Combined Convection–Conduction–Radiation Boundary Layer Flows Using Optimal Control Penalty Finite Elements

1989 ◽  
Vol 111 (2) ◽  
pp. 433-437 ◽  
Author(s):  
L. R. Utreja ◽  
T. J. Chung
Keyword(s):  
Boundary Layer ◽  
Optimal Control ◽  
Finite Elements ◽  
Optical Thickness ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Boundary Layer Flows ◽  
Combined Convection ◽  
Radiation Boundary ◽  
Plate Geometry

Numerical solutions for combined convection and radiation in a laminar boundary layer on an isothermal wall are obtained using optimal control penalty (OCP) finite elements. The integro-differential energy equation is solved without any limitation of optical thickness. The expression for the divergence of radiation flux containing integral terms is written in terms of a one-dimensional radiation field for a flat plate geometry. The radiation interaction effect on the temperature distribution in the boundary layer is described. The solution of the integro-differential energy equation is then compared with known solutions in the limits of optical thickness.

Approximate Solution—One-Dimensional Energy Equation for Transient, Compressible, Low Mach Number Turbulent Boundary Layer Flows

1989 ◽  
Vol 111 (3) ◽  
pp. 619-624 ◽  
Author(s):  
J. Yang ◽  
J. K. Martin
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Turbulent Boundary Layer ◽  
Internal Combustion Engines ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Empirical Relation ◽  
Approximate Solutions ◽  
Low Mach Number ◽  
One Dimensional

Unsteady surface heat-flux and temperature profiles in the transient, compressible, low Mach number, turbulent boundary layer typically found in internal combustion engines have been determined by numerically integrating a linearized form of the one-dimensional energy equation. An empirical relation for μt/μ has been used to consider turbulent conductivity. Approximate solutions have been acquired by multiparameter fits to the numerical solutions. Comparisons of the approximate solutions with motored engine experiments show good agreement.

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.

The Interaction of Thermal Radiation in Optically Thick Boundary Layers

1967 ◽  
Vol 89 (4) ◽  
pp. 309-312 ◽  
Author(s):  
J. L. Novotny ◽  
Kwang-Tzu Yang
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Optical Thickness ◽  
Asymptotic Expansions ◽  
Energy Equation ◽  
Two Dimensional ◽  
Small Temperature ◽  
Dimensional Boundary

An analysis is presented to examine the role of the Rosseland or optically thick approximation in convection-radiation interaction situations. The analysis is formulated for the flow of a gray gas in a laminar two-dimensional boundary layer under the restriction of small temperature differences within the flow field. The boundary-layer energy equation is treated using the method of matched asymptotic expansions based on a parameter which characterizes the optical thickness of the gas. Two illustrative examples of the resulting equations are presented.

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.

A Unified Treatment for Local Thermal Nonequilibrium Free, Forced, and Mixed Convective Boundary Layer Flows Over an Arbitrarily Shaped Nonisothermal Body in a Fluid Saturated Porous Medium

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Xiaohui Bai ◽  
Yuan Yi ◽  
Fujio Kuwahara ◽  
Akira Nakayama
Keyword(s):  
Boundary Layer ◽  
Convective Boundary Layer ◽  
Energy Equation ◽  
Solid Phase ◽  
Saturated Porous Medium ◽  
Thermal Boundary Layer Thickness ◽  
Boundary Layer Flows ◽  
Convective Boundary ◽  
Fluid Saturated Porous Medium ◽  
Integral Energy

Abstract A unified integral solution procedure has been proposed to analyze all possible Darcian local thermal nonequilibrium (LTNE) free, forced, and mixed convective boundary layer flows, commonly encountered in porous media engineering applications. The heated body may be arbitrarily shaped, and its temperature may vary over the surface. The integral energy equation for the solid phase yields an algebraic equation between the dimensionless fluid thermal boundary layer thickness and its ratio to the solid-phase counterpart, while the integral energy equation for the fluid phase reduces to a first order ordinary differential equation in terms of the dimensionless fluid thermal boundary layer thickness. This set of the equations for determining the local Nusselt number of our primary interest proved to be valid for all possible Darcian cases of LTNE free, forced, and mixed convective boundary layer flows over an arbitrarily shaped nonisothermal body in a fluid saturated porous medium. Asymptotic expressions for the cases of arbitrary shapes were also obtained analytically for both leading edge and far downstream regions. The results are found to agree well with available direct numerical integration results. Furthermore, the regime map has been constructed to show the boundary layer transition point from the LTNE to equilibrium. The proposed unified method is found quite useful when designing thermal engineering systems associated with fluid saturated porous media.

Sign in / Sign up

Export Citation Format

Share Document