CALCULATION:WITHOUT SCALE FORMATION OF SUPER HEATER TUBEInternal flow: Properties to be evaluated at bulk mean temperatureTm = = Tm = 500cProperties of steam at 500c : (from HMT data book p.no 39)Thermal conductivity (k) = 0.06838 w/mkKinematic viscosity ( ) = 78.8 x 10-6 m2/sPrandtl number (pr) = 0.90 Re = = Re = 3895.12Re > 2300 the flow is considered as turbulent flow.Fully developed flow :Dittus boelter equation:Nu = 0.023 x Re0.8 x Prn n = 0.4 for heating of fluidNu = 0.023 x (3895.12)0.8 x (0.90)0.4We know that,Nusselt number = 16.437 = hi = hi = 26.36 w/m2kExternal flow:Flow across banks of tubes : (staggered arrangement)Sl = Longitutional pitch (114 mm)St = Transverse pitch (114 mm) u = Free stream velocityFilm temperature :Tf = TW + T / 2 = Tf = 584cProperties of flue gas at 584c (from HMT data book p.no :36 )Thermal conductivity (k) = 0.07281 w/mk Kinematic viscosity ( ) = 90.84 x 10-4 m2/sPrandtl number (pr) =0.6216Maximum velocity Umax = u SD = [ Sl2 +( ) 2 ]0.5 = [ 1142 + (114/2)2]0.5SD= 127.45mmVmax = x u = Vmax = 5.14 m/sRe = = Re = 2695.04Inline flow :Nu = C x Ren = = 2.39 = = 2.67c = 0.287 ; n = 0.612 c = 0.287 x 1.13 x pr0.33 = 0.287 x 1.13 x (0.621)0.33 C= 0.277Nu = 0.277 x (2695.04)0.612Nu = 34.859 = 34.85 ho = ho = 53.287 w/m2kOverall heat transfer coefficient :U = = U = 10.020Q = UAT = 10.20 X 1039 X (588 42)Q = 5642.42 KJWITH SCALE FORMATION OF SUPER HEATER TUBE :Fouling factor : = +Rfo +Rfi+= +0.0000877 +x0.000877+ = 0.09931 Uo = 10.07 w/m2k = + Rfi +Rfo + + 0.0000877 +X 0.000877 + = 0.0890 Ui = 11.23 w/m2k U = 5.3106 Q = UAT= 5.3106 X 1039 X (588 42) Q = 3012.6 KJ