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220  HEAT TRANSFER  AND  HEAT  EXCHANGERS
                                        1-  I



                                          'I                        .IO
                Feed                           Convection
                                      t/
                To = 400 F                                          . oa
                195394 Ib/hr
                H = 248 BWlb              TLl
                V' = 0.920 cfs          Shield                      .06
                u = 5.08 fps, cold       vn        4-
                6  Sched 40.            Radiant                     .04


                                                      T2 = 900 F    .02
                                                      H,  = 609.6 Btullb
                                                                    0
                                                                           0          20         40          60
                                                                     tf            TUBE  NUMBER
                                                                     xt-
                                          Fuel
                                          + 25% excess air          Figure  8.22.  Effects  of  three  modes  of  heat  flux  distribution  on
                                                                    temperature and conversion in pyrolysis of  a fuel oil: (1) two levels,
                                                                    12,500 and 7500;  (2) linear variation between the same limits; (3)
                Figure 8.20. Flowsketch of process of  Example 8.16.   constant at 10,000 Btu/(hr)(sqft).  Obtained by method of  Example
                                                                    8.16.

                                                                    temperature  levels are in Tables 8.19-8.21.  Outdoors under windy
                                                                    conditions, heat losses are somewhat greater than indoors at natural
                                                                    convections.  Tabulations  of  economic  thicknesses  in  Chemical
                                                                    Engineers Handbook  (McGraw-Hill, New York, 1984, 11.55-11.58)
                                                                    suggest that  10-20%  greater  thickness of  insulation is  justified at
                                                                    wind velocity of  7.5 miles/hr.
                                                                       The  optimum  thickness  of  insulation  can  be  established  by
                                                                    economic analysis when  all  of  the  cost data  are  available, but  in
                                                                    practice a  rather  limited range  of  thicknesses is  employed. Table
                                                                    8.22 of piping insulation practice in one instance is an example.
                                                                       The procedure for optimum selection of  insulation thicknesses
                                                                    is  exemplified by  Happel  and Jordan  [Chem. Process Economics,
                                                                    380 (1975)l. They take into account the costs of  insulation and fuel,
                                                                    payout time,  and some minor factors. Although their costs of  fuel
                                                                    are  off  by  a  factor  of  10 or  more,  their  conclusions have  some
                                                                    validity if it is recognized that material costs likewise have gone up
                                                                    by  roughly the same factor. They conclude that with energy cost of
                                                                    $2.5/millionBtu  (adjusted  by  a  factor of  lo),  a payout  time of  2
                                                                    years,  for  pipe  sizes  of  2-8in.,  the  optimum  thicknesses  in


                                                                      0.70
                                                                      0.60
                                                                      0.50
                                                                      0 40
                                                                      0.30
                                                                    w
                                                                      0.20                                      3.0
                                                                    L                                           2.0   n
                                                                                                               1.2  --
                                                                    : 8rl%                                     0.8   m"  0
                                                                                                               0.6   +a-
                                                                      0.07
                                                                      0.06                                     0.4  *=
                                                                    L1)   0.05                                 If9
                                                                      0.06
                                                                      0.03                                     0.08
                                                                                                               0.06
                                                                      0.02
                                                                        LOO   600  800  1000   1200  lL00   1600  I800  20GO 2200  2L00  2600
                                                                                       Temperature  T, K
                                                                    Figure  8.23.  Total  emissivity  of  carbon  dioxide  and  water  with
                Figure  8.21.  Tube  and  box  configuration of  the  fired  heater  of   PH2,/Pc,,  = 1 and a total pressure of  1 atm [Haduig, J. Inst. Fuel
                Example 8.16.                                       43,  129 (1970)].
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