Abstract
Computational fluid dynamics (CFD) analysis using ANSYS Fluent software has been carried out to investigate velocity profiles and thermal characteristics of milk during heating under mechanically agitated condition. In earlier article experimental data on forced convection heat transfer coefficient \(\left(\stackrel{-}{\mathrm{h}}\right)\) and correlations of the form \(\mathrm{N}\mathrm{u}=\mathrm{a}\cdot {\mathrm{R}\mathrm{e}}^{\mathrm{b}}\cdot {\mathrm{P}\mathrm{r}}^{0.33}\) for cow milk, standardised milk and full cream milk in Baffled vessel and Unbaffled vessel with scraping, using Propeller, Flat Six Blade Turbine (FBT), Inclined Six Blade Turbine (IBT) and Paddle impellers were reported. It was noted milk in Baffled vessel with Paddle impeller provided highest \(\stackrel{-}{\mathrm{h}}\) even at lower rotational speeds followed by Propeller, FBT and IBT impellers. In Unbaffled vessel with scraping, Propeller provided the highest \(\stackrel{-}{\mathrm{h}}\) followed by FBT and IBT impellers. Hence, the present investigation has been carried out to validate and understand how different velocity of flow currents and their magnitude influence the heat transfer coefficient values in CFD simulation. It also justifies the relative performance of the impellers delineated in the earlier paper. In addition, theoretical values of heat transfer coefficients computed using CFD shows close agreement with experimental values.
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Abbreviations
- \({\mathrm{C}}_{\mathrm{p}\mathrm{m}}\) :
-
Specific heat \(\left(\frac{\mathrm{J}}{\mathrm{K}\mathrm{g} \mathrm{K}}\right)\)
- \({\mathrm{D}}_{\mathrm{a}}\) :
-
Diameter of impeller (mm)
- \({\mathrm{D}}_{\mathrm{t}}\) :
-
Diameter of milk vessel (mm)
- E:
-
Height of the impeller position from vessel bottom (mm)
- W:
-
Width of the impeller blade (mm)
- L:
-
Length of the impeller blade (mm)
- g:
-
Acceleration due gravity \(\left(\frac{\mathrm{m}}{{\mathrm{s}}^{2}}\right)\)
- \(\stackrel{-}{\mathrm{h}}\) :
-
Forced convection heat transfer coefficient \(\left(\frac{\mathrm{W}}{{\mathrm{m}}^{2}\mathrm{K}}\right)\)
- H:
-
Milk level in the vessel (mm)
- J:
-
Baffle width (mm)
- \({\mathrm{k}}_{\mathrm{m}}\) :
-
Thermal conductivity of milk \(\left(\frac{\mathrm{W}}{\mathrm{m} \mathrm{K}}\right)\)
- m:
-
Mass of milk (kg)
- n:
-
Speed of rotation of impeller (rpm)
- Nu:
-
Nusselt number dimensionless \(\left(\frac{\stackrel{-}{\mathrm{h}}{\mathrm{D}}_{\mathrm{t}}}{{\mathrm{k}}_{\mathrm{m}}}\right)\)
- p:
-
Pressure \(\left(\frac{\mathrm{N}}{{\mathrm{m}}^{2}}\right)\)
- Pr:
-
Prandtl numberdimensionless \(\left(\frac{\mathrm{C}\mathrm{p}\mathrm{m}{\upmu }_{\mathrm{m}}}{{\mathrm{k}}_{\mathrm{m}}}\right)\)
- q:
-
Heat transfer by conduction (Watt)
- Re:
-
Reynolds number dimensionless \(\left(\frac{\mathrm{n}}{60}\right)\left(\frac{{\mathrm{D}}_{\mathrm{a}}^{2} \uprho }{\upmu }\right)\)
- SS:
-
Stainless steel
- t:
-
Vessel thickness (mm), blade thickness (mm) and time (s)
- \({\mathrm{T}}_{\mathrm{m}}\) :
-
Milk temperature (K)
- \({\mathrm{T}}_{\mathrm{s}}\) :
-
Vessel bottom surface temperature (K)
- \({\mathrm{T}}_{\mathrm{m}\mathrm{o}}\) :
-
Initial temperature of milk (K)
- \({\mathrm{T}}_{\mathrm{m}\mathrm{f}}\) :
-
Final temperature of milk (K)
- V:
-
Velocity \(\left(\frac{\mathrm{m}}{\mathrm{s}}\right)\), Volume of milk in the vessel (m3)
- a, b, c, n:
-
Correlation constants in equations
- Exptl:
-
Experimental
- CFD:
-
Computational fluid dynamics
- FBT:
-
Flat six blade turbine
- \({\uprho }_{\mathrm{m}}\) :
-
Density of milk \(\left(\frac{\mathrm{K}\mathrm{g}}{{\mathrm{m}}^{3}}\right)\)
- \({\upmu }_{\mathrm{m}}\) :
-
Viscosity of milk \(\left(\frac{\mathrm{K}\mathrm{g}}{\mathrm{m} \mathrm{s}}\right)\)
- \(\uptau\) :
-
Shear stress \(\left(\frac{\mathrm{N}}{{\mathrm{m}}^{\mathrm{s}}}\right)\)
- \(\Delta \mathrm{T}\) :
-
Temperature differences (K)
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Acknowledgement
The authors are grateful to the University Grants Commission, Govt. of India (UGC) for providing grants and continuous support during the work. The authors are grateful for laboratory facilities provided by the Centre for AU-FRG institute for CAD/CAM, Anna University, Chennai, Tamil Nadu, India.
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Rajasekaran, E., Kumar, B., Muruganandhan, R. et al. CFD simulation of convective heat transfer in vessel with mechanical agitation for milk. J Food Sci Technol 57, 3667–3676 (2020). https://doi.org/10.1007/s13197-020-04399-1
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DOI: https://doi.org/10.1007/s13197-020-04399-1