A solution to the turbulent Graetz problem by matched asymptotic expansions - I The case of uniform wall temperature

✍ Scribed by C.A. Sleicher; R.H. Notter; M.D. Crippen

• Publisher: Elsevier Science
• Year: 1970
• Tongue: English
• Weight: 948 KB
• Volume: 25
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(70)85119-3

✦ Synopsis

Consideration of heat transfer to a constant property fluid in fully developed turbulent flow in a pipe with a step change in wall temperature leads to a Sturm-Liouville problem. A first order asymptotic technique applied to this problem leads to estimates of heat transfer rates that are in poor agreement with numerical calculations[l].

Presented here is an extension of the first order analysis which yields higher approximations for the lower eigenfunctions.

The extension is an unusual application of the method of matched asymptotic expansions in which the expansion parameter is the eigenvalue and matching of both amplitude and phase of functions are required. Analytical expressions are derived but no numerical calculations are given.