  
Vol 30 (6) ◽  
pp. 725-728
Author(s):  
A. F. Klement'ev ◽  
O. N. Balykina
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Difference Method ◽  
System Of Differential Equations

scholarly journals Modeling of heat and mass transfer processes in non-linearly viscous fluid film flows

2019 ◽  
Author(s):  
I. S. Tonkoshkur
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Film Thickness ◽  
Liquid Film ◽  
Heat And Mass Transfer ◽  
Boundary Layers ◽  
The Body ◽  
System Of Differential Equations ◽  
And Diffusion

The problem of heat and mass transfer in a liquid film of a nonlinearly viscous fluid flowing down the surface of a body of revolution under the influence of gravity is considered. The axis of the body is located at a certain angle to the vertical, and the film of liquid flows down from its top. It is assumed that the thermal and diffusion Prandtl numbers are large and the main changes in the temperature and diffusion fields occur in thin boundary layers near the solid wall and near the free surface separating the liquid and gas. A curvilinear orthogonal coordinate system (ξ, η, ζ) connected with the surface of the body is introduced. To describe the flow of a liquid film, a model of a viscous incompressible liquid is used, which is based on differential equations in partial derivatives - the equations of motion and continuity. As boundary conditions, the conditions of adhesion are used on the surface of a solid body, as well as the conditions of continuity of stresses and the normal component of the velocity vector - on the surface separating the liquid and gas. To simulate heat and mass transfer in a liquid film, the equations of thermal and diffusion boundary layers with boundary conditions of the first and second kind are used. To close the system of differential equations, the Ostwald-de-Ville rheological model is used. To simplify the system of differential equations, the small parameter method is used, in which the relative film thickness is selected. It is assumed that the generalized Reynolds number is of the order of unity. The solution of the equations of continuity and motion (taking into account the main terms of the expansion) is obtained in an analytical form. To determine the unknown film thickness, an initial-boundary-value problem is formulated for a first-order partial differential equation. The solution to this problem is found numerically using a running count difference scheme. To reduce the dimension of the problem for the equations of the boundary layer, the local similarity method is used. To integrate simplified equations, the finite-difference method is used.

scholarly journals Nonstationary flow of roiling liquid

1984 ◽  
Vol 6 (4) ◽  
pp. 12-20
Author(s):  
Duong Ngoc Hai
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Phase Boundary ◽  
Heat And Mass Transfer ◽  
Numerical Results ◽  
Linear Differential Equations ◽  
Nonstationary Flow ◽  
One Dimensional ◽  
Boiling Liquid ◽  
Linear Differential

Steady one-dimensional nonstationary flow of boiling liquid from finite or infinit pipe in a consideration of the effect of the phase-boundary heat and mass transfer. The Received system of quasi-linear differential equations has been decided by the modificati on of Lax - wendroff method in IBM. Numerical results are compared as xperimental data.

An Analytical Approach to the Heat and Mass Transfer Processes in Counterflow Cooling Towers

2006 ◽  
Vol 128 (11) ◽  
pp. 1142-1148 ◽  
Author(s):  
Chengqin Ren
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Analytical Model ◽  
Operating Conditions ◽  
Cooling Towers ◽  
Accurate Analysis ◽  
Transfer Resistance ◽  
Transfer Processes ◽  
Mass Transfer Processes

Quick and accurate analysis of cooling tower performance, outlet conditions of moist air, and parameter profiles along the tower height is very important in rating and design calculations. This paper developed an analytical model for the coupled heat and mass transfer processes in counterflow cooling towers based on operating conditions more realistic than most conventionally adopted Merkel approximations. In modeling, values of the Lewis factor were not necessarily specified as unity. Effects of water loss by evaporation and water film heat transfer resistance were also considered in the model equations. Within a relatively narrow range of operating conditions, the humidity ratio of air in equilibrium with the water surface was assumed to be a linear function of the surface temperature. The differential equations were rearranged and an analytical solution was developed for newly defined parameters. The analytical model predicts the tower performances, outlet conditions, and parameter profiles quickly and accurately when comparing with the numerical integration of the original differential equations.

g-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Noraihan Afiqah Rawi ◽  
Abdul Rahman Mohd Kasim ◽  
Mukheta Isa ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Keller Box Method ◽  
Unsteady Mixed Convection ◽  
Layer Flow

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Soraya Torkaman ◽  
Ghasem Barid Loghmani ◽  
Mohammad Heydari ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Operational Matrices ◽  
Nanofluid Flow ◽  
Content Type ◽  
Nonlinearly Stretching Sheet

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

scholarly journals MHD Slip Flow of Newtonian Fluid past a Stretching Sheet with Thermal Convective Boundary Condition, Radiation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Reda G. Abdel-Rahman
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary

An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.

Sign in / Sign up

Export Citation Format

Share Document