Heat Transfer in the Transitional Flow Regime

Abstract

Transitional flow, whereby the motion of a fluid changes from laminar to turbulent flow, was successfully identified by Reynolds (1883) almost 130 years ago. According to ASHRAE (2009), for a round pipe, in general, laminar flow exists when the Reynolds number is less than 2 300. Fully turbulent flow exists when the Reynolds number is larger than 10 000 and transitional flow exists for Reynolds numbers between 2 300 and 10 000. Despite much work on transition and even though it is of considerable importance in determining pressure drop and heat transfer in convective flow, the underlying physics and the implications of this phenomenon have eluded complete understanding (Obot et al., 1990). ASHRAE further states that predictions are unreliable in the transitional flow regime. Cengel (2006) mentions that although transitional flow exists for Reynolds numbers between 2 300 and 10 000, it should be kept in mind that in many cases the flow becomes fully turbulent when the Reynolds number is larger than 4 000. It is normally advised when designing heat exchangers to remain outside the transitional flow regime due to the uncertainty and flow instability in this region. For this reason, little design information is available with specific reference to heat transfer and pressure drop data in the transitional flow regime. It has been known that there is a relationship between pressure drop and heat transfer generally referred to as the Reynolds analogy. Therefore, the relationship between friction factor and Nusselt number was studied by many and an overview of all the contributions on the subject is given by Colburn (1933). Obot et al. (1990) followed up on this previous work to investigate the role of transition in determining friction and heat transfer in smooth and rough passages. Later on they (Obot et al., 1997) took measurements of heat transfer and pressure drop in smooth tubes in laminar, transitional and turbulent flow over a wide range of Prandtl numbers. Garcia et al. (2005) experimentally investigated helical wire coils fitted inside a round tube in order to characterise their thermohydraulic behaviour in laminar, transitional and turbulent flow. They did experiments over a wide range of Reynolds and Prandtl numbers and they found that at low Reynolds numbers, wire coils behave as a smooth tube but accelerate transition to critical Reynolds numbers down to 700. Furthermore, within the transition region, if wire coils are fitted inside a smooth tube heat exchanger, the heat transfer rate can be increased up to 200% while maintaining a constant pumping power. This is in comparison with the turbulent flow regime where wire coils increase pressure drop up to nine times and heat transfer up to four times compared with empty smooth