Page 341 - Design and Operation of Heat Exchangers and their Networks
P. 341

Dynamic analysis of heat exchangers and their networks  327



                                             _       _
                                       sC c + C c + U C h
                         e                                     e
                         θ h ¼                                2  θ h,in
                                                   _
                                    _
                              sC h + C h + U  sC c + C c + U  U
                                           _
                                          C c U
                                                              e
                         +                                   2  θ c,in
                                   _
                                                 _
                             sC h + C h + U  sC c + C c + U  U

                                        _
                                  sC c + C c + U ð t h,in  t h Þ
                                                                e _
                          +                                  2  ΔC h
                                                  _
                                   _
                             sC h + C h + U  sC c + C c + U  U
                                         ð
                                        U t c,in  t c Þ
                                                                e _
                          +                                  2  ΔC c
                                                  _
                                   _
                             sC h + C h + U  sC c + C c + U  U

                                             _
                                       sC c + C c ð t c  t h Þ
                                                               Δ e U
                           +                                  2
                                                   _
                                    _
                              sC h + C h + U  sC c + C c + U  U

                                      _
                                                        ð
                                sC c + C c + U ð ^ t h  t h Þ + U ^ t c  t c Þ
                                                                         (7.19)
                            +                                  2
                                     _
                                                    _
                               sC h + C h + U  sC c + C c + U  U
                                            _
                                            C h U
                         e                                     e
                         θ c ¼                                2  θ h,in
                                    _
                                                   _
                              sC h + C h + U  sC c + C c + U  U

                                           _       _
                                     sC h + C h + U C c
                                                             e
                         +                                  2  θ c,in
                                                 _
                                   _
                            sC h + C h + U  sC c + C c + U  U
                                         ð
                                       U t h,in  t h Þ         e _
                         +                                  2  ΔCh
                                                 _
                                   _
                            sC h + C h + U  sC c + C c + U  U

                                        _
                                  sC h + C h + U ð t c,in  t c Þ
                                                               e _
                         +                                  2  ΔC c
                                  _
                                                 _
                            sC h + C h + U  sC c + C c + U  U

                                           _
                                     sC h + C h ð t h  t c Þ
                                                             Δ e U
                         +                                  2
                                                 _
                                   _
                            sC h + C h + U  sC c + C c + U  U

                                   _
                                                     ð
                             sC h + C h + U ð ^ t c  t c Þ + U ^ t h  t h Þ
                         +                                  2            ð7:20Þ
                                                 _
                                   _
                            sC h + C h + U  sC c + C c + U  U
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