Turbulent graetz problem

Chemical

Engineering

Science,

197

1,Vol. 26, p. 567.

Pergamon

Press.

Printed

in Great

Britain.

Turbulent Graetz problem (Received

20 October

IN A RECENT interesting paper Sleicher, Notter and Crippen [8] give a solution to the turbulent Graetz problem using the method of matched asymptotic expansions. As one of the motivations for their work the authors mention the case of heat transfer to liquid metals (p. 845, [8]). It may be useful to remark that for that particular case their equation,

is applicable only with reservations: this equation implicitly assumes that the axial conduction term in the fluid may be neglected under all conditions, or otherwise put that the “turbulent P&let number” is large. It is fair to assume that for the how of liquid metals this is certainly not invariably the

case. Then the equation given would be insufficient to define the problem; see the authors’ Ref. [2]. p. I 17. Thus the solution of the complete problem would have to include a double coordinate asymptotic expansion, if such can be found. In this connexion authors’ Ref. [6] is not of great help. For the laminar case this is brought-out cf. in [9]. The writer would not like to comment upon the correctness of the order of matching at the present time. However, it may be interesting to note that a turbulent “Graetz problem” was solved by Latzko [ 101 some time ago, using a variational technique. He assumed a “l/7 power relationship” for the velocity distribution. Department of Mechanical Engineering University of British Columbia Vancouver 8, B.C., Canada

REFERENCES A., NOTTER R. H. and CRIPPEN M. D., Chem. Engng ZEEV and NEILSON J. E., Can.J. them. Engng 1969 47 341. H., 2. angew. Math. Mech. 1921 1268.

PI SLEICHERC. 191 ROTEM [lOI LATZKO

1970)

567 CESVol.26No.4-E

Sci. 1970 25 845.

ZEEV

ROTEM