Fin coil calculation with NTU

Fin coil calculation with NTU In all our software applications we never use values like Wi, Pi, Ri, NTUi and ϴ because one don't need it to calculate a heat exchanger like a fin coil. Somebody like the other way about the NTU (Number of Transfer Units). But 1 point it's clear. If one calculate a fin coil in 1 cell, the result include a big bug. n=1 n=1 n=2 n=... n=14 n=15 In Excel based applications we calculate with 15 cells to reduce the macro time. In high language applications we calculate with 50 cells to receive convergence. On bottom one can see all equations for each cell and a fin coil example. The cooler was calculated with 15 cells (Page 2-3) and with 50 cells (Page 4-6). General equations for each cell Q = ka t m = M 1 h 1e h 1a = M 2 h 2a h 2e = W 1 t 1e t 1a = W 2 t 2a t 2e c p1 = h 1e h 1a t 1e t 1a W 1 = M 1c p1 P 1 = t 1e t 1a t 1e t 2e c p2 = h 2a h 2e t 2a t 2e W 2 = M 2c p2 P 2 = t 2a t 2e t 1e t 2e Counter current flow x= t 1e t 2a y= t 1a t 2e R 1 = W 1 W 2 = 1 R 2 R 2 = W 2 W 1 = 1 R 1 NTU 1 = ka W 1 θ = P 1 NTU 1 = P 2 NTU 2 NTU 2 = ka W 2 t m = θ t 1e t 2e x = y t m max = x = y x y x y t m max = ln x y η = Δt m Δt m max Example Air humid Inlet temperature t1e C 20.000 Outlet temperature t1a C 2.305 Mass flow M1 kg/s 9.277 Heat capacity cp1 J/kgK 1310.451 Capacity Q W 215119.000 Capacity flow W1 W/K 12157.050 Temperature change P1 --- 0.786 Capacity flow quotient R1 --- 0.904 Number of transfer units NTU1 --- 4.170 Temperature quotient Ɵ --- 0.189 25%Et.glycol Inlet temperature t2e C -2.500 Outlet temperature t2a C 13.500 Mass flow M2 kg/s 3.640 Heat capacity cp2 J/kgK 3694.000 Capacity Q W 215119.000 Capacity flow W2 W/K 13444.938 Temperature change P2 --- 0.711 Capacity flow quotient R2 --- 1.106 Number of transfer units NTU2 --- 3.771 Temperature quotient Ɵ --- 0.189 Fin coil Capacity Q W 215119.000 Heat transfer coefficient k W/m2K 35.005 Surface A m2 1448.290 Mean temperature difference dtm K 4.243 Mean temp. diff. max. dtm max K 5.610 Efficiency η --- 0.756

RU G LH RH RO Cooler: 40/35/15-16R-36T-2946A-3.0PA-18C-Cu/Al/AlMg3 Capacity kw 215.119 ------ sensible: 167.058 Surface reserve % 0.001 latent: 47.647 Present surface m2 1448.310 frost: 0.413 Required surface m2 1448.290 Heat transfer coefficient W/m2K 35.005 ------------- ffi: 5.000E-05 Mean temp. diff. ( 75.64 % ) K 4.243 ffa: 5.000E-05 Zeller Consulting Suisse HVAC solutions Jurastrasse 35 CH-3063 Ittigen Air humid Inlet Outlet Definition Phone: +41-79-2226642 Fax:... Height over sea level m 0.000 Pressure hpa 1013.250 Temp. C 20.000 2.305 20.000 Rel. humidity % 45.000 100.000 40.000 Ittigen, 17.02.2011 Abs. humidity g/kg 6.515 4.470 Density humid kg/m3 1.199 1.278 Enthalpy humid kj/kg 36.658 13.515 Volume flow humid m3/h 28032.572 26254.873 28000.000 Mass flow dry kg/h 33397.863 33397.863 Condensat flow kg/h 68.294 Surface temperature C 15.505-0.515 Velocity m/s 1.836 1.719 Pressure drop (dry 102 Pa) Pa 113.341 25 % Et.glycol Inlet Outlet Medium Temp. C -2.500 13.500 5.500 Density kg/m3 1042.356 Heat cont. kj/kgk 3.694 Heat cond. W/mK 0.456 Viscosity Pas 2.874E-03 Volume flow m3/h 12.571 Velocity m/s 1.159 Pressure drop kpa 186.787 Tecnical datas Tubes total Piece 576 Tubes: flat Cu Tubes blanc Piece 0 staggered Internal ventings Piece 7 Collectors: 0.85 m/s Cu Internal drains Piece 7 Connections: 0.85 m/s Rg7 Tube rows on the depth Piece 16 Fins: flat Al Tube rows on the height Piece 36 Frame: 2.00 mm AlMg3 Tube coupling in series Piece 32 Circulations: 1 Default Number of circuits (NC) Piece 18 Protection: without Volume l 311 --- Weight kg 808 El. heat rods: --- Connections G --- 2 ½" Air flow direction: horizontal Frame height RH mm 1520 Special: Bottom plate perforated Frame width BT mm 3200 for perfect condensate drain Frame depth RT mm 670 Finned height LH mm 1440 Finned width LB mm 2946 Finned depth LF mm 560 Frame on top RO mm 40 Frame on bottom RU mm 40 Frame in front RV mm 30 Frame on back (~65mm) RN mm 69 Collector-Diameter K mm 76 Collector covering AD mm 185 Collector distance KA mm 567 Fin spacing LT mm 3.000 With the compliments of Cert. Eng. Marin Zeller TU Direct dialing +41-79-2226642 Software development Fin thickness LD mm 0.250 Delivery: 5-6 weeks Tube diameter DA mm 15.400 Validity: 12 weeks Tube thickness S mm 0.400 Condit.: net, prepaid adress Tube intervall on the height S1 mm 40.000 Payment: 30 days net Tube intervall on the depth S2 mm 35.000 Price net: Non el. rods EUR 11758.00 ØK AD RV LB LT BT RN 1 2 KA LF RT 3 4

Tecnical datas Capacity sensible (kw) Capacity latent (kw) Capacity frost (kw) 20 18 16 14 12 10 8 6 4 2 0 Capacity (%) Required surface (%) Heat transfer coefficient (%) Mean temp. diff. (%) 12 n=1 n=1 n=2 n=... n=14 n=15 Step ( n = 1 to 15 ) Zeller Consulting Suisse HVAC solutions Jurastrasse 35 CH-3063 Ittigen Phone: +41-79-2226642 Fax:... Ittigen, 17.02.2011 Cert. Eng. Marin Zeller TU Direct dialing +41-79-2226642 10 Software development 8 6 4 2 0 Step ( n = 1 to 15 ) Temp. ( C) 25 20 15 10 5 0-5 Length (---)

------------------------------------------------- Zeller Consulting Suisse Cooler: 40.0/35.0/15.4-16R-36T-2951A- 3.0PA-18C HVAC solutions ------------------------------------------------- Jurastrasse 35 Capacity kw 215.421 CH-3063 Ittigen Surface reserve % -3.242 Present surface m² 1450.788 +41 79 2226642 Req1uired surface m² 1499.400 ----- Heat transfer coefficient W/m²K 34.587 Temp. diff. (74.046%) K 4.154 Air humid (F = 0.500E-04 m²k/w) Inlet Outlet Definition Height m 0.000 Pressure hpa 1013.250 Temperature C 20.000 2.305 20.000 Relative humidity % 45.000 100.000 40.000 Absolute humidity g/kg 6.515 4.470 Density kg/m³ 1.199 1.278 Enthalpy J/kg 36658.259 13514.842 Volume flow humid m³/h 28032.572 26254.873 28000.000 Mass flow dry kg/h 33397.861 33397.861 Condensate flow kg/h 68.294 Surface temperature C 15.020-0.617 Velocity m/s 1.832 1.717 Pressure drop Pa 114.670 25%Et.glycol (F = 0.500E-04 m²k/w) Inlet Outlet Means Temperature C -2.500 13.500 5.500 Density kg/m³ 1044.521 1039.879 1042.356 Heat capacity J/kgK 3673.288 3714.531 3693.925 Thermal conductivity W/mK 0.444 0.466 0.456 Dyn. viscosity Pas 0.381E-02 0.224E-02 0.287E-02 Prandtl --- 31.515 17.866 23.294 Reynolds --- 4631.995 7845.781 6144.812 Volume flow m³/h 12.562 12.576 12.588 Velocity in tubes m/s 1.158 1.159 1.160 Velocity in collectors m/s 0.856 Pressure drop kpa 188.129 Technical data Estimated with 50 finite elements Tubes total Piece 576 Tubes Cu Tubes blanc Piece 0 Collectors Cu Internal ventings Piece 7 Joints Rg7 Internal drains Piece 7 Fins Al Tube rows on the depth Piece 16 Frame AlMg3 Tube rows on the height Piece 36 Protection Without Tube coupling in series Piece 32 Air direction Horizontal Number of circuits NC Piece 18 Circuits // 1 Volume l 310 Tubes Staggered Weight kg 808 Fins Non waves Joints G -- 2 1/2" Frame 2.0 mm Frame height RH mm 1520 Frame width BT mm 3200 Frame depth RT mm 670 Finned height LH mm 1440 Sensible 166.571 kw Finned width LB mm 2951 Latent 48.134 kw Finned depth LF mm 560 Freeze 0.715 kw Frame on top RO mm 40 Frame on bottom RU mm 40 Offer 17-Feb-2011 Frame in front RV mm 30 Frame on back RN mm 65 Exchange rate EUR/EUR 1.000 Collector diameter K mm 76 Collector covering AD mm 184 Delivery 3-4 weeks Collector distance KA mm 567 Validity 12 weeks Fin spacing LT mm 3.000 Conditions Net ex works Fin thickness LD mm 0.250 Payment 30 days net Tube diameter DA mm 15.400 Tube thickness S mm 0.400 Price gross EUR 11757.00 Tube interval height S1 mm 40.000 Discount EUR 0.00 Tube interval depth S2 mm 35.000 Price net EUR 11757.00

Cooler evaluation with 50 finite elements Zeller Consulting Suisse HVAC software solutions Process engineers know the "Pinch point" problem Evaluations in 1 piece results a to small surface +41 79 222 66 42 The counter flow temp. diff. go from 5.610 K to 4.154 K The real flow temp. diff. efficiency is 74.046 % only Finite Capacity Capacity Capacity Capacity Surface Heat tra Mean temp element sensible latent freeze total required coeff diff number kw kw kw kw m² W/m²K K 1 3.345 0.000 0.000 3.345 15.317 34.628 6.306 2 3.345 0.000 0.000 3.345 15.597 34.579 6.202 3 3.345 0.000 0.000 3.345 15.886 34.530 6.097 4 3.345 0.000 0.000 3.345 16.186 34.481 5.993 5 3.345 0.000 0.000 3.345 16.497 34.431 5.888 6 3.345 0.000 0.000 3.345 16.818 34.381 5.784 7 3.345 0.000 0.000 3.345 17.152 34.331 5.680 8 3.345 0.000 0.000 3.345 17.498 34.280 5.576 9 3.344 0.000 0.000 3.344 17.858 34.230 5.471 10 3.344 0.000 0.000 3.344 18.231 34.178 5.367 11 3.344 0.000 0.000 3.344 18.620 34.127 5.263 12 3.344 0.000 0.000 3.344 19.024 34.075 5.159 13 3.344 0.000 0.000 3.344 19.446 34.022 5.055 14 3.344 0.000 0.000 3.344 19.885 33.970 4.951 15 3.344 0.000 0.000 3.344 20.343 33.917 4.847 16 3.344 0.000 0.000 3.344 20.821 33.863 4.743 17 3.344 0.000 0.000 3.344 21.321 33.810 4.639 18 3.344 0.000 0.000 3.344 21.844 33.756 4.535 19 3.344 0.000 0.000 3.344 22.391 33.701 4.431 20 3.344 0.000 0.000 3.344 22.966 33.646 4.328 21 3.344 0.000 0.000 3.344 23.568 33.591 4.224 22 3.344 0.000 0.000 3.344 24.201 33.535 4.120 23 3.344 0.000 0.000 3.344 24.867 33.479 4.016 24 3.344 0.000 0.000 3.344 25.568 33.423 3.913 25 3.344 0.000 0.000 3.344 26.308 33.366 3.809 26 3.344 0.000 0.000 3.344 27.089 33.309 3.706 27 3.344 0.000 0.000 3.344 27.916 33.251 3.602 28 3.344 0.008 0.000 3.351 28.843 33.208 3.499 29 3.344 0.378 0.000 3.722 32.274 33.822 3.410 30 3.343 0.739 0.000 4.082 35.509 34.351 3.347 31 3.343 1.078 0.000 4.421 38.400 34.789 3.310 32 3.343 1.387 0.000 4.730 40.839 35.140 3.296 33 3.342 1.659 0.000 5.002 42.765 35.406 3.303 34 3.342 1.892 0.000 5.234 44.169 35.597 3.329 35 3.341 2.086 0.000 5.427 45.082 35.721 3.370 36 3.340 2.243 0.000 5.584 45.564 35.786 3.424 37 3.340 2.367 0.000 5.707 45.686 35.803 3.489 38 3.339 2.461 0.000 5.800 45.522 35.779 3.561 39 3.338 2.530 0.000 5.869 45.138 35.721 3.640 40 3.338 2.578 0.000 5.916 44.594 35.635 3.723 41 3.337 2.608 0.000 5.945 43.940 35.527 3.808 42 3.336 2.624 0.000 5.960 43.214 35.400 3.896 43 3.336 2.627 0.000 5.962 42.446 35.258 3.984 44 3.335 2.621 0.000 5.955 41.660 35.104 4.072 45 3.334 2.606 0.000 5.941 40.873 34.940 4.160 46 3.333 2.586 0.000 5.919 40.096 34.767 4.246 47 3.333 2.560 0.000 5.893 39.340 34.588 4.331 48 3.332 2.616 0.000 5.948 39.048 34.487 4.417 49 3.331 2.721 0.362 6.414 41.205 34.423 4.522 50 3.331 2.659 0.354 6.344 39.975 34.188 4.642 Total 166.571 48.134 0.715 215.421 1499.400 34.587 4.154 Energy systems modeling and analysis HVAC software development services

Finned coil heat exchanger BT RT <-----------------------------------> <----------> LB <-----------------------> +-------------------------------------+ --- +------------+ ^ +-------+ +-------------------------+ --- +-+ +-+ +-----+ ^ +-+ LT -> <- LH RH +-----+ v +-+ +-------+ +-------------------------+ --- +-+ +-+ v +-------------------------------------+ --- +------------+ Energy systems modeling and analysis HVAC software development services