Existence and Approximation Results for Thermal Boundary Layer Equations of Reactive Flows

1991 ◽  
Vol 28 (4) ◽  
pp. 1030-1046
Author(s):  
P. Lesaint ◽  
J. Pousin
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Reactive Flows ◽  
Boundary Layer Equations

A singularity in thermal boundary-layer flow on a horizontal surface

1992 ◽  
Vol 242 ◽  
pp. 419-440 ◽  
Author(s):  
P. G. Daniels
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Numerical Solutions ◽  
Rational Numbers ◽  
Velocity Fields ◽  
Boundary Layer Equations ◽  
Layer Flow ◽  
Buoyancy Flows ◽  
Temperature And Velocity Fields

A thermal boundary layer, in which the temperature and velocity fields are coupled by buoyancy, flows along a horizontal, insulated wall. For sufficiently low local Froude number the solution terminates in a singularity with rising skin friction and falling pressure. The structure of the singularity is obtained and the results are compared with numerical solutions of the horizontal boundary-layer equations. A novel feature of the analysis is that the powers of the streamwise coordinate involved in the structure of the singularity do not appear to be simple rational numbers and are determined from the solution of a pair of ordinary differential equations which govern the flow in an inner viscous region close to the wall. Modifications of the theory are noted for cases where either the temperature or a non-zero heat transfer are specified at the wall.

The thermal boundary layer in the flow between converging plane walls

1963 ◽  
Vol 59 (1) ◽  
pp. 225-229 ◽  
Author(s):  
N. Riley
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Analytical Solutions ◽  
Thermal Boundary Layer ◽  
Parallel Plane ◽  
Boundary Layer Equations ◽  
Converging Flow

AbstractThe thermal boundary layer in the converging flow between non-parallel plane walls is studied. Analytical solutions of the boundary-layer equations are derived and the heat transfer across the wall is obtained from these solutions.

Solution of Similarity Transformation Equations for Boundary Layers Using Spreadsheets

2004 ◽  
Author(s):  
Mohammad H. N. Naraghi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Mechanics ◽  
Flat Plate ◽  
Thermal Boundary Layer ◽  
Similarity Transformation ◽  
Present Approach ◽  
Published Data ◽  
Boundary Layer Equations ◽  
Transfer Courses

A spreadsheet based solution of the similarity transformation equations of laminar boundary layer equations is presented. In this approach the nonlinear third order differential equations, for both the hydrodynamic and the thermal boundary layer equations, are discretesized using a simple finite difference approach which is suitable for programming spreadsheet cells. This approach was implemented to solve the similarity transform equations for a flat plate (Blasius equations). The thermal boundary layer result was used to obtain the heat transfer correlation for laminar flow over a flat plate in the form of Nu = Nu(Pr,Re). The relative difference between results of the present approach and those of published data are less than 1%. This approach can be easily covered in the undergraduate. Fluid Mechanics and Heat Transfer courses. Also, it can be incorporated in graduate Viscous Fluid Mechanics and Convection Heat Transfer courses. Application of the present approach is not limited to the flat plat boundary layer analysis. It can be used for the solution of a number of similarity transformation equations, including wedge flow problem and natural convection problems that are covered in graduate level courses.

Unified theory for the solutions of the unsteady thermal boundary-layer equation

1965 ◽  
Vol 61 (3) ◽  
pp. 809-825 ◽  
Author(s):  
G. N. Sarma
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Thermal Boundary Layer ◽  
Boundary Layer Equation ◽  
Steady Motion ◽  
Unsteady Motion ◽  
Main Stream ◽  
Unified Theory ◽  
Boundary Layer Equations ◽  
Special Cases

AbstractThe unsteady two-dimensional thermal boundary-layer equation linearized as by Lighthill is studied. Two different problems are considered mainly, one in Part I and the other in Part II. Part I deals with the solution when the temperature of the main stream is constant and that of the wall is unsteady and Part II when the temperature of the main stream is constant and the heat transfer from the wall is unsteady. Unified methods are developed from which the results for the stagnation flow and the flow along a flat plate, etc., can be derived as special cases. The results of the unsteady velocity boundary-layer equations analysed by Sarma are used and solutions are obtained in two cases, first, when the main stream is in steady motion and the wall is in an arbitrary motion and secondly when the main stream is in unsteady motion and the wall is at rest. The flat plate problem is considered in detail; the results agree with those given by Lighthill and Moore.

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