Wall heat recirculation and exergy preservation in flow through a small tube with thin heat source

Abstract

Theoretical studies have been made on heat transfer and exergy analysis of flow through a narrow tube with heat recirculating wall and embedded thin heat source. Heat transfer analysis is based on numerical solution of conservation equations of mass, momentum and energy, while the exergy analysis is based on flow exergy balance and entropy transport equation. It has been observed that the ratio of heat recirculation to heat loss (QR/QL) increases with increase in the ratio of thermal conductivity of solid wall to that of working fluid (ks/kg) and Peclet number of flow (Pe), while it decreases with an increase in external Nusselt number (NuE). The ratio QR/QL has a maximum with the ratio of wall thickness to tube radius (tw/R). The optimum value of tw/R depends only on ks/kg and reduces from a value of 0.2 at ks/kg=330 to a value of 0.125 at ks/kg=850, and then remains almost constant for any further increase in ks/kg. The volumetric entropy generation rate in the fluid flow reaches a maximum at a radial location close to the inner surface of the wall, while the entropy generation in solid wall, being more than that of the fluid, is radially uniform. The volumetric entropy generation is found to be confined within the upstream region of the heat source. Second law efficiency increases with a decrease in tw/R and NuE, but with an increase in Pe. It remains almost constant with ks/kg.