When a fluid at supercritical pressure approaches the pseudo-critical temperature it experiences a strong variation in physical properties putting applicability of various turbulent flow modelings in question. Earlier numerical calculations showed, without exception, unrealistic over-predictions, as soon as the fluid temperature approached the pseudo-critical temperature. The over-predictions might have been resulted either from an inapplicability of widely used turbulence models or from an unrealistic treatment of the turbulent Prandtl number (Pr-t) as a constant. Recent research, both numerical and experimental, indicates that Pr-t is very likely a function of fluid-thermal variables as well as physical properties, when the gradients of physical properties of a fluid are significant. This paper describes the procedure fora new formulation of Pr-t which varies with physical properties and fluid-thermal variables. The application of the variable Pr-t was surprisingly successful in reproducing the fluid temperature in supercritical fluids flowing in small-diameter vertical tubes ranging from 4.57 to 20 mm. (C) 2015 Elsevier Ltd. All rights reserved.