Calculate Heat Loss in a Long, Thin-Walled Pipe

What is the heat loss per 1m length of the pipe?

Given a fluid at 300 K flowing through a long, thin-walled pipe of 0.2-m diameter enclosed in a concrete casing with outer surfaces maintained at 500 K.

Answer

The correct answer is "1341.288 W/m".

To calculate the heat loss per 1m length of the pipe, we need to use the shape factor formula and apply it to the given values of temperature, diameter, and length.

Given data:
Temperature T₁ = 300 K
Temperature T₂ = 500 K
Diameter d = 0.2 m
Length l = 1 m

First, we calculate the shape factor (SF) using the formula:
SF = 2πl / ln[(1.08b) / d]
SF = 2πl / ln[(1.08 x 1) / 0.2]
SF = 3.7258 x l

Next, we calculate the heat loss (Q) using the formula:
Q = SF x K(T₂ - T₁)
Q = 3.7258 x 1 x 1.8 x (500 - 300)
Q = 3.7258 x 1.8 x 200
Q = 1341.288 W/m

Therefore, the heat loss per 1m length of the pipe is 1341.288 W/m.