Evaporation, Condensation and Heat Transfer 190 Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 191 Δ ∆ π ⎛⎞ ⎜⎟ ⎝⎠ Δ ρ ⎛⎞ ⎜⎟ ⎝⎠ Δ ρ π ⎛⎞ ⎛⎞ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ ρ π ⎛⎞ ⎛⎞ ⎜⎟ ⎜⎟ ⎝⎠ ⎝⎠ Evaporation, Condensation and Heat Transfer 192 Δ Δ Δ Δ Δ Δ Δ A B A B Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 193 Δ ⎛⎞ ⎜⎟ ⎜⎟ ⎝⎠ ε ε ε () () () ε ⎧ ⎫ ⎡ ⎤ ⎛⎞ ⎪ ⎪ ⎢ ⎥ ⎜⎟ ⎜⎟ ⎪ ⎪ ⎢ ⎥ ⎝⎠ ⎨ ⎬ ⎢ ⎥ ⎛⎞ ⎪ ⎪ ⎢ ⎥ ⎜⎟ ⎪ ⎪ ⎜⎟ ⎢ ⎥ ⎝⎠ ⎣ ⎦ ⎩⎭ Evaporation, Condensation and Heat Transfer 194 Type of fitting or valve Loss coefficient (K) Type of fitting or valve Loss coefficient (K) θ θ Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 195 () ε () ε T H T 1 T 2 t 1 t 2 T 1 t 2 T 2 t 1 T H T 1 T 2 t 1 t 2 T 1 t 2 T 2 t 1 Evaporation, Condensation and Heat Transfer 196 C1 C3 C4 H1 H2 H3 H4 Cooling water C5 H5 C2 t 1 t 2 t 3 t 4 t 5 t 6 t 7 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T 8 T 9 T 10 V 1 V 2 V 3 V 4 V T C1 C3 C4 H1 H2 H3 H4 Cooling water C5 H5 C2 t 1 t 2 t 3 t 4 t 5 t 6 t 7 T 1 T 2 T 3 T 4 T 5 T 6 T 7 T 8 T 9 T 10 V 1 V 2 V 3 V 4 V T ⎛⎞ ⎜⎟ ⎜⎟ ⎝⎠ ∑ Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 197 Evaporation, Condensation and Heat Transfer 198 From heat balance determine V; estimate a value for K Determine ΔP Fix exchanger geometry: length, shell diameter,tube diameter, tube pitch, tube arrangement. Determine No. tubes Calculate ΔP calc ΔPcalc - ΔP ≤ error Yes Final design New shell diameter and No. of tubes Calculate overall heat transfer Coefficients and ΔTlm From heat balance determine V; estimate a value for K Determine ΔP Fix exchanger geometry: length, shell diameter,tube diameter, tube pitch, tube arrangement. Determine No. tubes Calculate ΔP calc ΔPcalc - ΔP ≤ error Yes Final design New shell diameter and No. of tubes Calculate overall heat transfer Coefficients and ΔTlm [...]... 202 Evaporation, Condensation and Heat Transfer , Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 203 204 Evaporation, Condensation and Heat Transfer Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit ε Δ ρ 205 2 06 Evaporation, Condensation and Heat Transfer 10 Heat. .. evaluate the heat transfer coefficient A summary of the estimation of the heat transfer coefficient is shown in Table 6 More detailed data are presented in an earlier work (Plascencia, 2004) In the case of the heat transfer coefficient between the molten phase and the lining, we use a value of h of 1500 W/m2/K as suggested by (Utigard et al., 1994) u (m/s) 2 4 6 8 Re 867 92 173583 260 375 347 167 Pr 5.83... front of the cooler (cm) 26. 0 13.0 2 .6 0.0 26. 0 13.0 2 .6 0.0 Thot Calc (ºC) 261 3 56 613 1018 491 794 1098 1070 Thot Exp (ºC) 1102 1092 Heat flux Calc (kW/m2) 135 187 310 4 76 94 144 382 733 Heat flux Exp (kW/m2) 574 427 Table 7 Comparison of calculated and experimental results When the refractory lining remains un-attacked, the hot end of the cooling elements does not exceed 500 ºC and the rate of oxidation... f(ΔPCxallow, Fhx) and compare with KCx Calculate ht, hs and Uoverall Calculate tout’s= f(QCx-req, tin, VCx) Nt = Nta Calculate temperature correction factor Calculate LMTD’s Calculate heat transfer area, ACx’s Calculate number of tubes, Nt End 200 Evaporation, Condensation and Heat Transfer Δ Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit... are in good agreement, while the calculated and experimental heat fluxes 222 Evaporation, Condensation and Heat Transfer present a bigger difference Such difference can be attributed to the material lost due dissolution, since the distance for heat transfer decreases, it results in an increased heat flux At the same time the difference in the calculated heat fluxes when there is no refractory protection... cooling Water leaks, develop mechanical stresses Limited heat flux in thick sections Corrosion in the outer shell, limited heat flux Very low heat fluxes Table 1 Cooling systems industrially available, after Legget and Gray (Legget & Gray, 19 96) 208 Evaporation, Condensation and Heat Transfer Another factor that affects the difference in the heat flux removal is that the systems that are embedded in... interfacial heat transfer, Metallurgical Transactions B, 16B, 3, pp 585 - 594 Incropera F P and DeWitt D P, Fundamentals of Heat and Mass Transfer 4th Edition, John Wiley & sons., New York, U.S.A., 19 96 Legget A.R., Gray N.B (19 96) , Development and application of a novel refractory cooling system Proceedings of Advances in Refractories for the Metallurgical Industries II, Montréal, QC, Canada, August 19 96 224... the cylinder cavity and once solidified; the cylinder was machined to the dimensions specified in Figure 4 The motivation for this design was to allow copper to extract heat while being protected from being oxidized by the alloy Figure 9 shows details of these coolers Results from immersing these coolers in matte and slag are shown in Table 4 2 16 Evaporation, Condensation and Heat Transfer Cooler Composite... evaluate the heat transfer coefficient between the cooling water and the cooling element as well as the heat transfer coefficient between the molten slag and the refractory lining Given that the cooling water is forced to run through a circular closed channel, the DittusBoelter correlation is the one that better correlates the heat transfer coefficient in turbulent flows (Incropera & DeWitt, 19 96) The Dittus-Boelter... alloy Ni plated cooler Bare copper Water flow rate (L/min) 1.0 1.5 1.5 1.0 1.5 1.5 1.0 1.5 1.5 Cooling water temperature change (ºC) 16 13 15 26 25 24 28 27 28 Mass change (g) Heat flux (kW/m2) Remarks - 80 - 63 - 128 198 150 165 98 158 59 350 427 492 569 820 788 61 3 8 86 919 Not treated Not treated Pre-oxidized Not treated Not treated Pre-oxidized Not treated Not treated Pre-oxidized Table 2 Immersion . Nta Evaporation, Condensation and Heat Transfer 200 Δ Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 201 Δ Evaporation, . Evaporation, Condensation and Heat Transfer 202 , Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 203 Evaporation, Condensation. Condensation and Heat Transfer 204 Modelling the Thermo-Hydraulic Performance of Cooling Networks and Its Implications on Design, Operation and Retrofit 205 ε Δ ρ Evaporation, Condensation and