Convection Film Coefficient of a Tube Bundle
When organizing heat exchange between the heat carrier and a group of pipes located in several rows, the heat transfer process becomes somewhat more complicated. In this case, heat transfer depends on the relative position of the pipes and the row in which a particular pipe is located. At that, correction factors are introduced in the calculation of the Nusselt number, taking into account the location of the pipes in the group:
εs = (S2 / d)-0.15 - at in-lined pipe arrangement;
εs = (S1 / S2)0.167 - at staggered pipe arrangement.
As the first row of pipes is in undisturbed fluid flow, the heat transfer of the pipes of the first row is less than that of the subsequent ones. In this regard, to take into account the unevenness of heat transfer, coefficients are introduced for the first, second and subsequent rows of pipes:
ε1 = 0.6 - for first row;
ε2 = 0.9 - for second row at in-line arrangement;
ε2 = 0.7 - for second row at staggered arrangement;
εi = 1 - for third and next rows.
When calculating the Nusselt number, the similarity constants also depend on the relative position of the pipes in a turbulent flow:
Nuf = 0.56×Ref0.5×Pr0.36 - at laminar flow;
Nuf = 0.26×Ref0.65×Pr0.33 - at in-lined pipe arrangement in turbulent flow;
Nuf = 0.41×Ref0.6×Pr0.33 - at staggered pipe arrangement in turbulent flow.
In this calculation, the process of heat transfer from a bundle of pipes of diameter D is considered. The pipes are in contact with a fluid flow with dynamic viscosity μ, density ρ, thermal conductivity λ and specific heat Cp. The flow crosses the pipes at an angle ψ with an average velocity W.
As a result of calculations, the average convective film coefficient α of pipe outer surfaces is determined. In addition, similarity criteria for a given design case are determined, including Reynolds number Re, Prandtl number Pr, Peclet number Pe and Nusselt number Nu.
For the calculation, the number of pipe rows z and the distances between the pipes in transverse S1 and longitudinal S2 directions should be specified.