Thermal analysis of aquatic mammal such as a dolphin can provide insights into n

Question

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.

Explanation / Answer

For Turbulent flow over a flat plate

given :

v=3m/s ;

internal temp = 37C;

thermal conductivity k = 0.2 W/m-k;

length of dolphin = 2m;

Pr=7, Kf=0.6 W/m-C;

dynamic viscosity=1.08e^-3 N-s/m;

Rex = v*D/  dynamic viscosity;

L/D = 10 ; d= 2/10;

D=0.2 m

Rex= 3*  0.2/ 1.08e^-3 = 11.14

we know q = hA(t-to);

t=?;

Nu for flat palte turbulent flow =

Nux = 0.0296 * 11.14 ^4/5 * 7 ^1/3;

= 0.383;

now Nux= hL/k ;

we get h = Nux*k/L;

h= 0.0383;

q = hA (t -310);

A=pi*d*t    t =0.01                       

A= 6.28*10^-3;

we can thus get the value of t ;

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