Question

Hot liquid is flowing in a steel pipe with an inner diameter of $D_{1}=22 \mathrm{~mm}\( and an outer diameter of \)D_{2}=27 \mathrm{~mm}$. The inner surface of the pipe is coated with a thin fluorinated ethylene propylene (FEP) lining. The thermal conductivity of the pipe wall is $15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}$. The pipe outer surface is subjected to a uniform flux of \(1200 \mathrm{~W} / \mathrm{m}^{2}\) for a length of \(1 \mathrm{~m}\). The hot liquid flowing inside the pipe has a mean temperature of $180^{\circ} \mathrm{C}\( and a convection heat transfer coefficient of \)50 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. The interface between the FEP lining and the steel surface has a thermal contact conductance of $1500 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. Determine the temperatures at the lining and at the pipe outer surface for the pipe length subjected to the uniform heat flux. What is the total thermal resistance between the two temperatures? The ASME Code for Process Piping (ASME B31.3-2014, A.323) recommends a maximum temperature for FEP lining to be \(204^{\circ} \mathrm{C}\). Does the FEP lining comply with the recommendation of the code?

Short answer

Question: Determine the temperatures at the lining and the pipe outer surface, and check if the FEP lining complies with the ASME Code for Process Piping, given the heat transfer rate through the wall, the thermal resistance of the steel wall, FEP lining-steel interface, and convection at the pipe inner surface.

Step-by-step solution

Calculate the heat transfer rate

We are given that the pipe outer surface is subjected to a uniform flux of \(1200\mathrm{~W/m^2}\). To find the total heat transfer rate (\(\dot{Q}\)) through the wall, we multiply the flux by the surface area (assuming a length of 1m, and using the outer diameter): $$\dot{Q} = 1200 \frac{\text{W}}{\text{m}^2} \cdot \pi D_2 \times 1\text{m}$$

Calculate the thermal resistance of the steel wall

The thermal resistance of the steel wall (\(R_{steel}\)) can be found using the formula: $$R_{steel} = \frac{D_2 - D_1}{2 \pi \lambda_\text{steel} L}$$ where \(\lambda_\text{steel}\) is the thermal conductivity of the steel (15 W/mK) and \(L\) is the length of the pipe (1m).

Calculate the thermal resistance of the FEP lining-steel interface

The thermal resistance of the FEP lining-steel interface (\(R_\text{fep-steel}\)) can be found using the formula: $$R_\text{fep-steel} = \frac{1}{h_\text{fep-steel} A}$$ where \(h_\text{fep-steel}\) is the thermal contact conductance (1500 W/m²K) and \(A\) is the surface area of the interface (using the inner diameter, and assuming a length of 1m): $$A = \pi D_1 \times 1\text{m}$$

Calculate the thermal resistance of the convection at the pipe inner surface

The thermal resistance of the convection at the pipe inner surface (\(R_\text{convection}\)) can be found using the formula: $$R_\text{convection} = \frac{1}{h_\text{convection} A}$$ where \(h_\text{convection}\) is the convection heat transfer coefficient (50 W/m²K).

Calculate the total thermal resistance

The total thermal resistance (\(R_\text{total}\)) is the sum of the three resistances calculated in steps 2-4: $$R_\text{total} = R_{steel} + R_\text{fep-steel} + R_\text{convection}$$

Calculate the temperatures at the lining and the pipe outer surface

To find the temperature at the lining (\(T_\text{lining}\)), we add the product of the heat transfer rate and the thermal resistance of the FEP lining-steel interface to the temperature of the hot liquid: $$T_\text{lining} = T_\text{liquid} + \dot{Q} R_\text{fep-steel}$$ To find the temperature at the pipe outer surface (\(T_\text{outer}\)), we add the product of the heat transfer rate and the total thermal resistance to the temperature of the hot liquid: $$T_\text{outer} = T_\text{liquid} + \dot{Q} R_\text{total}$$

Check if the FEP lining complies with the Code

To check if the FEP lining complies with the ASME Code for Process Piping, we compare the temperature at the lining with the maximum temperature recommended for FEP lining (\(204^{\circ}\text{C}\)). If the temperature at the lining is less than or equal to the maximum recommended temperature, the FEP lining complies with the Code. After calculating the temperatures and comparing them to the given limits, we will have a complete solution to the problem.