Determine the equilibrium temperature of the outside

Question

QUESTION 1

Hot water at 73^oC is flowing through an insulated steel pipe (od 25.4 mm, id 21.7 mm, k = 53 W/mK) across a room with an air temperature of 28^oC. The water flow has a convection coefficient of 190 W/m²K, and the air outside the pipe has a convection coefficient of 12 W/m²K (including any radiation effects). The steel pipe has a layer of rust (k = 0.15 W/mK) 1 mm thick on the inside, and a layer of insulation (k= 0.025 W/mK) 5 mm thick on the outside.

Prove that the steel pipe outer radius is greater than the critical radius.

Calculate the rate of heat transfer from a 4 metre length of the pipe.

QUESTION 2

Water with an average temperature of 17^oC (Ρ = 1000 kg/m³, k = 0.59 W/mK, Pr = 8.1, μ = 1.14x10^-3 kg/ms) flows through a 15 mm (inside) diameter pipe with a wall temperature of 16^oC at a flow rate of 0.3 litres/sec. (Note: 1 m³ = 1000 litres)

Calculate the Reynolds number and the Nusselt Number.

Calculate the rate of heat transfer from the water to the pipe wall per metre of pipe length.

QUESTION 3

A shell-and-tube heat exchanger with two shell passes and eight tube passes is used to heat ethanol (Cp = 2650 J/kgK) from 15^oC to 65^oC at a flow rate of 4.5 kg/s. The heat is provided by 3 kg/sec. of hot water (C_p = 4180 J/kgK) which enters the tubes at 97^oC. The overall heat transfer coefficient for the heat exchanger is 780 W/m²K.

Calculate the average temperature difference between the two fluids. Calculate the required heat transfer surface area.

QUESTION 4

The temperature on the outside surface of a wall is 40^oC, and the air temperature is 20^oC. The wall is 6 m high and 20 m long. There is no wind.

Calculate the Rayleigh number and the Nusselt number.

Calculate the rate of heat transfer by natural convection from the wall.

QUESTION 5

The wall of a building is exposed to 650 W/m² of solar radiation. The surrounding surfaces are at an average temperature of 30^oC, and the air temperature is 26^oC. Heat is conducted through the wall into the building at a rate of 280 W/m². Heat is both radiated and convected from the outside surface of the wall to the surrounding surfaces and the air. The emissivity of the outside surface of the wall is 0.95 at 300 K, and the solar absorptivity is 0.62. The convection coefficient from the outside surface of the wall is 4 W/m²K.

Determine the equilibrium temperature of the outside surface of the wall.