Summary
Based on the spiral of Archimedes, an analytical solution is developed which describes the thermal behaviour of the countercurrent Spiral Heat Exchanger (SHE) including the characteristic maximum of effectiveness occurring with increasing values of NTU. For the analysis, the overall heat transfer coefficient and both heat capacities are assumed to be constant along the flow path. Additionally, such a high number of turns is presumed that the special situation in the first and last turn does not have to be taken into account. The analytical solution of the energy balance equations yields a simple, universal formula for the log mean temperature difference correction factor F as function of NTUI and NTUII, as well as the number of channels and further geometrical parameters.
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Abbreviations
- Ac=hob:
-
m cross-sectional area of flow channel
- Ao :
-
m total heat transfer surface area
- b:
-
m channel spacing
- \(C = \sqrt {C_I C_{II} } \) :
-
W/K mean heat capacity rate
- \(CN = 2NTU\sqrt {\pi A_c /A_o } \) :
-
Criterion Number
- F:
-
log mean temperature difference correction factor
- f=CNo/CN:
-
adjustment factor for Criterion Number
- ho :
-
m height of exchanger
- k:
-
W/m2K overall heat transfer coefficient
- n:
-
number of channels equal to double number of turns
- NTU=kAo/C:
-
number of transfer units (mean value)
- P:
-
effectiveness, dimensionless temperature change
-
: -
W/rad heat flux Q, related to angle F (see Fig. 2.)
- R = CI/CII :
-
heat capacity rate ratio
- r=r/b:
-
dimensionless radius, r’ real radius
-
: -
dimensionless temperature, t’ real temperature of fluid I or II
- x=ψr:
-
coordinate proportional to distance measured along main spiral
- Δ(r) = tI(r)-tII(r):
-
local temperature difference
- Θ:
-
mean temperature difference
- ψ = 2πkAc/C:
-
cross-sectional number of transfer units (mean value)
- κ(t) = ψr[tI(r+l)-tII(r-l)]:
-
reduced heat flux density
- â„“:
-
rad angle in polar coordinate system (see Fig. 2.)
:
:References
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© 1992 Springer-Verlag Berlin Heidelberg
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Bes, T., Roetzel, W. (1992). Approximate Theory of Spiral Heat Exchanger. In: Roetzel, W., Heggs, P.J., Butterworth, D. (eds) Design and Operation of Heat Exchangers. EUROTHERM Seminars, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84450-8_21
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DOI: https://doi.org/10.1007/978-3-642-84450-8_21
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