Determine the temperature rise in metal temperature due to

Question

An investigator conducts a study on the heat transfer and the effects of inter- nal scale thicknesses on a reheater tube metal temperature of a boiler, which operates with a steam temperature 530°C under pressure 13,700 kPa. The boiler tube has an OD of 2.0 inch with a 0.2 inch wall thickness, made of steel grade SA-213 T-22.

Using the following information:

Thermal conductivity of tube metal, k_T: 28.884 W/m.K

Thermal conductivity for scale, k_D: 0.592 W/m.K

Flue gas temperature, T_O: 800°C
Steam side heat transfer coefficient, h_S: 1702 W/m²K

Gas side heat transfer coefficient, h₀: 92 W/m²K

Determine the temperature rise in metal temperature due to the increase in scale thickness from 30 microns to 500 microns. The overall heat transfer coefficient is given by:

U_O={[1/h_O]+[r_OIn(r_O/r_i)/k_T]+[r_oIn(r_i/r_S)/k_D]+[r_O/r_Sh_S]}^-1

where the subscript ‘O' denotes the gas side, "i" denotes the inner surface of the tube, "S" denotes the steam side, "T" denotes the tube, and "D" denotes the scale deposit. The temperatures and radii are illustrated in the following schematic diagram of a boiler tube section.