An uninsulated, thin-walled pipe of 100-mm diameter is used to transport water to equipment that operates outdoors and uses the water as a coolant. During particularly harsh winter conditions, the pipe wall achieves a temperature of -15 degree C and a cylindrical layer of ice forms on the inner surface of the wall If the mean water temperature is 3 degree C and a convection coefficient of 2000 W/m^2 middot K is maintained at the inner surface of the ice, which is at 0 degree C, what is the thickness of the ice layer?

4.6 mm

Explanation:

Given data includes:

thin-walled pipe diameter = 100-mm =0.1 m

Temperature of pipe = -15° C = (-15 +273)K =258 K

Temperature of water = 3° C = (3 + 273)K = 276 K

Temperature of ice = 0° C = (0 +273)K =273 K

Thermal conductivity (k) from the ice table = 1.94 W/m.K  ;  R = 0.05

convection coefficient =2000 W/m².K

The energy balance can be expressed as:

where;

      -------------   equation (1)

 ------------ equation(2)

Equating both equation (1) and (2); we have;

Replacing the given data; we have:

r = 0.0454

The thickness (t) of the ice layer can now be calculated as:

t = (R - r)

t = (0.05 - 0.0454)

t = 0.0046 m

t = 4.6 mm

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