The Turbulent Boundary Layer With Mass Transfer and Pressure Gradient

1971 ◽  
Vol 38 (3) ◽  
pp. 688-698 ◽  
Author(s):  
S. C. Lubard ◽  
F. L. Fernandez
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Pressure Gradient ◽  
Transfer Rate ◽  
Energy Equation ◽  
Mechanical Energy ◽  
Mass Transfer Rate ◽  
Equilibrium Flow ◽  
Gradient Parameter ◽  
Good Agreement

An analysis of the incompressible, turbulent boundary layer, including the combined effects of mass transfer and pressure gradient is presented in this paper. An integral method employing the integral mechanical energy equation forms the basis of the analysis. Stevenson’s velocity profiles are used to obtain the functional dependence of the integral properties and also obtain a skin-friction law. A definition of an equilibrium flow with mass transfer and pressure gradient is given in order to evaluate the dissipation integral (CD) which appears in the integral mechanical energy equation. This definition requires a pressure gradient parameter similar to Clauser’s βT with a modification to include the effect of mass transfer to be held constant. An expression for CD in the case of equilibrium turbulent flows is then obtained which depends directly on this new pressure gradient parameter (βT*). In order to treat the general case of nonequilibrium flows, this expression for CD is uncoupled from βT*, through the use of a single empirical curve fit of the existing no mass transfer equilibrium flow data relating βT to the Clauser shape parameter. In addition to unhooking CD from the pressure gradient parameter, several specified variations in mass transfer rate are assumed in order to obtain an expression for CD which is not a function of the mass transfer rate derivative. The numerical results are found to be weakly dependent on which of these variations is used. Comparisons of the numerical results with a wide variety of experimental data, including cases where the blowing rate and pressure are varying simultaneously, show good agreement. In addition, several problems with discontinuities in blowing or suction are solved and seem to be in good agreement with the data.

Mass transfer from a laminar stream to a flat plate

1954 ◽  
Vol 221 (1144) ◽  
pp. 100-104 ◽  
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Flat Plate ◽  
Transfer Rate ◽  
Kinematic Viscosity ◽  
Mass Transfer Rate ◽  
Leading Edge ◽  
Square Root ◽  
Transfer Number ◽  
Very High

The Kármán-Pohlhausen-Kroujiline method is used to calculate the mass-transfer rate from a laminar stream to a flat plate, for fluids of which the diffusion coefficient is not greatly different from the kinematic viscosity. Particular attention is paid to the very high rates of mass transfer occurring when the transfer number B approaches -1; under these circumstances it is shown that the transfer rate is proportional to (1+ B ) -½ . In aerodynamic terms the problem may be regarded as that of a laminar boundary layer with suction distributed in proportion to the reciprocal of the square root of the distance from the leading edge.

Highly Accelerated Compressible Laminar Boundary Layer Flows With Mass Transfer

1971 ◽  
Vol 93 (3) ◽  
pp. 281-289 ◽  
Author(s):  
A. Wortman ◽  
A. F. Mills
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Laminar Boundary Layer ◽  
Transfer Rate ◽  
Numerical Solutions ◽  
Mass Transfer Rate ◽  
Solution Procedure ◽  
Boundary Layer Flows ◽  
Displacement Thickness ◽  
Simplifying Assumptions

Exact numerical solutions have been obtained for highly accelerated self-similar laminar boundary layer flows with and without mass transfer. Values of the acceleration parameter β in the range 0 to 20 were considered. Variable gas properties were realistically modeled by assuming ρ ∝ h−1, μ ∝ hω, and Pr = constant. The results presented show the dependence of wall shear stress, heat transfer rate, and displacement thickness on the problem parameters which include β, Mach number, wall enthalpy ratio, mass transfer rate, ω and Pr. The inadequacy of solutions obtained under the simplifying assumptions of Pr = 1.0 and ω = 1.0 is clearly displayed. The numerical solution procedure employed proved quite adequate for a class of problem which has presented serious difficulties to previous investigators.

Natural Convective Boundary-Layer Flow Over a Vertical Cylinder Embedded in a Porous Medium Saturated With a Nanofluid

2012 ◽  
Vol 3 (3) ◽  
Author(s):  
Rama Subba Reddy Gorla ◽  
Waqar Khan
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Porous Medium ◽  
Friction Factor ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Vertical Cylinder ◽  
Surface Heat

In this paper, a boundary layer analysis is presented for the natural convection past a vertical cylinder in a porous medium saturated with a nanofluid. Numerical results for friction factor, surface heat transfer rate, and mass transfer rate have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate on these parameters has been discussed. The results indicate that as Nr, Nb, and Nt increase, the friction factor and heat transfer rate (Nusselt number) decrease. The mass transfer rate (Sherwood number) increases with Le, Nb, and Nt.

scholarly journals Unsteady nano-bioconvective channel flow with effect of nth order chemical reaction

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1011-1024 ◽  
Author(s):  
Md Faisal Md Basir ◽  
Kohilavani Naganthran ◽  
Ehtsham Azhar ◽  
Zaffar Mehmood ◽  
Swati Mukhopadhyay ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Channel Flow ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Lower Wall ◽  
Layer System ◽  
Boundary Layer Equations ◽  
Order Chemical Reaction

Abstract Nanofluid bioconvective channel flow is an essential aspect of the recent healthcare industry applications, such as biomedical processing systems. Thus, the present work examined the influence of nth order chemical reaction in an unsteady nanofluid bioconvective channel flow in a horizontal microchannel with expanding/contracting walls. The suitable form of the similarity transformation is exercised to transform the governing boundary layer equations into a more straightforward form of system to ease the computation process. The Runge–Kutta method of fifth-order integration technique solved the reduced boundary layer system and generated the numerical results as the governing parameters vary. It is found that the destructive second-order chemical reaction enhances the mass transfer rate at the lower wall but deteriorates the mass transfer rate at the upper wall. The upper channel wall has a better heat transfer rate than the lower wall when the Reynolds number increases.

Free Convective Mass Transfer at Isosceles Triangular Surfaces of Varying Inclination

2003 ◽  
Vol 68 (11) ◽  
pp. 2080-2092 ◽  
Author(s):  
Martin Keppert ◽  
Josef Krýsa ◽  
Anthony A. Wragg
Keyword(s):  
Mass Transfer ◽  
Transfer Rate ◽  
Mass Transfer Rate ◽  
Mass Transfer Process ◽  
Sulfate Solution ◽  
Convective Mass Transfer ◽  
Varying Length ◽  
Inclined Surface ◽  
Vertical Case ◽  
Limiting Diffusion Current

The limiting diffusion current technique was used for investigation of free convective mass transfer at down-pointing up-facing isosceles triangular surfaces of varying length and inclination. As the mass transfer process, copper deposition from acidified copper(II) sulfate solution was used. It was found that the mass transfer rate increases with inclination from the vertical to the horizontal position and decreases with length of inclined surface. Correlation equations for 7 angles from 0 to 90° were found. The exponent in the ShL-RaL correlation ranged from 0.247 for the vertical case, indicating laminar flow, to 0.32 for inclinations of 60 to 90°, indicating mixed or turbulent flow. The general correlation ShL = 0.358(RaL sin θ)0.30 for the RaL sin θ range from 7 × 106 to 2 × 1011 and inclination range from 15 to 90° was obtained.

Distributed mass transfer rate for modelling the leaching of porous granular materials containing soluble pollutants

2000 ◽  
Vol 55 (7) ◽  
pp. 1257-1267 ◽  
Author(s):  
Tiruta-Barna Ligia ◽  
Barna Radu ◽  
Moszkowicz Pierre ◽  
Bae Hae-Ryong
Keyword(s):  
Mass Transfer ◽  
Granular Materials ◽  
Transfer Rate ◽  
Mass Transfer Rate

Enhancement of formic acid production from CO2 in formate dehydrogenase reaction using nanoparticles

RSC Advances ◽  
2016 ◽  
Vol 6 (111) ◽  
pp. 109978-109982 ◽  
Author(s):  
Young-Kee Kim ◽  
Sung-Yeob Lee ◽  
Byung-Keun Oh
Keyword(s):  
Mass Transfer ◽  
Formic Acid ◽  
Acid Production ◽  
Transfer Rate ◽  
Formate Dehydrogenase ◽  
Mass Transfer Rate ◽  
Liquid Mass ◽  
Dehydrogenase Reaction ◽  
Liquid Mass Transfer ◽  
Mesoporous Nanoparticles

In an enzyme process using a gas substrate, the enhanced gas liquid mass transfer rate of the gas substrate by methyl-functionalized mesoporous nanoparticles could improve the productivity.

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