Energies, Vol. 18, Pages 4074: Methods for Measuring and Computing the Reference Temperature in Newton’s Law of Cooling for External Flows

Energies doi: 10.3390/en18154074

Authors:
James Peck
Tom I-P. Shih
K. Mark Bryden
John M. Crane

Newton’s law of cooling requires a reference temperature (Tref) to define the heat-transfer coefficient (h). For external flows with multiple temperatures in the freestream, obtaining Tref is a challenge. One widely used method, referred to as the adiabatic-wall (AW) method, obtains Tref by requiring the surface of the solid exposed to convective heat transfer to be adiabatic. Another widely used method, referred to as the linear-extrapolation (LE) method, obtains Tref by measuring/computing the heat flux (qs′′) on the solid surface at two different surface temperatures (Ts) and then linearly extrapolating to qs′′=0. A third recently developed method, referred to as the state-space (SS) method, obtains Tref by probing the temperature space between the highest and lowest in the flow to account for the effects of Ts or qs′′ on Tref. This study examines the foundation and accuracy of these methods via a test problem involving film cooling of a flat plate where qs′′ switches signs on the plate’s surface. Results obtained show that only the SS method could guarantee a unique and physically meaningful Tref where Ts=Tref on a nonadiabatic surface qs′′=0. The AW and LE methods both assume Tref to be independent of Ts, which the SS method shows to be incorrect. Though this study also showed the adiabatic-wall temperature, TAW, to be a good approximation of Tref (<10% relative error), huge errors can occur in h about the solid surface where |Ts−TAW| is near zero because where Ts=TAW, qs′′≠0.

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