RESEARCH PAPERS: Forced Convection

Forced Convection Heat Transfer From Microstructures

[+] Author and Article Information
S. W. Ma, F. M. Gerner

Department of Mechanical, Industrial, and Nuclear Engineering, University of Cincinnati, Cincinnati, OH 45221-0072

J. Heat Transfer 115(4), 872-880 (Nov 01, 1993) (9 pages) doi:10.1115/1.2911382 History: Received April 01, 1992; Revised March 01, 1993; Online May 23, 2008


For many microstructures, which utilize forced convection cooling, the average thickness of the thermal boundary layer is of the same order as the length of the heated element. For these cases, thermal boundary layer theory is invalid. The elliptic energy equation for steady, two-dimensional incompressible flow over a finite flat plate with insulated starting and ending lengths is analyzed utilizing matched asymptotic expansions. A conventional Blasius technique transforms the energy equation into an elliptic-to-parabolic equation. A new technique is used that treats the boundary layer solution as the outer expansion of the elliptic-to-parabolic equation. The inner expansion, or leading-edge equation, is found by stretching to independent variables simultaneously. Trailing-edge effects are considered using superposition methods. A first-order composite formula is constructed based on the outer and inner expansions, which is uniformly valid over the entire surface of the plate. With the aid of statistics, a correlation is developed for the average Nusselt number

Nul = 0.6626Pr1/3Rex0 + l1/2 1 − x0x0 + l3/42/3 1 + 0.3981(x0/l)0.5987Pr0.3068Rex00.4675
  for 0.5 ≤ Pr ≤ 100, x0/l ≤ 50, and Rex0 ≥ 100
where x0 and l represent the lengths of the insulated starting section and the heated element, respectively. This correlation is accurate to within 2 percent as compared with the entire composite solution.

Copyright © 1993 by The American Society of Mechanical Engineers
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