A pipe is wrapped in an insulating material. The radial distances to the inner a

Question

A pipe is wrapped in an insulating material. The radial distances to the inner and outer surfaces of the insulation are ri =1 cm and ro = 2 cm , respectively. Temperature measurements are made across the thickness of the insulation, and the temperature profile is found to have the form: T(r) - C1 ln r / ro + C2 . Do the temperature measurements agree with a steady-state temperature profile in the insulation? Suppose the pipe is filled with frozen ice at Ti = 0 degree C. The outer surface temperature of the insulation is at To =18 degree C. After tau 1/2 = 3 hours, half of the water (by weight) is still ice. Using your experimental measurements, determine the thermal conductivity of the insulation material. For ice, the latent heat release on melting is hlv = 334.0 kJ/kg, and density is rho ice =0.9167 g/cm3.

Explanation / Answer

yes, it agrees with the steady state temperature profile in te insulation,

vh/2 is the amount of heat energy transferredto ice, where h= latent heat of melting=18*dx*K/(2**x*l)which continously changes

integrate it from r1 to r2 =9k/l *ln(r2/r1)

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