Pressurized steam at 400 K flows through a long, thin-walled pipe of 0.6-m diameter. The pipe is enclosed in a concrete (stone mix) casing that is of square cross section and 1.75 m on a side. The axis of the pipe is centered in the casing, and the outer surfaces of the casing are maintained at 300 K. What is the rate of heat loss per unit length of pipe, in W/m

Rate of heat loss per unit length of pipe, q' = 767.01 W/m

Explanation:

Let q' be the Rate of heat loss per unit length

Let q be the Rate of heat loss

q' = q/L

Where L is the length of the pipe

Diameter, D= 0.6m

The rate of heat loss q is given by the formula: q = Sk(T₂ - T₁)

Where k is the thermal conductivity of the concrete at 300 K

k = 1.4 Wb/m-K (at 300K)

And S is the shape factor given by the formula:

S = 2πL/ ln(1.08w/D)

S = (2π*L) / ln(1.08*1.75/0.6))

S = (2π*L) / 1.147

S = 5.48 L

q = 5.48L*1.4(400-300)

q = 767.01 L

q' = q/L

q' = 767.01L/L

q' = 767.01 W/m