Monrad-Pelton Concentric Annulus Heat Transfer Formula (Double-Pipe Exchangers)

Why substituting hydraulic diameter D_h = D_o - D_i into Dittus-Boelter misses inner-tube curvature!

In a concentric double-pipe (hairpin) heat exchanger, heat transfers across the outer surface of the inner tube (diameter D_i) into fluid flowing through the annular gap bounded by outer shell D_o! Because convex transverse curvature thins the thermal boundary layer on the inner pipe relative to the insulated outer pipe, Carl C. Monrad and John F. Pelton (1942, AIChE Transactions) established the inner-wall turbulent correlation Nu_i = 0.020 * Re_Dh^0.8 * Pr^(1/3) * (D_o / D_i)^0.53 (for Re_Dh > 10,000)!

For an annulus with outer shell ID D_o = 0.050 m and inner pipe OD D_i = 0.025 m (D_o / D_i = 2.0 -> curvature factor 2^0.53 = 1.4439) at Re_Dh = 28,000 and Pr = 4.5, inner-wall Nusselt reaches Nu_i = 172.20—rising to 213.49 when outer jacket diameter widens to D_o = 0.075 m (D_o / D_i = 3.0)!

Monrad-Pelton Inner-Wall Turbulent Annulus Nusselt Number Nu_i

Evaluates 0.020 * Re^0.8 * Pr^(1/3) * (D_o / D_i)^0.53 from outer diameter B2 (m), inner diameter B3 (m), turbulent Reynolds B4 (>= 10,000), and Prandtl B5.

=IF(OR(B3 <= 0, B2 <= B3, B4 < 10000, B5 <= 0), "Requires Do > Di and Turbulent Re >= 10000", ROUND(0.020 * (B4 ^ 0.8) * (B5 ^ (1 / 3)) * ((B2 / B3) ^ 0.53), 2))

Annular Curvature Enhancement Multiplier (D_o / D_i)^0.53

Computes the geometric curvature boost on the inner heated wall.

=IF(OR(B3 <= 0, B2 <= B3), "Requires Do > Di and Turbulent Re >= 10000", ROUND((B2 / B3) ^ 0.53, 4))

Further reading

• Microsoft Support — POWER function