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Section summary |
---|

1. Heat transfer on
the tube side of a shell tube heat exchanger |

2. Calculation of
the heat transfer coefficient on the tube side |

The pressure drop on the shell side of a shell-tubes heat exchanger is made of several components : the pressure drop in the inlet nozzle, the pressure drop in the outlet nozzle and the pressure drop through the tube bundle in the shell.

**ΔP _{t} = ΔP_{i} + ΔP_{o}
+ ΔP_{s}**

With

ΔP_{t} = total pressure drop in the heat exchanger (shell
side)

ΔP_{i} = pressure drop in the inlet nozzle

ΔP_{o} = pressure drop in the outlet nozzle

ΔP_{s} = pressure drop in the shell

The most complex is to calculate the pressure drop in the shell.

The Bell Delaware method expresses the pressure drop inside the shell with the following formula :

ΔP_{s} = [(N_{ch}-1).ΔP_{CT}K_{BP}+N_{ch}.ΔP_{CF}].K_{F}+2.ΔP_{CT}K_{BP}.(1+N_{OF}/N_{CT})

With

ΔP_{s} = pressure drop in the shell (Pa)

N_{ch} = number of baffles

ΔP_{CT} = pressure drop in between 2 baffles for ideal cross
flow (Pa)

ΔP_{CF} = pressure drop in the baffle window section (Pa)

K_{BP} = correction factor for bypass flow

K_{F} = correction factor for leakage in between shell /
baffles and tubes / baffles

N_{OF} = number of tubes in baffle window

N_{CT} = Number of tube rows crossed between baffle tips in
one baffle section

The following equation allows to calculate the pressure drop :

Nu = 1.86.Re^{1/3}.Pr^{1/3}.(d_{i} / L)^{1/3}.(μ/μ_{t})^{0.14}

With :

Re = Reynolds number

Pr = Prandtl number = Cp.μ / λ

d_{i} = internal diameter of the tube in m

L = length of the tube in m

μ = viscosity of the fluid at bulk temperature in Pa.s (kg/m/s)

μ_{t} = viscosity of the fluid a wall temperature in Pa.s
(kg/m/s)

Cp = specific heat of the fluid in J/kg/K (m^{2}/s^{2}/K)

λ = thermal conductivity of the fluid (W/(m.K)) (m⋅kg⋅s^{−3}⋅K^{−1})

The following correlation is from Colburn.

Nu = 0.027.Re^{0.8}.Pr^{1/3}.(μ/μ_{t})^{0.14}

The Reynolds number can be calculated as a function of the mass flow, number of tubes, number of passes, tube diameter.

Re = G.d_{i} / μ

G = m / [(Nt/nt).π.d_{i}^{2}/4]

With

G = mass flux in the tube in kg/s/m^{2}

ṁ = mass flow in the heat exchanger on the tube side in kg/s

N_{t} = number of tubes in the shell tube heat exchanger

n_{t} = number of passes tube in the shell tube heat
exchanger

μ = viscosity of the fluid at bulk temperature in Pa.s (kg/m/s)