Use of boundary-layer theory to predict the effect of heat transfer on the laminar-flow field in a vertical tube with a constant-temperature wall

AIChE Journal ◽  
1961 ◽  
Vol 7 (1) ◽  
pp. 112-123 ◽  
Author(s):  
Edward M. Rosen ◽  
Thomas J. Hanratty
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Laminar Flow ◽  
Flow Field ◽  
Constant Temperature ◽  
Vertical Tube ◽  
Boundary Layer Theory

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.

Boundary-layer theory for blast waves

1975 ◽  
Vol 71 (1) ◽  
pp. 65-88 ◽  
Author(s):  
K. B. Kim ◽  
S. A. Berger ◽  
M. M. Kamel ◽  
V. P. Korobeinikov ◽  
A. K. Oppenheim
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Flow Field ◽  
Classical Problem ◽  
Outer Region ◽  
Inviscid Flow ◽  
Boundary Layer Theory ◽  
Blast Waves ◽  
Matched Asymptotic Expansion ◽  
Flow Equations

The necessity for developing a boundary-layer theory in the case of blast waves stems from the fact that inviscid flow solutions often yield physically unrealistic results. For example, in the classical problem of the so-called non-zero counterpressure explosion, one obtains infinite temperature and zero density in the centre at all times even after the shock front deteriorates into a sound wave. In reality, this does not occur, as a consequence, primarily, of heat transfer that modifies the structure of the flow field around the centre without drastically affecting the outer region. It is profitable, therefore, to consider the blast wave as a flow field consisting of two regions: the outer, which retains the properties of the inviscid solution, and the inner, which is governed by flow equations including terms expressing the effects of heat transfer and, concomitantly, viscosity. The latter region thus plays the role of a boundary layer. Reported here is an analytical method developed for the study of such layers, based on the matched asymptotic expansion technique combined with patched solutions.

An Analytical Study of Laminar Film Condensation: Part 2—Single and Multiple Horizontal Tubes

1961 ◽  
Vol 83 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Michael Ming Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Horizontal Tube ◽  
Vertical Tube ◽  
Film Condensation ◽  
Transfer Coefficients ◽  
Inertia Effects ◽  
Horizontal Tubes ◽  
Laminar Film ◽  
Laminar Film Condensation

The boundary-layer equations for laminar film condensation are solved for (a) a single horizontal tube, and (b) a vertical bank of horizontal tubes. For the single-tube case, the inertia effects are included and the vapor is assumed to be stationary outside the vapor boundary layer. Velocity and temperature profiles are obtained for the case μvρv/μρ ≪ 1 and similarity is found to exist exactly near the top stagnation point, and approximately for the most part of the tube. Heat-transfer results computed with these similar profiles are presented and discussed. For the multiple-tube case, the analysis includes the effect of condensation between tubes, which is shown to be partly responsible for the high observed heat-transfer rate for vertical tube banks. The inertia effects are neglected due to the insufficiency of boundary-layer theory in this case. Heat-transfer coefficients are presented and compared with experiments. The theoretical results for both cases are also presented in approximate formulas for ease of application.

Utilizing the Integral Technique to Determine the Similarity Variable in Classical Heat Transfer Problems: One Dimensional Heat Conduction in a Finite or Semi-Infinite Solid

2013 ◽  
Author(s):  
Chris J. Kobus
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Boundary Layer ◽  
Variable Temperature ◽  
Boundary Layer Theory ◽  
Good Tool ◽  
Similarity Variable ◽  
Integral Technique ◽  
Independent Variable ◽  
Transfer Problems

In advanced heat transfer courses, a technique exists for reducing a partial differential equation where the dependent variable is a function of two independent variables, to an ordinary differential equation where that same dependent variable becomes a function of only one independent variable. The key to this technique is finding out what the similarity variable to make this transformation is. The difficulty is that the form of the similarity variable is not intuitive, and many heat transfer textbooks do not reveal how this variable is found in classical problems such as viscous and thermal boundary layer theory. It turns out that one way to find this variable is by utilizing the integral technique. By employing the integral technique to boundary layer theory, it will be shown that when the approximate functional relationship for the dependent variable (temperature, velocity, etc) can be represented by an nth order polynomial, the similarity variable can be found very simply. This is seen to be a good tool especially in heat transfer education, but has applications in research as well.

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