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D Steady-state moving-boundaries heat exchanger model 3. The calculated heat transfer area is compared to the actual heat transfer area. If it is higher, the temperature profile is updated to increase the pinch point. If it is lower, the temperature profile is updated to decrease the pinch point. Failure occurs if: 1. The initial conditions are poorly defined, leading the situation of Figure 101. 2. The update of the temperature profile during iterations leads to a negative pinch point. To avoid failures when these cases occur, the LMTD equations are slightly modified to avoid logarithms of negative numbers. A penalty is assigned in terms of required area when this is the case. The code below corresponds to the case of a moving boundaries counterflow condenser model and is applied for each of the three zones: if Tsf,su < Tr,ex - 1 then if Tsf_ex < Tr,su - 1 then ΔTlog=(Tsf ,su−Tr,ex)−(Tsf ,ex−Tr ,su) ln(Tsf ,su−Tr ,ex ) Tsf ,ex−Tr,su ΔTlog=Tsf ,su−Tr ,ex+1⋅ 1 ln(Tr ,ex−Tsf ,su) 1+ξ⋅(Tsf ,ex−Tr ,su+1) else if Tsf,ex < Tr,su - 1 then ΔTlog=Tsf ,ex−Tr,su+1⋅ 1 ln(Tr,su−Tsf,ex) 1+ξ⋅(Tsf,su−Tr,ex+1) else endif endif A= Q ̇ U⋅ΔTlog else ΔTlog= 1 (1+ξ⋅(Tsf ,su−Tr,ex+1))⋅(1+ξ⋅(Tsf ,ex−Tr ,su+1)) ξ is the penalty factor. It is set arbitrarily to 104. When the difference between the secondary fluid temperature profile and the refrigerant temperature profile is lower than 1K, the expression of the LMTD is "freezed" to that temperature difference and divided by a penalty term proportional to the difference between refrigerant and secondary fluid temperatures. By doing this, the calculation of A is artificially impacted and leads to very high required heat transfer areas when the temperature XIVPDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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