Eur. Phys. J. Plus (2014) 129: 120
https://doi.org/10.1140/epjp/i2014-14120-5

Regular Article

A note on the exact temperatures of free two-dimensional and circular jets

Department of Mathematics, Hacettepe University, Beytepe, 06532, Ankara, Turkey

^* e-mail: turkyilm@hacettepe.edu.tr

Received: 7 March 2014
Revised: 12 April 2014
Accepted: 18 May 2014
Published online: 17 June 2014

Abstract

A two-dimensional laminar free jet and a circular axisymmetric free jet issuing into an otherwise quiescent fluid are revisited. Making use of the well-documented flow results in the literature, exact temperature profiles of both jets are shown to exist, some of which are presented for a variety of Prandtl numbers of interest. In particular, closed-form solutions are presented valid for the entire Prandtl numbers for the circular-free-jet problem. These can be easily made use of as test cases in practical applications. Circular free jet is shown to admit higher temperature values as compared with the two-dimensional free jet. It is also ensured that for these profiles a temperature integral condition due to the thermal flux is satisfied.