Structural and numerical identifiability of thermal resistances in plate fin-and-tube heat exchangers using manufacturer catalog data

Abstract

Plate fin-and-tube heat exchangers, commonly known as heating/cooling coils, are widely used in HVAC systems to transfer heat to or from air. A problem of practical interest in coil simulation is to identify the thermal resistances on the air and liquid sides using manufacturer catalog data. Manufacturers rarely provide detailed information (geometry and circuitry) of the coils they sell or install in factory-made equipment such as air handling units or fan-coils; they just report the performance of the coil at a few typical operating conditions. This paper examines whether it is mathematically possible to back-calculate the thermal resistances on the air and liquid sides using a set of performance data that is disturbed by noise (e.g. measurement errors) and consists of operating cases in which none of the two thermal resistances can be neglected. The first part of the paper discusses the structural identifiability problem, that is, the mathematical possibility of fitting Nusselt-type correlations for air and liquid, as well as a constant resistance for the wall. The second part of the paper discusses the possibility of calculating the numerical value of the parameters of the Nusselt correlations (constant or constant and exponent) using noisy data. The analysis is applied to a typical coil, which is simulated by means of a mathematical model