Abstract
This article studies how the natural convection in the annular space between a pair of cylinders is affected by a number of parameters including Rayleigh number, type, number and geometry of fins, and injection of water particles. To this aim, the finite volume method is employed. Various fin types including a linear fin with an arbitrary number of blades, annular fins with different pitch values, straight and curved twisting fins, and conical fins are considered. The results indicate that by adding to the quantity of fins and decreasing the distance between them, the effective thermal conductivity coefficient grows compared to the case without fins. The shape of these fins plays a significant role in the amount of the heat transfer from the annular space such that the highest percentage increase, i.e. 67%, belongs to the curved twisting fin. When the two cylinders are not concentric, the effective thermal conductivity coefficient grows which can be further increased by increasing the Rayleigh number. Using two-phase modeling, it is observed that in the presence of water particles, the heat transfer from the cylindrical space is reduced. Compared to the single-phase scenario, this corresponds to a reduction of about 70% and 23% in the case of four linear fins and annular fins with a pitch of 20 mm, respectively.
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Abbreviations
- \(k_{{eff}}\) :
-
Effective thermal conductivity coefficient, W/m2.K
- \({\text{h}}\) :
-
Convective heat transfer coefficient, \(~{\text{W/m}}^{{\text{2}}} {\text{K}}\)
- \(D\) :
-
External tube diameter, \({\text{m}}\)
- \(L\) :
-
Length of the tube, \({\text{m}}\)
- \(Nu\) :
-
Nusselt number
- \(P\) :
-
Pressure, \(~{\text{kPa}}\)
- \(Ra\) :
-
Rayleigh number
- \(T\) :
-
Temperature, \(~{\text{K}}\)
- \(V\) :
-
Velocity, \(~{\text{m/s}}\)
- \(d\) :
-
Inner tube diameter, \({\text{m}}\)
- \(f\) :
-
Volume fraction
- \(g\) :
-
Gravity acceleration, \(~{\text{m/s}}^{{\text{2}}}\)
- \(k\) :
-
Thermal conductivity coefficient, W/m.K
- \(q\) :
-
Heat transfer rate per tube’s unit length, \(~{\text{W/m}}\)
- \(t\) :
-
Time \(~{\text{s}}\)
- \(\alpha\) :
-
Thermal diffusion coefficient, \(~{\text{m}}^{{\text{2}}} {\text{/s}}\)
- \(\beta\) :
-
Thermal expansion coefficient, \({\text{K}}^{{ - 1}}\)
- \(\mu\) :
-
Dynamic viscosity, Pa.s
- \(\rho\) :
-
Density, \(~{\text{kg/m}}^{{\text{3}}}\)
- \(\vartheta\) :
-
Kinetic viscosity \(~{\text{m}}^{{\text{2}}} {\text{/s}}\)
- \(H\) :
-
Hot
- \(c\) :
-
Cold
- \(m\) :
-
Mixture
- \(o\) :
-
Operating condition
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Farahani, S.D., Sheikhi, R. & Kisomi, M.S. Natural convection heat transfer in the annular space by using novel fins and water droplets injection. Braz. J. Chem. Eng. 39, 441–454 (2022). https://doi.org/10.1007/s43153-021-00123-4
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DOI: https://doi.org/10.1007/s43153-021-00123-4