Page 166 - Design and Operation of Heat Exchangers and their Networks
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154   Design and operation of heat exchangers and their networks


          For cryogenic fluids such as N 2 ,H 2 , and O 2
                                   n ¼ 0:9 0:3p 0:3                   (4.20)
                                                r

                                                   1
                                     0:27
                               ¼ 1:2p   +2:5+                         (4.21)
                                     r
                            F p r                      p r
                                                 1 p r
             The effect of the wall properties and surface roughness is taken into
          account by
                                       2=15               0:25
                                                 ð
                          F w ¼ R a =R a0 Þ  ð λρcÞ = λρcÞ            (4.22)
                               ð
                                               w      Cu
          where R a0 ¼0.4μm, (λρc p ) w is the square of the effusivity of the surface
                                        9   2   4  2
          material, and (λρc p ) Cu ¼1.250 10 W s/m K .
             For finned tubes, the earlier correlations are modified as
                                         ðÞ
                                  ðÞ
                                n R p r ¼ np r  0:1h f =s fs          (4.23)
                                                 p ffiffiffiffi
                                     ðÞ       p r = ψ                 (4.24)
                                F p r ,R p r ¼ F p r
                                       F w,R ¼ 1                      (4.25)
          where h f is the fin height, s fs is the fin free spacing, s fs ¼s s  δ f , and ψ is area
          enlargement factor that is the ratio of the surface area of the finned tube to
          that of a plain tube of the same core diameter. The validity range of
          Eqs. (4.23)–(4.25) is s f >1mm, 0.02 p r  0.3, or 1bar p 10bar.

             Example 4.1 Nucleate boiling of R134a on a horizontal tube
             Calculate the nucleate boiling heat transfer coefficient of R134a on a
             horizontal plain copper tube at the saturation temperature of 15.12°C
                              2
             and q¼12.77kW/m . The roughness of the tube surface is assumed to
             be 0.4μm.
             Solution
             The molecular mass and critical pressure of R134a are M¼102.03kg/kmol
             and p cr ¼40.593bar, respectively. At t s ¼15.12°C, the properties of
             R134a are calculated by the use of RefProp as p s ¼4.903bar,
             p 0 ¼0.1p cr ¼4.903bar, (dp/dT) sat,p0 ¼0.1363bar/K, σ p0 ¼0.01013Nm.
              1.  Cooper correlation
             Since the reduced pressure p r ¼p s /p cr ¼4.903/40.593¼0.1208, we use the
             Cooper correlation, Eq. (4.11), and take C¼90 to calculate the heat transfer
             coefficient as

              α ¼ 90q 0:67 M  0:5 p r 0:12 0:2lgR a  ½  lg p r   0:55
                                         ðފ
                           0:67       0:5      0:12 0:2lg0:4        0:55
                ¼ 90 12,770    102:03    0:1208         ½  lg 0:1208ފ
                                                            ð
                          2
                ¼ 3453W=m K
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