PhD Thesis - Energy Systems Research Unit - University of Strathclyde

Applying basic energy and mass conservation individually on the three nodes, threepartial differential equations, one for each node are obtained as follows:For Node i (having Mass M i in kg and an average mass weighted specific heat inkJ/kgK), for an incoming chilled water mass flow rate in kg/s and heatcapacity in kJ/kgK:, where - (3.2)- (3.3)For Node j (having Mass M j in kg and an average mass weighted specific heat inkJ/kgK), for an incoming cooling water mass flow rate in kg/s and heatcapacity in kJ/kgK:, where - (3.4)- (3.5)For Node g (having Mass M g in kg and an average mass weighted specific heat inkJ/kgK), for an incoming hot water mass flow rate of in kg/s and heat capacityin kJ/kgK:, where - (3.6)- (3.7)The numbers in subscript refer to the individual state points within the chiller cycleshown in Figure 3.3 and Figure 3.5. The term UA(T env – T g ) associated with theanalysis of Node g represents the heat transfer to and from the environment and h isthe specific enthalpy in kJ/kg.Solving equations (3.2), (3.4) and (3.6) yields the temperatures of the three nodes, T i ,T j , and T g - the outlet temperatures of the three water circuits, the chilled water (T 18 ),the cooling water (T 16 ) and hot water circuits (T 12 ), respectively. For the interestedreader, Appendix ‘D’ provides full detail of the mathematical process used to solve110