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.

Spreadsheets Solutions of the Boundary Layer Equations

2004 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Fluid Mechanics ◽  
Undergraduate Students ◽  
Classical Problem ◽  
Boundary Layer Equations ◽  
Specialized Software ◽  
Layer Flow ◽  
Basic Course ◽  
The Impact

A classical problem in fluid mechanics and heat transfer is boundary layer flow over a flat plate. This problem is used to demonstrate a number of important concepts in fluid mechanics and heat transfer. Typically, in a basic course, the equations are derived and the solutions are presented in tabular or chart from. Obtaining the actual solutions is mathematically and numerically too involved to be covered in basic courses. In this paper, it is shown that the similarity solution and the solution to boundary layer equations in the primitive variables can easily be obtained using spreadsheets. Without needing much programming skills, or needing to learn specialized software, undergraduate students can use this approach and obtain the solution and study the impact of different parameters.

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.

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.

A New Algorithm on the Solutions of Forced Convective Heat Transfer in a Semi-Infinite Flat Plate

2011 ◽  
Vol 27 (1) ◽  
pp. 63-69 ◽  
Author(s):  
P.-Y. Tsai ◽  
C.-K. Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Decomposition Method ◽  
Thermal Boundary Layer ◽  
Adomian Decomposition Method ◽  
Padé Approximant ◽  
Temperature Fields ◽  
Pade Approximant ◽  
Adomian Decomposition

ABSTRACTIn this paper, a new algorithm is proposed to solve the velocity and temperature fields in the thermal boundary layer flow over a semi-infinite flat plate. Both the flow and heat transfer solutions are calculated accurately by the Laplace Adomian decomposition method, Padé approximant and the optimal design concept. The Laplace Adomian decomposition method (LADM) is a combination of the numerical Laplace transform algorithm with the Adomian decomposition method (ADM). A hybrid method of the LADM combined with the Padé approximant, named the LADM-Padé approximant technique, is introduced to solve the thermal boundary layer problems directly without any small parameter assumptions, linearizatons or transformations of the boundary value problems to a pair of initial value problems. The LADM-Padé approximant solutions here in are given to show the accuracy in comparison with different method solutions.

The Two-Flux Model Applied to Radiative Transfer and Forced Convection in the Laminar Boundary Layer on a Flat Plate

2000 ◽  
Author(s):  
Freddy Malpica ◽  
Nathaly Moreno ◽  
Andrés Tremante
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flat Plate ◽  
Thermal Boundary Layer ◽  
Radiative Heat ◽  
Heat Fluxes ◽  
Partial Differential ◽  
Approximate Methods ◽  
Combined Convection ◽  
Flux Model

This study presents the analysis of the thermal boundary layer considering combined convection and radiation in an absorbing, emitting and scattering medium flowing over a flat plate. At high temperatures the presence of thermal radiation alters the temperature distribution in the boundary layer, which in turn affects the heat transfer at the wall. In many industrial applications, such as in the cooling of turbine and compressors blades, radiative heat transfer plays an important role. The treatment of heat transfer by combined convection and radiation in the boundary layer leads to a set of partial differential and integrodifferential equations, which must be solved simultaneously. The exact solutions are seldom possible and the investigators resort to approximate methods. In the present analysis the two-flux model is used to describe the radiative heat flux in the energy equation. This model reduces the equations that govern the problem to a set of coupled partial differential equations. A finite difference scheme, called “method of columns”, is used to transform the resulting equations into an ordinary differential equation system which simplifies the solution. Results for the temperature profile and heat fluxes showed close agreement with the thin and thick limits. The method proposed proves to be useful to investigate the effect of the different radiation parameters on the thermal boundary layer, and also to be accurate enough for engineering applications.

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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