Function HEAT-RATE


Slots on this function:

Documentation:
the rate at which energy is transferred in across the system boundary by heat transfer
Instance-Of: Function, Quantity-function
Arity: 2
Range: Everywhere-continuous-quantity

Other Related Axioms:

(Forall 
    (?Self ?Time)
    (=> (Active ?Time Cycle-Heat-Input ?Self)
        (C+ (Lambda (?T)
                    (If (= ?T ?Time)
                        (Value-At (Heat-Rate (Process-Involved ?Self))
                                  ?T)))
            (Lambda 
                (?T)
                (If (= ?T ?Time)
                    (Value-At (Net-Heat-Input-Rate 
                                  (Cycle-Involved ?Self))
                              ?T))))))

(Inherited-Facet-Value 
    Slot-Documentation
    Thermal-Process
    Heat-Rate
    The Rate At Which Energy Is Transferred In Across The System Boundary By Heat Transfer)

(Quantity.Dimension (Heat-Rate ?Self) Power-Dimension)

(Inherited-Facet-Value Slot-Cardinality Thermal-Process Heat-Rate 1)

(Has-Quantity-Function Thermal-Process Heat-Rate)

(Slot-Documentation 
    Thermal-Process
    Heat-Rate
    The Rate At Which Energy Is Transferred In Across The System Boundary By Heat Transfer)

(=> (Thermal-Process ?Self)
    (And (Value-Cardinality ?Self Work-Rate 1)
         (Quantity.Dimension (Work-Rate ?Self) Power-Dimension)
         (Value-Cardinality ?Self Heat-Rate 1)
         (Quantity.Dimension (Heat-Rate ?Self) Power-Dimension)
         (Value-Cardinality ?Self Heat-Transfer-Temperature 1)
         (Quantity.Dimension (Heat-Transfer-Temperature ?Self)
                             Temperature-Dimension)
         (Value-Cardinality ?Self Entropy-Generation-Rate 1)
         (Quantity.Dimension (Entropy-Generation-Rate ?Self)
                             Entropy-Rate-Dimension)
         (Value-Cardinality ?Self Irreversibility-Rate 1)
         (Quantity.Dimension (Irreversibility-Rate ?Self)
                             Power-Dimension)
         (Value-Cardinality ?Self Internally-Reversible-P 1)))

(=> (Heat-Rate $X $Y) (Everywhere-Continuous-Quantity $Y))

(Forall 
    (?Self ?Time)
    (=> (Active ?Time Steady-State-Steady-Flow-Process ?Self)
        (And (Forall (?Cv)
                     (=> (Process-Cv ?Self ?Cv)
                         (= (- (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Heat-Rate ?Self)
                                                     ?T)))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Work-Rate ?Self)
                                                     ?T))))
                            (+ (- (Lambda 
                                      (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Enthalpy-Rate-Out ?Cv)
                                              ?T)))
                                  (Lambda 
                                      (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Enthalpy-Rate-In ?Cv)
                                              ?T))))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (D-Pe-Rate ?Cv)
                                                     ?T)))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (D-Ke-Rate ?Cv)
                                                     ?T)))))))
             (Forall 
                 (?Cv)
                 (=> (Process-Cv ?Self ?Cv)
                     (= (Lambda 
                            (?T)
                            (If (= ?T ?Time)
                                (Value-At 
                                    (Entropy-Generation-Rate ?Self)
                                    ?T)))
                        (+ (- (Lambda (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Entropy-Rate-Out ?Cv)
                                              ?T)))
                              (Lambda (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Entropy-Rate-In ?Cv)
                                              ?T))))
                           (- (/ (Lambda (?T)
                                         (If (= ?T ?Time)
                                             (Value-At (Heat-Rate ?Self)
                                                       ?T)))
                                 (Lambda 
                                     (?T)
                                     (If (= ?T ?Time)
                                         (Value-At 
                                             (Heat-Transfer-Temperature ?Self)
                                             ?T)))))))))
             (Forall (?Cv)
                     (=> (Process-Cv ?Self ?Cv)
                         (= (Lambda (?T)
                                    (If (= ?T ?Time)
                                        (Value-At (Mass-Rate-In ?Cv)
                                                  ?T)))
                            (Lambda (?T)
                                    (If (= ?T ?Time)
                                        (Value-At (Mass-Rate-Out ?Cv)
                                                  ?T)))))))))

(Forall (?Self ?Time)
        (=> (Active ?Time Steady-Flow-Adiabatic-Process ?Self)
            (= (Lambda (?T)
                       (If (= ?T ?Time)
                           (Value-At (Heat-Rate ?Self) ?T)))
               0)))

(Forall 
    (?Self ?Time)
    (=> (Active ?Time Non-Steady-State-Flow-Process ?Self)
        (And (Forall (?Cv)
                     (=> (Process-Cv ?Self ?Cv)
                         (= (- (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Heat-Rate ?Self)
                                                     ?T)))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Work-Rate ?Self)
                                                     ?T))))
                            (+ (- (Lambda 
                                      (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Enthalpy-Rate-Out ?Cv)
                                              ?T)))
                                  (Lambda 
                                      (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Enthalpy-Rate-In ?Cv)
                                              ?T))))
                               (- (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At 
                                                  (Pe-Rate-Out ?Cv)
                                                  ?T)))
                                  (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At (Pe-Rate-In ?Cv)
                                                        ?T))))
                               (- (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At 
                                                  (Ke-Rate-Out ?Cv)
                                                  ?T)))
                                  (Lambda (?T)
                                          (If (= ?T ?Time)
                                              (Value-At (Ke-Rate-In ?Cv)
                                                        ?T))))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Energy-Rate ?Cv)
                                                     ?T)))))))
             (Forall 
                 (?Cv)
                 (=> (Process-Cv ?Self ?Cv)
                     (= (Lambda (?T)
                                (If (= ?T ?Time)
                                    (Value-At (Energy-Rate ?Cv) ?T)))
                        (+ (Lambda 
                               (?T)
                               (If (= ?T ?Time)
                                   (Value-At (Internal-Energy-Rate ?Cv)
                                             ?T)))
                           (Lambda (?T)
                                   (If (= ?T ?Time)
                                       (Value-At (Ke-Rate ?Cv) ?T)))
                           (Lambda (?T)
                                   (If (= ?T ?Time)
                                       (Value-At (Pe-Rate ?Cv) ?T)))))))
             (Forall 
                 (?Cv)
                 (=> (Process-Cv ?Self ?Cv)
                     (= (Lambda 
                            (?T)
                            (If (= ?T ?Time)
                                (Value-At 
                                    (Entropy-Generation-Rate ?Self)
                                    ?T)))
                        (+ (- (Lambda (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Entropy-Rate-Out ?Cv)
                                              ?T)))
                              (Lambda (?T)
                                      (If (= ?T ?Time)
                                          (Value-At 
                                              (Entropy-Rate-In ?Cv)
                                              ?T))))
                           (- (/ (Lambda (?T)
                                         (If (= ?T ?Time)
                                             (Value-At (Heat-Rate ?Self)
                                                       ?T)))
                                 (Lambda 
                                     (?T)
                                     (If (= ?T ?Time)
                                         (Value-At 
                                             (Heat-Transfer-Temperature ?Self)
                                             ?T)))))
                           (Lambda (?T)
                                   (If (= ?T ?Time)
                                       (Value-At (Entropy-Rate ?Cv)
                                                 ?T)))))))
             (= (Lambda (?T)
                        (If (= ?T ?Time)
                            (Value-At (Irreversibility-Rate ?Self)
                                      ?T)))
                (* (Lambda (?T)
                           (If (= ?T ?Time)
                               (Value-At (Entropy-Generation-Rate ?Self)
                                         ?T)))
                   (Lambda (?T)
                           (If (= ?T ?Time)
                               (Value-At 
                                   (State-Temperature *Dead-State*)
                                   ?T)))))
             (Forall (?Cv)
                     (=> (Process-Cv ?Self ?Cv)
                         (= (Lambda (?T)
                                    (If (= ?T ?Time)
                                        (Value-At (Mass-Rate ?Cv) ?T)))
                            (- (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Mass-Rate-In ?Cv)
                                                     ?T)))
                               (Lambda (?T)
                                       (If (= ?T ?Time)
                                           (Value-At (Mass-Rate-Out ?Cv)
                                                     ?T))))))))))

(Forall 
    (?Self ?Time)
    (=> (Active ?Time Power-System-Eight-One ?Self)
        (And (= (Lambda (?T)
                        (If (= ?T ?Time)
                            (Value-At (Thermal-Efficiency ?Self) ?T)))
                (/ (- (- (Lambda 
                             (?T)
                             (If (= ?T ?Time)
                                 (Value-At 
                                     (Specific-Enthalpy 
                                         (Outlet-Stream 
                                             (Blr-Cv (Blr-System ?Self))))
                                     ?T)))
                         (Lambda 
                             (?T)
                             (If (= ?T ?Time)
                                 (Value-At 
                                     (Specific-Enthalpy 
                                         (Outlet-Stream 
                                             (Tbn-Cv (Tbn-System ?Self))))
                                     ?T))))
                      (- (Lambda 
                             (?T)
                             (If (= ?T ?Time)
                                 (Value-At 
                                     (Specific-Enthalpy 
                                         (Outlet-Stream 
                                             (Pmp-Cv (Pmp-System ?Self))))
                                     ?T)))
                         (Lambda 
                             (?T)
                             (If (= ?T ?Time)
                                 (Value-At 
                                     (Specific-Enthalpy 
                                         (Outlet-Stream 
                                             (Hf-Cv (Cdnsr-System ?Self))))
                                     ?T)))))
                   (- (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Blr-Cv (Blr-System ?Self))))
                                  ?T)))
                      (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Pmp-Cv (Pmp-System ?Self))))
                                  ?T))))))
             (= (Lambda (?T)
                        (If (= ?T ?Time)
                            (Value-At (Back-Work-Ratio ?Self) ?T)))
                (/ (- (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Pmp-Cv (Pmp-System ?Self))))
                                  ?T)))
                      (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Hf-Cv (Cdnsr-System ?Self))))
                                  ?T))))
                   (- (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Blr-Cv (Blr-System ?Self))))
                                  ?T)))
                      (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Tbn-Cv (Tbn-System ?Self))))
                                  ?T))))))
             (= (Lambda 
                    (?T)
                    (If (= ?T ?Time)
                        (Value-At (Heat-Rate 
                                      (Htfr-Prcs (Blr-System ?Self)))
                                  ?T)))
                (* (Lambda 
                       (?T)
                       (If (= ?T ?Time)
                           (Value-At 
                               (Mass-Rate-In (Blr-Cv (Blr-System ?Self)))
                               ?T)))
                   (- (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Blr-Cv (Blr-System ?Self))))
                                  ?T)))
                      (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Pmp-Cv (Pmp-System ?Self))))
                                  ?T))))
                   (/ 1 3600000)))
             (= (Lambda (?T)
                        (If (= ?T ?Time)
                            (Value-At (Cycle-Mass-Rate ?Self) ?T)))
                (* 3.6
                   (/ (Lambda (?T)
                              (If (= ?T ?Time)
                                  (Value-At (Net-Work-Output-Rate ?Self)
                                            ?T)))
                      (- (- (Lambda 
                                (?T)
                                (If (= ?T ?Time)
                                    (Value-At 
                                        (Specific-Enthalpy 
                                            (Outlet-Stream 
                                                (Blr-Cv 
                                                    (Blr-System ?Self))))
                                        ?T)))
                            (Lambda 
                                (?T)
                                (If (= ?T ?Time)
                                    (Value-At 
                                        (Specific-Enthalpy 
                                            (Outlet-Stream 
                                                (Tbn-Cv 
                                                    (Tbn-System ?Self))))
                                        ?T))))
                         (- (Lambda 
                                (?T)
                                (If (= ?T ?Time)
                                    (Value-At 
                                        (Specific-Enthalpy 
                                            (Outlet-Stream 
                                                (Pmp-Cv 
                                                    (Pmp-System ?Self))))
                                        ?T)))
                            (Lambda 
                                (?T)
                                (If (= ?T ?Time)
                                    (Value-At 
                                        (Specific-Enthalpy 
                                            (Outlet-Stream 
                                                (Hf-Cv (Cdnsr-System ?Self))))
                                        ?T))))))))
             (= (Lambda (?T)
                        (If (= ?T ?Time)
                            (Value-At (Cycle-Mass-Rate ?Self) ?T)))
                (Lambda 
                    (?T)
                    (If (= ?T ?Time)
                        (Value-At (Mass-Rate-In 
                                      (Blr-Cv (Blr-System ?Self)))
                                  ?T))))
             (= (Lambda (?T)
                        (If (= ?T ?Time)
                            (Value-At (Cycle-Mass-Rate ?Self) ?T)))
                (Lambda 
                    (?T)
                    (If (= ?T ?Time)
                        (Value-At (Mass-Rate-In 
                                      (Tbn-Cv (Tbn-System ?Self)))
                                  ?T))))
             (= (Lambda 
                    (?T)
                    (If (= ?T ?Time)
                        (Value-At 
                            (Condensor-Heat-Out-Rate 
                                (Cdnsr-System ?Self))
                            ?T)))
                (* (Lambda 
                       (?T)
                       (If (= ?T ?Time)
                           (Value-At 
                               (Cycle-Mass-Rate 
                                   (Hf-Cv (Cdnsr-System ?Self)))
                               ?T)))
                   (- (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Tbn-Cv (Tbn-System ?Self))))
                                  ?T)))
                      (Lambda 
                          (?T)
                          (If (= ?T ?Time)
                              (Value-At 
                                  (Specific-Enthalpy 
                                      (Outlet-Stream 
                                          (Hf-Cv (Cdnsr-System ?Self))))
                                  ?T)))))))))