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

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, j_H (St·Pr^2/3) and the Fanning friction factor (c_f) is popularly considered to hold when St·Pr^2/3 equals to c_f/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·Pr^2/3 and c_f 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·Pr^2/3 decreases with decreasing c_f. The validity of Chilton–Colburn analogy is also verified by the inverse dependence of Reynolds number (Re) with c_f. Two modified nondimensional parameters “Π_Sμ and Π_Sk” 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 Π_Sμ and Π_Sk in flow friction is also investigated. The higher values of Π_Sμ and Π_Sk indicate the stronger influence on microconvection due to large variations in fluid properties.