Chapter 4

Heat transfer and diffusion of particles

Steam pipe insulation

Take 15 minutes to prepare this exercise.

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A detailed solution is then proposed to you.

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Let us consider a cylindrical steel line of internal radius, of external radius and of length.

We note the thermal conductivity of steel.

It canalizes overheated steam at the temperature .

The outer air temperature is .

The pipeline is insulated with a cylindrical insulator of , thickness, and with its conductivity.

Steam pipe insulation

Question

Determine the thermal resistancesof the steel pipeline and of the insulator.

Hint

Solution

We consider a steel cylinder of radius, with the same axis than the steam line.

In stationary mode, the flux through the lateral surface of this cylinder is constant :

Thus :

After integrating between and  :

We can deduce the thermal resistance of steel :

Likewise, the thermal resistance of the insulator is :

Question

We note  the convective heat transfer coefficient between the steam and the steel, and the one between the insulator and the outer air.

Using Newton's law, determine the convection resistance of the pipeline that is insulated.

Hint

Solution

The convective heat flow between the water and the steel is (oriented towards the ouside of the line) :

Thus, the convective thermal resistance is :

Likewise, the resistance between the insulator and the outer air is :

Question

Determine the equivalent thermal resistance of the insulated pipe .

Hint

Solution

The different thermal resistances, carrying the same heat flow, are series resistances.

Thus, the equivalent resistance is the sum of the resistances that were calculated in the previous questions :

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