Fin coil calculation with NTU

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1 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 Outlet temperature t1a C Mass flow M1 kg/s Heat capacity cp1 J/kgK Capacity Q W Capacity flow W1 W/K Temperature change P Capacity flow quotient R Number of transfer units NTU Temperature quotient Ɵ %Et.glycol Inlet temperature t2e C Outlet temperature t2a C Mass flow M2 kg/s Heat capacity cp2 J/kgK Capacity Q W Capacity flow W2 W/K Temperature change P Capacity flow quotient R Number of transfer units NTU Temperature quotient Ɵ Fin coil Capacity Q W Heat transfer coefficient k W/m2K Surface A m Mean temperature difference dtm K Mean temp. diff. max. dtm max K Efficiency η

2 RU G LH RH RO Cooler: 40/35/15-16R-36T-2946A-3.0PA-18C-Cu/Al/AlMg3 Capacity kw sensible: Surface reserve % latent: Present surface m frost: Required surface m Heat transfer coefficient W/m2K ffi: 5.000E-05 Mean temp. diff. ( % ) K ffa: 5.000E-05 Zeller Consulting Suisse HVAC solutions Jurastrasse 35 CH-3063 Ittigen Air humid Inlet Outlet Definition Phone: Fax:... Height over sea level m Pressure hpa Temp. C Rel. humidity % Ittigen, Abs. humidity g/kg Density humid kg/m Enthalpy humid kj/kg Volume flow humid m3/h Mass flow dry kg/h Condensat flow kg/h Surface temperature C Velocity m/s Pressure drop (dry 102 Pa) Pa % Et.glycol Inlet Outlet Medium Temp. C Density kg/m Heat cont. kj/kgk Heat cond. W/mK Viscosity Pas 2.874E-03 Volume flow m3/h Velocity m/s Pressure drop kpa 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 Weight kg 808 El. heat rods: --- Connections G 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 With the compliments of Cert. Eng. Marin Zeller TU Direct dialing Software development Fin thickness LD mm Delivery: 5-6 weeks Tube diameter DA mm Validity: 12 weeks Tube thickness S mm Condit.: net, prepaid adress Tube intervall on the height S1 mm Payment: 30 days net Tube intervall on the depth S2 mm Price net: Non el. rods EUR ØK AD RV LB LT BT RN 1 2 KA LF RT 3 4

3 Tecnical datas Capacity sensible (kw) Capacity latent (kw) Capacity frost (kw) 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: Fax:... Ittigen, Cert. Eng. Marin Zeller TU Direct dialing Software development Step ( n = 1 to 15 ) Temp. ( C) Length (---)

4 Zeller Consulting Suisse Cooler: 40.0/35.0/ R-36T-2951A- 3.0PA-18C HVAC solutions Jurastrasse 35 Capacity kw CH-3063 Ittigen Surface reserve % Present surface m² Req1uired surface m² Heat transfer coefficient W/m²K Temp. diff. (74.046%) K Air humid (F = 0.500E-04 m²k/w) Inlet Outlet Definition Height m Pressure hpa Temperature C Relative humidity % Absolute humidity g/kg Density kg/m³ Enthalpy J/kg Volume flow humid m³/h Mass flow dry kg/h Condensate flow kg/h Surface temperature C Velocity m/s Pressure drop Pa %Et.glycol (F = 0.500E-04 m²k/w) Inlet Outlet Means Temperature C Density kg/m³ Heat capacity J/kgK Thermal conductivity W/mK Dyn. viscosity Pas 0.381E E E-02 Prandtl Reynolds Volume flow m³/h Velocity in tubes m/s Velocity in collectors m/s Pressure drop kpa 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" 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 kw Finned width LB mm 2951 Latent kw Finned depth LF mm 560 Freeze 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 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 Conditions Net ex works Fin thickness LD mm Payment 30 days net Tube diameter DA mm Tube thickness S mm Price gross EUR Tube interval height S1 mm Discount EUR 0.00 Tube interval depth S2 mm Price net EUR

5 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 The counter flow temp. diff. go from K to K The real flow temp. diff. efficiency is % 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 Total Energy systems modeling and analysis HVAC software development services

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

Proses = 0 / 0 Proses = 0 / 36 16" 4576 / 2.3 Barat : 4833 / Utara : 5941 / 3.05 Proses = 63 / 37 Flow : 9936 / 3.2

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