A calculation problem involving temperature increase

The diameter of the steam tracing pipe is Φ10

There are too many missing conditions. The size of the steam pipeline is assumed to be DN25. The heat transfer coefficient is taken as 50 W/m2·K, based on the assumptions for air coolers; the steam flow velocity is estimated at 15 m/s. The temperature of the steam after heat exchange is assumed to be 167 degrees. If phase change heat needs to be taken into account, further calculations would be required. The heat transfer area is assumed to be calculated based on half of the surface area of the heating tube: 3.14*25/1000*50*6 = 23.55 m2.

For the hot fluid side: Flow rate = 15*0.7854*0.025*0.025*3600*6 = 159 m3/h. The average temperature is taken as (173 + 167)/2 = 170°C. The specific heat capacity is 2773.3 kJ/kg·°C, and the density is 4.113 kg/m3. Thus, the mass flow rate is 159/4.113 = 39 kg/h. The inlet temperature is 173°C, and the outlet temperature is 167°C.

For the cold fluid side: Flow rate = 10,000 m3/h. The density is 1.29 kg/m3, so the mass flow rate is 10,000/1.29 = 7752 kg/h. The specific heat capacity is 1.004 kJ/kg·°C. The temperature of the air after heat exchange is 20.08°C

The diameter of the steam tracing pipe is Φ10. Although the steam flow rate is not certain, in practice, a tracing pipe 50 meters long experiences virtually no heat loss, with the temperature at the hot end remaining constant

Is the air mass flow rate incorrect?

If estimated based on DN10, the steam flow rate is 15*0.7854*0.01*0.01*3600*6 = 25.5 m3/h; the mass flow rate is 25.5/4.113/1000 = 0.062 ton/h. The heat transfer area, calculated as half of the surface area of the heating tube, is 3.14*10/1000*50*6/2 = 4.7 m2. The temperature of the air after heating is 35°C

I have two questions: 1. When the steam temperature drops from 173 degrees to 167 degrees, doesn’t some of the steam liquefy? Doesn’t the latent heat need to be taken into account? 2. In the second calculation table, both the heat exchange area and the steam flow rate have decreased; why then has the temperature of the heated air increased?

Saturation steam at 1.0 MPa should be at 180 degrees; here it is 173 degrees, so it is not saturated steam either. So, assume no liquefaction; otherwise, calculations need to be done in stages, as the specific heat capacities of steam and liquid are different. It’s also difficult to determine the amount of liquefaction, as this amount needs to be multiplied by the latent heat. In the second calculation table, the air flow rate is lower; this is due to an error in the unit conversion – it is necessary to divide by 1000. There is a clear mistake in this calculation: the specific heat of steam should be 1.85 kJ/kg, and 2773 represents the latent heat of vaporization. Therefore, the formula flow rate × specific heat × temperature difference cannot be used. Simulations using AspenPlus showed that the temperature increase is very limited, not exceeding 2°C, because if the heat transfer coefficient is estimated at 50 W.m2/K, the amount of heat that can be transferred by such a small heat exchange area is limited.