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.

scholarly journals Compressible laminar boundary-layer flows of a dusty gas over a semi-infinite flat plate

1988 ◽  
Vol 186 ◽  
pp. 223-241 ◽  
Author(s):  
B. Y. Wang ◽  
I. I. Glass
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Laminar Boundary Layer ◽  
Leading Edge ◽  
Expansion Method ◽  
Boundary Layer Flows ◽  
Two Phase ◽  
Displacement Thickness ◽  
Slip Region ◽  
Two Phases

The compressible laminar boundary-layer flows of a dilute gas-particle mixture over a semi-infinite flat plate are investigated analytically. The governing equations are presented in a general form where more reasonable relations for the two-phase interaction and the gas viscosity are included. The detailed flow structures of the gas and particle phases are given in three distinct regions: the large-slip region near the leading edge, the moderate-slip region and the small-slip region far downstream. The asymptotic solutions for the two limiting regions are obtained by using a series-expansion method. The finite-difference solutions along the whole length of the plate are obtained by using implicit four-point and six-point schemes. The results from these two methods are compared and very good agreement is achieved. The characteristic quantities of the boundary layer are calculated and the effects on the flow produced by the particles are discussed. It is found that in the case of laminar boundary-layer flows, the skin friction and wall heat-transfer are higher and the displacement thickness is lower than in the pure-gas case alone. The results indicate that the Stokes-interaction relation is reasonable qualitatively but not correct quantitatively and a relevant non-Stokes relation of the interaction between the two phases should be specified when the particle Reynolds number is higher than unity.

Singularities in solutions of the three-dimensional laminar-boundary-layer equations

1985 ◽  
Vol 160 ◽  
pp. 257-279 ◽  
Author(s):  
James C. Williams
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
New Type ◽  
Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

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.

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.

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.

An Investigation of Simple Evaporation Models Used in Spray Simulations

2003 ◽  
Vol 125 (1) ◽  
pp. 179-182 ◽  
Author(s):  
G. F. Yao ◽  
S. I. Abdel-Khalik ◽  
S. M. Ghiaasiaan
Keyword(s):  
Mass Transfer ◽  
Transfer Rate ◽  
Numerical Solutions ◽  
Film Theory ◽  
Mass Transfer Rate ◽  
High Mass ◽  
Transfer Processes ◽  
Mass Transfer Processes ◽  
Model Predictions ◽  
Evaporation Models

In the present work, an unified derivation of simple evaporation models used in spray simulation is described and a new evaporation model is formulated. In the model, the Nusselt number, Sherwood number, and evaporation mass flux are derived using the traditional film theory. However, instead of determining the film thicknesses using the Nusselt and Sherwood numbers derived in the absence of high mass transfer rate, the film thicknesses are calculated from those derived from the fully numerical solutions which represent the realistic heat and mass transfer processes around a droplet. The model predictions are compared with the fully numerical solutions.

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