### Counter & Parallel Flow Heat Exchanger Tube Length Calculation

Counter & Parallel Flow Heat Exchanger Tube Length Calculation
Input data in YELLOW

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Heat transfer, Q = U*A*∆Tm

Plane wall heat transfer coefficient, U = 1 / (1/ho + L/K + 1/h1

Cylindrical wall heat transfer coefficient, U = 1 / (1/hi + [RoLn(Ro/Ri)]/K + Ri/Ro)
i and o refer to inside and outside tube surfaces.

Large temperature difference, ΔTbc = Ta - Td
ΔTbc = From Input Data below.
Small temperature difference, ΔTad = Tb - Tc
ΔTad = From Input Data below.
The added resistance to heat transfer caused by corrosion is called fouling.
Fouling factor, R ranges between 0.0005 and 0.002. See manufactures data.
Fouling factor, R = (1/Udirty) - (1/Uclean)

Forced Convection - in Coiled Tube Heat Exchangers
Turbulent flow in coiled tube. Input Data
Temp. of Fluid (Liquid) flowing in, Ta = deg C
Temp. of Fluid (Liquid) flowing out, Tb = deg C
Tc = deg C
Td = deg C
Tube inside diameter, Di = mm
Tube outside diameter, Do = mm
Velocity of Fluid (Liquid) in tube, V = m / s

Water properties at temperature Tb deg C from the table above:
Fluid (Liquid) density, ρ = kg / m^3
Cp = k*J/kg*K
Fluid (Liquid) dynamic viscosity, μ = kg / m*s
Fluid (Liquid) conductivity, k = W / m*K
Prandtl number, Pr = -
Factor, n =
Velocity of Fluid (Liquid) in tube, V = m / s

Results
Fluid (Liquid) bulk temperature, Tb = (Tin + Tout) / 2 deg C
Reynolds Number, Re = V*D / ν
or, Re = V*D*ρ / μ
Answer: Re = Turbulent Re >4000

Convective heat transfer coefficient, h = 0.023*(Re^.8)*(Pr^n)*(k/d)
S.I. Answer: h = W / m^2*K
U.S. Answer: h = (W/m^2*K)/5.5956 Btu/hr-ft^2*F

S.I. Answer from above: h = W / m^2*K
Large temperature difference, ΔTbc = Tb - Tc

Small temperature difference, ΔTad = Ta - Td

Overall heat transfer coefficient = Uo
Heat flow rate, Q = Uo*A*ΔTm
Heat flow rate thru inside tube wall, Qi = Uo*π*di*L*ΔTm
Heat flow rate thru outside tube wall, Qo = Uo*π*do*L*ΔTm
Uo = h *Ai / Ao

Tube inside area, Ai = π*di*L
Tube outside area, Ao = π*do*L
Overall heat transfer coefficient, Uo = h *di / do
Answer: Uo = W / m^2*K

Cp = Cp*1000 1000*J/kJ

Disregarding tube fouling, determine the tube length required:
The tube length required, L = ρ*V*(di)^2*Cp*(Tout -Tin) / (4*Uo*do*ΔTm)