Appendix B: Tube-Side Heat Transfer Coefficients and Pressure Drop

Appendix B: Tube-Side Heat Transfer Coefficients and Pressure Drop

Estimating the tube-side convective heat transfer coefficient h c for single-phase fluids is an important task in boiler performance evaluation whether it is a fire tube or water tube boiler or a fluid heater. It is also important as h c impacts the tube wall temperatures in the case of superheaters, economizers, and air heaters. Simplified procedures for estimating h c for steam, water, air, flue gas, or any fluid are presented in the following text. Appendix D shows how the nonluminous heat transfer coefficient inside the tubes may be estimated.

Then the total inside heat transfer coefficient h i is the sum of h n and h c . From h i , one may estimate the overall heat transfer coefficient U as shown in Appendix A.

Tube-side coefficients may be estimated using the following correlation:

. Re 08 Nu . Pr 04 . = 0 023 (B.1) where

Nusselt number Nu = h c d i /k

Reynolds number Re = ρVd i /µ = ρ (4w/ρ/π/d i 2 )d i /µ = 1.273 w/(d i µ ) Prandtl number = µC p /k w is the fluid flow per tube = W/number of streams, kg/s W is the total flow, kg/s

C p is the specific heat, J/kg K µ is the viscosity of fluid, kg/m s

V is the fluid velocity, m/s k is the thermal conductivity, W/m K ρ is the density, kg/m 3

d i is the tube inner diameter, m

h c is the tube-side convective heat transfer coefficient in W/m 2 K

(All fluid properties are estimated at the average fluid temperature.) Simplifying equa- tion (B.1), we have

18 . = . 0 0278 w C 18

= .  k 06  (B.3)  µ 

Table B.1 shows this equation in SI, metric, and British units. Tables B.2 through B.4 show the values of C for air, flue gas, water, and steam. Plant engineers as an exercise may develop C values as a function of fluid temperature for other fluids such as thermic fluids, oils, and waste flue gas in fire tube boilers in their plant.

378 Appendix B: Tube-Side Heat Transfer Coefficients and Pressure Drop

TABLE B.1

Equations for Tube-Side Heat Transfer Coefficient and Velocity

SI Units

British Units

Metric Units

h c = 0.0278 w 0.8 (C p /µ) 0.4 k 0.6 /d i 1.8 h c = 2.44 w 0.8 (C p /µ) 0.4 k 0.6 /d i 1.8 h c = 0.0278 (C p /µ) 0.4 k 0.6 w 0.8 /d i 1.8 h c = 0.0278 Cw 0.8 /d i 1.8 h c = 2.44 Cw 0.8 /d i 1.8 h c = 0.0278 Cw 0.8 /d i 1.8 h c , W/m 2 K

h c , kcal/m 2 h °C w, kg/s

h c , Btu/ft 2 h °F

w, lb/h

w, kg/h

C p , kcal/kg °C µ , kg/ms

C p , J/kg K

C p , Btu/lb° F

µ , kg/m h k, W/m K

µ , lb/ft h

k, Btu/ft h °F

k, kcal/m h °C

C, multiply C SI by 0.001229 V = 1.246 wv/d i 2 V = 0.05 wv/d i 2 V = 3.461 × 10 −4 wv/d i 2 v, m 3 /kg

C SI = (C p /µ) 0.4 k 0.6 C, multiply C SI by 0.001134

ft 3 /lb

m 3 /kg

V, velocity in m/s

ft/s

m/s

Re = 1.273 w/(d i µ )

Re = 1.273 w/(d i µ ) Note:

Re = 15.2 w/(d i µ )

C is defined in equation B.3.

TABLE B.2

C for Dry Air, Flue Gases from Combustion of Natural Gas, Fuel Oil

Temperature, °C

Dry Air

Natural Gas (Flue Gas)

Fuel Oil (Flue Gas)

211.7 Notes: This table shows C values using SI units. To obtain h c in British units, multiply C by 0.0011343,

and in metric units, multiply by 0.001229; Natural gas products of combustion: % volume CO 2 = 8, H 2 O = 18, N 2 = 71.5, O 2 = 2.5. Fuel oil products of Combustion: % volume CO 2 = 12, H 2 O = 12, N 2 = 73.5, O 2 = 2.5. Gas pressure is atmospheric. Due to the presence of water vapor, the specific heat and thermal conductivity increases while the viscosity decreases, and hence, h c is higher for natural gas products of combustion than air or for flue gas from com- bustion of oil.

Appendix B: Tube-Side Heat Transfer Coefficients and Pressure Drop 379

TABLE B.3

C for Compressed Water

Temperature, °C

Notes: This table shows C values using SI units. To obtain h c in British units, multiply C by 0.0011343, and in metric units, multiply by 0.001229; The equation C = 250 + 4.023t −

0.0063t 2 describes this trend, where T is the temperature of water in °C.

TABLE B.4

C Values for Saturated and Superheated Steam

Pressure, KPa

C-sat steam

306.3 321.0 Note: This table shows C values using SI units. To obtain h c in British units, multi-

ply C by 0.0011343, and in metric units, multiply by 0.001229.