g The inside surface of a 17 mm inner diameter tube with a 2.4 mm thick wall indicates a temperature of 46 deg C. The outside temperature is 43 deg C. The tube is 5 m long. If the tube material has a conductivity of 0.15 W/m/K, estimate the heat transfer rate through the tube wall assuming SS 1D conduction. Indicate the direction of heat transfer with a or - sign ( meaning outward and vice versa). Express your answer using two significant digits in W.

-50 W

Explanation:

The heat transfer rate Q = kA(T₂ - T₁)/d where k = thermal conductivity of material = 0.15 W/m-K, A = surface area of tube = πdL where d = diameter of tube = 17 mm = 0.017 m and L = length of tube = 5 m, T₁ = inside temperature = 46 °C, T₂ = outside temperature = 43 °C and d = thickness of tube = 2.4 mm = 0.0024 m

Since Q = kA(T₂ - T₁)/d ,

Q = kπdL(T₂ - T₁)/d

substituting the values of the variables into the equation, we have

Q = 0.15 W/m-K × π × 0.017 m × 5 m(43 °C  - 46 °C )/0.0024 m

Q = 0.01275π Wm/K(-3 K )/0.0024 m

Q = -0.03825π Wm/0.0024 m

Q = -0.1202 Wm/0.0024 m

Q = -50.07 W

Q = -50 W

So, the heat transfer rate is -50 W meaning heat transfer out of the tube.