Review of Some Experimental Studies of Turbulent Mixed Convection Covering a Wide Range Prandtl Number
NURETH-14 - 2011 September 25-30

Presented at:
2011 September 25-30
Toronto, Canada
Session Title:
A12-1 Introductory Session on Non-Unity Prandtl Number Flows

J.D. Jackson (University of Manchester)


The early experimental studies of buoyancy-influenced turbulent convective heat transfer to fluids flowing upwards and downwards in long uniformly heated vertical tubes were mainly performed using water at atmospheric pressure as the working fluid.  In addition, some experiments using air were reported and even some using mercury.  At that time there was also quite a lot of interest in heat transfer to water at supercritical pressure and also carbon dioxide. More recently, experimental results have been obtained using liquid sodium.  The Prandtl numbers in the studies referred to above cover a wide range of values, being well in excess of unity under some conditions in the case of the supercritical pressure fluids and atmospheric pressure water, just under unity in the case of air, much less than unity in the case of mercury and even lower in the case of liquid sodium.  Over the years a good general understanding has gradually been achieved of the complex manner in which buoyancy affects heat transfer in conventional fluids such as water and air.  Up to a point, the behaviour in the case of a liquid metal such as mercury can be reconciled with such arguments.  However, this is certainly not so in the case of liquid sodium.  In the present paper results from a number of experimental studies of buoyancy-influenced heat transfer in vertical tubes are reviewed.  This is done with the aim of providing a picture of observed behaviour consistent with our understanding of the basic mechanisms of convective heat transfer, taking account of the complicated manner in which the mean motion, turbulence and the heat transfer are affected by buoyancy.  The starting point is to view convective heat transfer in wall shear flows in terms of the local balance between diffusion of heat (turbulent and molecular) and advection of heat by the flowing fluid.  Prandtl number affects the radial temperature profile and therefore the variation of density across the shear flow and, in turn, the extent of the buoyancy-influenced region across the shear layer.  Buoyancy affects the mean motion, aiding it in the case of upward flow and opposing it in the case of downward flow.  Thus, in the case of buoyancy-aided flow advection of heat is increased and for buoyancy-opposed flow it is reduced.  Buoyancy also has the effect of modifying the distribution of shear stress across a wall shear flow which affects the production of turbulence, reducing it with onset of buoyancy influence for upward flow and impairing heat transfer by diffusion.  This trend eventually changes with further increase of buoyancy influence.  For downward flow, turbulence production and turbulent heat transfer are systematically enhanced with increase of buoyancy influence.  In turbulent flow at sufficiently high Peclet number (turbulent flow of fluids with Prandtl numbers of about unity and above), the diffusion of heat by turbulence is of dominant importance and so the effects of buoyancy on heat transfer are as just indicated.  However in the case of fluids having Prandtl numbers very much less than unity (where the Peclet number is smaller), diffusion of heat by turbulence is of secondary importance and so, even if buoyancy has had a significant effect on the turbulence in the flow, its effect on heat transfer is no longer dominant.   So, enhancement of heat transfer occurs with upward flow due to the increased advection and impairment occurs with downward flow.  These simple physical ideas enable the seemingly anomalous heat transfer behavior in the case of fluids having very low Prandtl number to be reconciled with the completely different behavior of fluids with higher Prandtl number.  The main objective of this paper is to illustrate these ideas with reference to a selection of experimental data and to discuss them.  The data used to do this was mostly produced by the author, his colleagues and students.  Some of investigations are not widely known about.  So, this paper should be helpful to those who currently have a particular interest in the topic covered.

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