New correlations for heat transfer in parallel-plate ducts at low Peclet number

Abstract

Calculations of heat transfer in duct flows generally neglect the effect of axial heat conduction within the fluid. However, in some situations, this effect must be taken into account. The decision on whether or not to consider this phenomenon is driven by the value of the Peclet number. A low value, with 100 commonly considered the threshold, indicates that axial conduction, i.e., conduction parallel to the flow, should be accounted for in the calculations. Microfluidic devices, systems using liquid metal coolant or microchannel heat exchangers are some examples of applications where low Peclet flow conditions may be encountered. While exact analytical solutions exist for such cases, they are often impractical to use for common engineering design purposes due to their mathematical complexity. The present work proposes three new correlations for the estimation of the fully developed Nusselt number, thermal entry length and local Nusselt number in the entrance region of a laminar flow within a parallel-plate duct with constant wall temperature. These correlations allow the simple and accurate evaluation of useful engineering quantities, thus avoiding lengthy and complex calculations. They were developed using rational approximation theory and are effective on a wide range of Peclet numbers and axial coordinates. Accuracy of under 1% relative error is achieved with each of the three correlations when results are compared against exact analytical series solution values.