Chemical Engineering - Heat Transfer - Discussion

Please give valid explanation.

Please give explanation for this question.

It is about the insulation done on the bodies, as a graph of " heat loss vs radius of insulation".

In my opinion, the increase of the heat transfer area may be a high cost.

This is because the fixed costs of the equipment (such as the cost of the shell, tube sheets, and other components) are spread over a larger surface area, leading to economies of scale.

What does it mean to pass through maxima?

Please explain.

Why cost per unit area decreases with increasing area?

This is due to economies of scale in heat exchanger manufacturing. The purchased cost of a shell-and-tube heat exchanger does not increase linearly with area; instead, it follows a power-law relationship:

Typically, for shell-and-tube exchangers, the exponent is approximately $n approximately 0.6$ .

Cost per unit area:
Since $n-1$ is negative, the cost per unit area decreases as area $A$ increases .

Practical reason:

Fixed costs (design, fabrication setup, shells, heads) are spread over more surface area
Larger exchangers use material more efficiently (less material per unit area)
Manufacturing and installation costs don't scale linearly.

So, the correct Answer is : Option B — decreases.