Free convection boundary layer heat transfer analysis of isothermal horizontal square plates

Author

• Konstantinos E. Tsouras, New Jersey Institute of Technology

Document Type

Thesis

Date of Award

5-31-1985

Degree Name

Master of Science in Mechanical Engineering - (M.S.)

Department

Mechanical Engineering

First Advisor

P. Hrycak

Second Advisor

Lawrence Jay Schmerzler

Third Advisor

E. S. Geskin

Abstract

The theoretical study presented here examines free convective boundary layer flow and heat transfer over isothermal horizontal square plates.

The boundary layer equations subjected to the appropriate boundary conditions were solved by using Von Karman's approximate integral technique. The analysis was performed by considering an axisymmetric boundary layer because the analyzed phenomenon is three-dimensional in nature. Three-dimensional boundary layer analysis, however, is complicated and the work involved is rather tedious. Consequently, the axisymmetric boundary layer offers a useful alternative. Unfortunately, it was found that this type of analysis is applicable to the case of an upward-facing heated plate only; for the case of a downward-facing heated plate it fails to effect a solution. Analytical expressions were derived for the average Nusselt number Nu_L based on the side L of the square plate both for the laminar and for the turbulent boundary layer. The derived closed-form solutions are presented in the form Nu_L=cPr^mGrⁿ, where c=const is a numerical coefficient, Pr is the Prandtl number, Gr is the Grashof number and m, n are fractional powers. Comparison with available theoretical expressions and experimental correlations reveals satisfactory agreement.

The second part of the analysis considers solutions of the boundary layer region around the stagnation point of the flow. In this region the flow is always laminar. To the author's knowledge, axisymmetric stagnation point flow has never been investigated before as far as natural convection is concerned. It is found that for the case of a downward-facing heated plate the solution is identical to the solution of the same problem in forced convection. Important results presented include the variations of the similarity function f and its derivatives f' and f" with the vertical coordinate and the variation of the wall temperature gradient (dθ/dη)_w with Prandtl number. For the case of the upward-facing heated plate the same solution technique is used - modified, of course, to correspond to the geometry of the problem. However, it is found that in this case the function f diverges from its constant value of unity at infinity - which violates an important boundary condition of the problem - so that solution cannot be achieved.

Recommended Citation

Tsouras, Konstantinos E., "Free convection boundary layer heat transfer analysis of isothermal horizontal square plates" (1985). Theses. 3485.
https://digitalcommons.njit.edu/theses/3485