Page 255 - Mechanical Engineers' Handbook (Volume 4)
P. 255

244   Furnaces

                             As an illustration, find the time required to heat a steel plate to 2350 F in a furnace at
                          a uniform temperature of 2400 F. The plate is 0.25 in. thick with a unit weight of 10.2 lb/
                           2
                          ft and is to be heated from one side. Overall emissivity–absorptivity is e   0.80. Specific
                                                                                   m
                                                        1. MTD is
                          heat is 0.165. The view factor is F s
                                              (2400   70)   (2400   2350)
                                                                         588 F
                                              ln(2400   70)/(2400   2350)
                                            0.1713   0.80   1[28.6   (28.6   5.88) ]
                                                                             4
                                                               4
                                       H                                         93.8
                                        r
                                                           588
                                            10.2   0.165(2350   70)
                                        t                         0.069 hr
                                               1   93.8   588
           8.11  Newman Method
                          For loads heated from two or more perpendicular sides, final maximum temperatures will
                          be at exposed corners, with minimum temperatures at the center of mass for heating from
                          all sides, or at the center of the face in contact with the hearth for hearth-supported loads
                          heated equally from the remaining sides. For surfaces not fully exposed to radiation, the
                          corrected H factor must be used.
                             The Newman method can be used to determine final load temperatures with a given
                          heating time t. To find time required to reach specified maximum and minimum final load
                          temperatures, trial calculations with several values of t will be needed.
                                                                 and Y can be found from charts in Figs.
                             For a selected heating time t, the factors Y s  c
                                                                            , T , H, k, and r—for each
                          23 and 24 for the appropriate values of the other variables—T s  c
                                                     , r , and r . If one of these paths is much longer than the
                          of the heat flow paths involved—r x  y  z
                          others, it can be omitted from calculations:
                                                     Y   Y   Y   Y   cz
                                                       c
                                                           cx
                                                                cy
                                                      Y   Y   Y   Y  sz
                                                           sx
                                                       s
                                                                sy
                             For two opposite sides with equal exposure only one is considered. With T known, T s
                                                                                         c
                               (furnace temperature, T or T ) can be calculated.
                          and T ƒ                 g   w
                             As an example, consider a carbon steel ingot, with dimensions 2 ft   4ft   6 ft, being
                          heated in a direct-fired furnace. The load is supported with one 2 ft   4 ft face in contact
                          with the refractory hearth and other faces fully exposed to gas and wall radiation. Maximum
                          final temperature will be at an upper corner, with minimum temperature at the center of the
                          2ft   4 ft bottom surface. Assuming that the load is a somewhat brittle steel alloy, the
                          initial heating rate should be suppressed and heating with a constant gas temperature will
                          be assumed. Heat-transfer factors are then
                             Flow paths r s   1 ft and r y   2 ft, the contribution of vertical heat flow, on axis r z , will
                               be small enough to be neglected.
                                                        2250 F and T (to be found) about 2300 F, with trial
                             Desired final temperatures: T c
                                                                  s
                               factor t   9hr.
                             H from gas to load   50
                             k mean value for load   20 and D   0.25
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