Mass transfer in laminar flow

1954 ◽  
Vol 221 (1144) ◽  
pp. 78-99 ◽  
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Natural Convection ◽  
Laminar Flow ◽  
Flat Plate ◽  
The Body ◽  
Liquid Fuels ◽  
Fluid Stream ◽  
Mean Values ◽  
Fluid Properties

Starting from the differential equation of mass transfer in laminar flow and the appropriate boundary condition, expressions are derived for the rate of mass transfer from ( a ) a flat plate in a longitudinal fluid stream, ( b ) a vertical flat plate by natural convection, ( c ) the forward stagnation point of a sphere in a fluid stream. Only outward mass transfer is considered; this corresponds to blowing outwards from the plate at a rate inversely proportional to the boundary-layer thickness. The Kármán-Pohlhausen-Kroujiline method is used. Where appropriate the Prandtl or Schmidt number has been taken as 0⋅71. The calculations are valid for all mass-transfer processes for which a single diffusion coefficient can be ascribed to the diffusing property, but are particularly relevant to the combustion of liquid fuels, for which the outward mass-transfer rates are so high that important deviations occur from boundary-layer profiles without mass transfer. Despite the great temperature variations present in boundary layers with combustion, mean values for the fluid properties are assumed. In the case of natural convection, it is assumed that the body forces on the fluid in the boundary layer are everywhere zero; this leads to a less serious over-estimate of the buoyancy than the usual assumptions which are valid only for small temperature differences.

Numerical Simulation of Laminar Boundary Layer Flow Over a Horizontal Flat Plate in External Incompressible Viscous Fluid

2021 ◽  
Author(s):  
Ali Belhocine ◽  
Nadica Stojanovic ◽  
Oday Ibraheem Abdullah
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Solution Procedure ◽  
Dimensionless Temperature ◽  
Plane Plate ◽  
Fluid Properties ◽  
Layer Flow

In this paper, steady laminar boundary layer flow of a Newtonian fluid over a flat plate in a uniform free stream was investigated numerically when the surface plate is heated by forced convection from the hot fluid. This flow is a good model of many situations involving flow over fins that are relatively widely spaced. All the solutions given here were with constant fluid properties and negligible viscous dissipation for two-dimensional, steady, incompressible laminar flow with zero pressure gradient. The similarity solution has shown its efficiency here to transform the governing equations of the thermal boundary layer into a nonlinear, third-order ordinary differential equation and solved numerically by using 4th-order Runge-Kutta method which in turn was programmed in FORTRAN language. The dimensionless temperature, velocity, and all boundary layer functions profiles were obtained and plotted in figures for different parameters entering into the problem. Several results of best approximations and expressions of important correlations relating to heat transfer rates were drawn in this study of which Prandtl’s number to the plate for physical interest was also discussed across the tables. The same case of solution procedure was made for a plane plate subjected to other thermal boundary conditions in a laminar flow. Finally, for the validation of the treated numerical model, the results obtained are in good agreement with those of the specialized literature, and comparison with available results in certain cases is excellent.

NATURAL CONVECTION BOUNDARY LAYER FLOW PAST A FLAT PLATE OF FINITE DIMENSIONS

2012 ◽  
Vol 15 (6) ◽  
pp. 585-593
Author(s):  
M. Jana ◽  
S. Das ◽  
S. L. Maji ◽  
Rabindra N. Jana ◽  
S. K. Ghosh
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Flat Plate ◽  
Boundary Layer Flow ◽  
Convection Boundary Layer ◽  
Flow Past ◽  
Convection Boundary ◽  
Layer Flow

Mass transfer between a plane surface and an impinging turbulent jet: the influence of surface-pressure fluctuations

1982 ◽  
Vol 119 ◽  
pp. 91-105 ◽  
Author(s):  
K. Kataoka ◽  
Y. Kamiyama ◽  
S. Hashimoto ◽  
T. Komai
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Flat Plate ◽  
Stagnation Point ◽  
Surface Pressure ◽  
Velocity Gradient ◽  
Large Scale ◽  
Pressure Fluctuations ◽  
Wall Region ◽  
Local Measurement

Local measurement of the mass-transfer rate and velocity gradient when an axisymmetric jet impinges on a flat plate was carried out using an electrochemical technique. Local measurement of the surface pressure on the flat plate was carried out separately using piezoelectric pressure transducers. The stagnation-point mass-transfer coefficient reaches a maximum when the flat plate is placed at 6 nozzle diameters from a convergent nozzle. It has been confirmed that the mass transfer to the flat plate for a high Schmidt number is greatly enhanced owing to the velocity-gradient disturbances in the wall region of the boundary layer, while the momentum transfer is insensitive to such disturbances. The relative intensity of the velocity-gradient fluctuations on the wall has an extremely large value at and near to the stagnation point, and decreases downstream, approaching a large constant value.These velocity-gradient disturbances are not due to the usual interaction of Reynolds stress with the shear stress of the mean flow, but are due to the interaction with the surface-pressure fluctuations converted from the velocity fluctuations of the oncoming jet.The three co-ordinate dimensions of large-scale eddies are calculated from the auto- and spatial correlations of the surface-pressure fluctuations. It is considered that such large-scale eddies play an important role in the production of a velocity-gradient disturbance in the wall region of the boundary layer from the velocity turbulence of the approaching jet.

Heat and mass transfer from a flat plate of finite thickness to a boundary layer flow with transpiration

1997 ◽  
Vol 38 (10-13) ◽  
pp. 1209-1218 ◽  
Author(s):  
Shigeru Mori ◽  
Mikio Kumita ◽  
Tohru Takahashi ◽  
Akira Tanimoto ◽  
Mikio Sakakibara
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Flat Plate ◽  
Heat And Mass Transfer ◽  
Boundary Layer Flow ◽  
Finite Thickness ◽  
Layer Flow

The dispersion of contaminant released from instantaneous sources in laminar flow near stagnation points

1974 ◽  
Vol 66 (4) ◽  
pp. 753-766 ◽  
Author(s):  
P. C. Chatwin
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Bluff Body ◽  
Velocity Potential ◽  
Tangent Plane ◽  
The Body ◽  
Centre Of Mass ◽  
Stagnation Points ◽  
Molecular Diffusivity ◽  
Instantaneous Source

This paper considers the dispersion of a cloud of passive contaminant released from an instantaneous source in the steady two-dimensional laminar flow near the forward stagnation point on a bluff body. The body is replaced by its tangent plane y = 0 with x measuring distance along the plane. Far away from y = 0 the flow is irrotational with velocity potential ½l(x2 – y2), where l is a positive constant. When the boundary layer is ignored the equation governing the distribution of concentration can be solved exactly. Consequences of this solution are that for large times the centre of mass moves parallel to the body at a speed proportional to exp (lt) while the cloud spreads out along the body symmetrically about the centre of mass with the magnitude of the spread also proportional to exp (lt). However, this solution is unrealistic because most of the contaminant is confined to a layer adjoining the body of thickness of order (k/l)½, where k is the molecular diffusivity, and this layer normally lies within the boundary layer, which is of thickness of order (v/l)½, where v is the kinematic viscosity. An approximate analysis, based on ideas similar to those supporting the Pohlhausen method in boundary-layer theory, suggests that when the boundary layer is taken into account the conclusions above remain true provided that exp (lt) is replaced by exp (βlt), where β is a constant depending on v/k. Calculations give values of β ranging from 0·73 when v/k = 0·5 to 0·10 when v/k = 103.

Heat Transfer in the Laminar Boundary Layer Over an Impulsively Started Flat Plate

1975 ◽  
Vol 97 (3) ◽  
pp. 482-484 ◽  
Author(s):  
C. B. Watkins
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Flat Plate ◽  
Constant Temperature ◽  
Laminar Boundary Layer ◽  
Temperature Difference ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Prandtl Numbers

Numerical solutions are described for the unsteady thermal boundary layer in incompressible laminar flow over a semi-infinite flat plate set impulsively into motion, with the simultaneous imposition of a constant temperature difference between the plate and the fluid. Results are presented for several Prandtl numbers.

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