Thermal analysis of aquatic mammal such as a dolphin can provide insights into naturally occurring size distribution. The following data are pertinent to a particular species: length to diameter ratio L/D=10, blubber thickness to diameter ratio t/D=0.05. Average swimming speed V=3 m/s, metabolic heat generation rate q=23.5 kW/m^2, internal temperature 37 C degree, and blubber thermal conductivity of 0.2 W/m-K.
Which is the minimum water temperature of a dolphin of 2 meters long to survive? Use for the calculation of heat transfer coefficient the correlation for turbulen flow over a flat plate.
Thermal Properties of water are assumed: Pr=7, Kf=0.6 W/m-C and dynamic viscosity=1.08e^-3 N-s/m.