Heat Exchanger Design

Double Pipe Heat Exchanger

Heat load

Heat load by energy balance equation,
Q= m_H.C_pH(T_{Hot in} − T_{Hot out}) = m_C.C_pC(t_{Cold out} − t_{Cold in})
where,
m_H, m_C - Mass flow rate of hot and cold fluid
C_pH, C_pC - Specific Heat of Hot and Cold fluid
T_{Hot In}, T_{Hot Out} - Inlet and outlet temperature of hot fluid
t_{Cold in}, t_{Cold out} - Inlet and outlet temperature of cold fluid

Logarithmic Mean Temperature Difference

LMTD = (ΔT₁ − ΔT₂)/ln( ΔT₁ / ΔT₂)
Counter-current flow,
ΔT₁ = T_{Hot in} − t_{Cold out}
ΔT₂ = T_{Hot out} − t_{Cold in}
Co-current flow,

ΔT₁ = T_{Hot in} − t_{Cold in}

ΔT₂ = T_{Hot out} − t_{Cold out}

Film Coefficient

Inner Tube,

D_e = D_i

A_f = π × D_i²/4

Annular,

D_e = D₁ − D_o

A_f = π(D₁² − D_o²)/4

where,

D_e - Equivalent diameter

D_i - Inner diameter of inside pipe

D_o - Outer diameter of inside pipe

D₁ - Inner diameter of outside pipe

A_f - Flow area

Calculate velocity (V), Reynolds number (Re) and Prandtl number (Pr) to find the flow, weather the flow is laminar or turbulent.

Overall Heat Transfer Coefficient

1/U = (D_o/h_i × D_i) + (D_o × ln(D_o/D_i)/2k_t) + (1/h_o) + (R_i × D_o/D_i) + R_o

where,

R_i - Fouling factor (inner pipe)

R_o - Fouling factor (annular pipe)

k_t - Thermal conductivity of tube

h_i - Film coefficient (inner pipe)

h_o - Film coefficient (annular pipe)

Area and length,

Area = Q/(U × LMTD)

L = Area/π × D_o