Numerical Re-examination of Chilton–Colburn Analogy for Variable Thermophysical Fluid Properties

Abstract

The Chilton–Colburn analogy is very helpful for evaluating the heat transfer in internal forced flows. The Chilton–Colburn analogy between the Chilton–Colburn j-factor for heat transfer, jH (St·Pr2/3) and the Fanning friction factor (cf) is popularly considered to hold when St·Pr2/3 equals to cf/2, for constant fluid properties. The physical fluid properties, namely, viscosity and thermal conductivity, are generally a function of temperature for microconvective water flow due to a quite steep temperature gradient. Therefore, in present investigation, the validity of Chilton–Colburn analogy between St·Pr2/3 and cf is re-examined for laminar microconvective flow with variable thermophysical fluid properties. It is observed that the Chilton–Colburn analogy is valid only for that portion of the flow regime, where St·Pr2/3 decreases with decreasing cf. The validity of Chilton–Colburn analogy is also verified by the inverse dependence of Reynolds number (Re) with cf. Two modified nondimensional parameters “ΠSμ and ΠSk” are emerged from the nondimensional form of 2D, steady-state, incompressible, pure continuum-based, laminar conservation of momentum and energy equations, respectively. These modified nondimensional parameters show the significance of variable fluid properties in momentum transport and energy transport. Additionally, the role of ΠSμ and ΠSk in flow friction is also investigated. The higher values of ΠSμ and ΠSk indicate the stronger influence on microconvection due to large variations in fluid properties.