Abstract
Investigation of wall-liquid mass transfer and heat transfer phenomena with gas-Newtonian and non-Newtonian fluids in vertically helical coil reactor have been reported in this article. Experiments were conducted to investigate the effect of various dynamic and geometric parameters on mass and heat transfer coefficients in the helical coil reactor. The flow pattern-based heat and mass transfer phenomena in the helical coil reactor are highlighted at different operating conditions. The study covered a wide range of geometric parameters such as diameter of the tube (d t ), diameter of the coil (D c ), diameter of the particle (d p ), pitch difference (p/D c ) and concentrations of non-Newtonian liquid. The correlation models for the heat and mass transfer coefficient based on the flow pattern are developed which may be useful in process scale-up of the helical coil reactor for industrial application. The frictional drag coefficient was also estimated and analyzed by mass transfer phenomena based on the electrochemical method.
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Abbreviations
- A e :
-
Area of transfer surface of the electrode (m2)
- C p :
-
Specific heat (J/kg K)
- d e :
-
Electrode diameter (m)
- d t :
-
Tube diameter (m)
- d p :
-
Particle diameter (μm)
- D c :
-
Coil diameter (m)
- D L :
-
Diffusivity of reacting ion (m2 s−1)
- E :
-
Applied potential (V)
- F :
-
Faraday constant (96,500 C/g-equivalent)
- F f :
-
Frictional drag force (N)
- g :
-
Acceleration due to gravity (m s−2)
- i d :
-
Limiting current density (A m−2)
- i L :
-
Limiting current (A)
- J D :
-
Mass transfer factor (−)
- k L :
-
Mass transfer coefficient (m s−1)
- L c :
-
Length of coil (m)
- L e :
-
Equivalent electrode length (m)
- L p :
-
Pitch length (m)
- n :
-
Flow behavior index (−)
- R :
-
Radius of the electrode (m)
- T w :
-
Temperature at the wall (K)
- U l :
-
Superficial liquid velocity (m s−1)
- U g :
-
Superficial gas velocity (m s−1)
- h :
-
Heat transfer coefficient in (W/m2 K)
- q :
-
Rate of heat transfer (watt)
- q w :
-
Wall heat flux (W/m2)
- κ :
-
Thermal conductivity (W/m K)
- ρ :
-
Fluid density (kg/m3)
- μ:
-
Viscosity (kg/m s)
- v :
-
Kinematic viscosity of the fluid (m2/s)
- σ:
-
Surface tension (N/m)
- p :
-
Pitch (m)
- ρ l :
-
Density of liquid (kg m−3)
- ρ m :
-
Mixed density (kg m−3)
- ρ s :
-
Density of solids (kg m−3)
- μ eff :
-
Effective viscosity (kg m−1 s−1)
- σ l :
-
Surface tension (N m−1)
- ε g :
-
Gas holdup (−)
- Ca :
-
Capillary number (U gl μ gl /σ l ) (−)
- Br :
-
Brinkham number (μU 2 /k (T w –T o )) (−)
- Bs :
-
Bodenstein number (U gl d t /D L ) (−)
- Nu :
-
Nusselt number (hd t /k) (−)
- Pr :
-
Prandtl number (μ/(αρ)) (−)
- Ra :
-
Rayleigh number (gβΔTd 3 t ρ/αμ) (−)
- Re :
-
Reynolds Number (d t Uρ/μ) (−)
- Re cm :
-
Coil Reynolds Number (Re cm = Re (1 − (8dt )/(πD c ))) (−)
- Sc :
-
Schmidt number (μ/ρD L ) (−)
- St :
-
Stanton number (k L /U l ) (−)
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Thandlam, A.K., Das, C. & Majumder, S.K. Flow pattern-based mass and heat transfer and frictional drag of gas-non-Newtonian liquid flow in helical coil: two- and three-phase systems. Heat Mass Transfer 53, 1183–1197 (2017). https://doi.org/10.1007/s00231-016-1898-y
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DOI: https://doi.org/10.1007/s00231-016-1898-y