Determining the Rate of Heat Loss per Unit Length of a Pipe

To determine the rate of heat loss per unit length of the pipe, we can use the formula for heat transfer by conduction, which is given by:

Q = k * A * (ΔT/Δx)

Where:

Q is the heat transfer rate

k is the thermal conductivity

A is the cross-sectional area of the pipe

ΔT is the temperature difference between the steam and the casing

Δx is the length of the pipe

Since the pipe is long and thin-walled, heat loss occurs through the sides of the pipe and the bottom surface of the casing. We can neglect the top surface for this calculation.

The rate of heat loss per unit length can be calculated by dividing the total heat loss by the length of the pipe. To calculate the shape factor, thermal conductivity, and other relevant parameters, we can follow the steps mentioned:

Step 1: Calculate Shape Factor (S)

The shape factor (S) can be calculated using the formula:

S = (2π*L) / ln(1.08*1.75/0.6))

Step 2: Calculate Rate of Heat Loss (q)

The rate of heat loss (q) can be calculated using the formula:

q = 5.48L * 1.4 * (400-300)

Step 3: Determine Rate of Heat Loss per Unit Length (q')

The rate of heat loss per unit length can be determined by dividing the total heat loss by the length of the pipe:

q' = q / L

By following these steps and calculations, we can determine the rate of heat loss per unit length of the pipe when pressurized steam at 400 K flows through the long, thin-walled pipe enclosed in a concrete casing with maintained outer surfaces at 300 K.