Flow and Heat Transfer from a Rotating Sphere Partially Immersed in a Bounded Stationary Fluid

Document Type : Research Article

Authors

Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, I.R. IRAN

Abstract

For the first time, a numerical study has been carried out to investigate the flow and heat transfer from a partially immersed rotating sphere in a bounded boundary stationary fluid with variable distances from its surface. The simulations are performed for different boundary distances under various types of rotational speed of the sphere using the two-phase VOF model. The flow and thermal fields are investigated through streamlines, isotherm, and volume fraction contours, as well as through the average Nusselt number and the thickness of the water film. The numerical results demonstrate that the water is drawn up the sphere's lower pole because of the centrifugal force generated by the rotation, and its motion continues due to the water film formation. Then, the water film is radially thrown out because of the inertial forces dominance. Moreover, the sinusoidal pulsation rotational speed indicates higher heat transfer performance among various functions. Compared with the exponential function by increasing the boundary radius from [ ] to [ ] the time-surface-averaged Nusselt number increases by about 35%. Also, it is found that as the immersion angle increases from  to , the time-surface-averaged Nusselt number increases about 51% on average for the uniform rotational speed of the sphere.

Keywords

Main Subjects

References

[1] Langley K.R., Maynes D., Truscott T.T., Eggs and Milk: Spinning Spheres Partially Immersed in a Liquid Bath, Physics of Fluids, 27(3): 032102 (2015).
[2] von Karman T., Uber Laminare Und Turbulente Reibung, Z. Angew. Math. Mech., 1: 233-252 (1921).
[3] Nematollahzadeh A., Jangara H., Exact Analytical and Numerical Solutions for Convective Heat Transfer in a Semi-Spherical Extended Surface with Regular Singular Points, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 40(3): 980-989 (2021).
[4] Habibi M.R., Amini M., Arefmanesh A., Ghasemikafrudi E., Effects of Viscosity Variations on Buoyancy-Driven Flow from a Horizontal Circular Cylinder Immersed in Al2O3-Water Nanofluid, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 38(1): 213-232 (2019).
[5] Naseri Nia S., Rabiei F., Rashidi M.M., Kwang T.M., Lattice Boltzmann Simulation of Natural Convection Heat Transfer of a Nanofluid in a L-Shape Enclosure with a Baffle, Results in Physics, 19: 103413 (2020).
[6] Rashidi M.M., Sadri M., Sheremet M.A., Numerical Simulation of Hybrid Nanofluid Mixed Convection in a Lid-Driven Square Cavity with Magnetic Field Using High-Order Compact Scheme, Nanomaterials, 11(9): 2250 (2021).
[7] Zahmatkesh R., Mohammadiun H., Mohammadiun M., Dibaei Bonab M.H., Sadi M., Theoretical Investigation of Entropy Generation in Axisymmetric Stagnation Point Flow of Nanofluid Impinging on the Cylinder Axes with Constant Wall Heat Flux and Uniform Transpiration, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 40(6): 1893-1908 (2021).
[8] Mohammadiun H., Montazeri M., Mohammadiun M., dibaee bonab M.h., Vahedi M., Inverse Estimation of Time-Dependent Heat Flux in Stagnation Region of Annular Jet on a Cylinder Using Levenberg–Marquardt Method, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 41(3): 971-988 (2021).
[9] Majeed A., Amin N., Zeeshan A., Ellahi R., Sait S.M., Vafai K., Numerical Investigation on Activation Energy of Chemically Reactive Heat Transfer Unsteady Flow with Multiple Slips, International Journal of Numerical Methods for Heat & Fluid Flow, 30(11): 4955-4977 (2020).
[10] Ellahi R., Alamri S.Z., Basit A., Majeed A., Effects of Mhd and Slip-on Heat Transfer Boundary Layer Flow over a Moving Plate Based on Specific Entropy Generation, Journal of Taibah University for Science, 12(4): 476-482 (2018).
[11] Goodarzi M., Tlili I., Moria H., Abdullah Alkanhal T., Ellahi R., Anqi A.E., Reza Safaei M., Boiling Heat Transfer Characteristics of Graphene Oxide Nanoplatelets Nano-Suspensions of Water-Perfluorohexane (C6F14) and Water-N-Pentane, Alexandria Engineering Journal, 59(6): 4511-4521 (2020).
[12] Bhatti M.M., Ellahi R., Zeeshan A., Marin M., Ijaz N., Numerical Study of Heat Transfer and Hall Current Impact on Peristaltic Propulsion of Particle-Fluid Suspension with Compliant Wall Properties, Modern Physics Letters B, 33(35): 1950439 (2019).
[13] Montazeri M., Mohammadiun H., Mohammadiun M., Dibaee Bonab M.H., Vahedi M., Inverse Analysis of the Time-Dependent Heat Flux in Stagnation Point Flow of Incompressible Fluid Impinging on a Cylinder with Uniform Surface Suction-Blowing Using Levenberg–Marquardt Method, Inverse Problems in Science and Engineering, 29(9): 1219-1259 (2021).
[14] Bilal Ashraf M., Chemically Radiative Flow of Viscoelastic Fluid over Stretching Cylinder with Convective Condition, Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 40(5): 1683-1692 (2021).
[15] Alsabery A.I., Selimefendigil F., Hashim I., Chamkha A.J., Ghalambaz M., Fluid-Structure Interaction Analysis of Entropy Generation and Mixed Convection inside a Cavity with Flexible Right Wall and Heated Rotating Cylinder, International Journal of Heat and Mass Transfer, 140: 331-345 (2019).
[16] Wang T., Wang Z., Xi G., Huang Z., Periodic Unsteady Mixed Convection in Square Enclosure Induced by Inner Rotating Circular Cylinder with Time-Periodic Pulsating Temperature, International Journal of Heat and Mass Transfer, 111: 1250-1259 (2017).
[17] Liao C.-C., Lin C.-A., Mixed Convection of a Heated Rotating Cylinder in a Square Enclosure, International Journal of Heat and Mass Transfer, 72:  9-22 (2014).
[18] Sasmal C., Gupta A.K., Chhabra R.P., Natural Convection Heat Transfer in a Power-Law Fluid from a Heated Rotating Cylinder in a Square Duct, International Journal of Heat and Mass Transfer, 129: 975-996 (2019).
[19] Kareem A.K., Gao S., Mixed Convection Heat Transfer of Turbulent Flow in a Three-Dimensional Lid-Driven Cavity with a Rotating Cylinder, International Journal of Heat and Mass Transfer, 112: 185-200 (2017).
[20]   Selimefendigil F., Öztop H.F., Mixed Convection of Nanofluids in a Three-Dimensional Cavity with Two Adiabatic Inner Rotating Cylinders, International Journal of Heat and Mass Transfer, 117: 331-343 (2018).
[21] Shirazi M., Shateri A., Bayareh M., Numerical Investigation of Mixed Convection Heat Transfer of a Nanofluid in a Circular Enclosure with a Rotating Inner Cylinder, Journal of Thermal Analysis and Calorimetry, 133(2): 1061-1073 (2018).
[22] Souayeh B., Hdhiri N., Alam M.W., Hammami F., Alfannakh H., Convective Heat Transfer and Entropy Generation around a Sphere within Cuboidal Enclosure, Journal of Thermophysics and Heat Transfer, 34(3): 605-625 (2020).
[23] Lee D., Jang H., Lee B.J., Choi W., Byon C., Internal Natural Convection around a Sphere in a Rectangular Chamber, International Journal of Heat and Mass Transfer, 136: 501-509 (2019).
[24] Gallegos A.D., Málaga C., Natural Convection in Eccentric Spherical Annuli, European Journal of Mechanics - B/Fluids, 65: 464-471 (2017).
[25] Chen Z., Yang L.M., Shu C., Zhao X., Liu N.Y., Liu Y.Y., Mixed Convection between Rotating Sphere and Concentric Cubical Enclosure, Physics of Fluids, 33(1): 013605 (2021).
[26]   D’Alessio S., An Analytical Study of the Early Stages of Unsteady Free Convective Flow from a Differentially Heated Rotating Sphere at Large Grashof Numbers, International Journal of Computational Methods and Experimental Measurements, 7(1): 57-67 (2018).
[27] Jabari Moghadam A., Baradaran Rahimi A., A Numerical Study of Flow and Heat Transfer between Two Concentric Rotating Spheres with Time-Depenent Angular Velocities, Scientia Iranica (Transaction B: Mechanical Engineering), 16(3): 197-211 (2009).
[28] Jabari Moghadam A., Baradaran Rahimi A., Similarity Solution in the Study of Flow and Heat Transfer between Two Rotating Spheres with Constant Angular Velocities, Scientia Iranica (Transaction B: Mechanical Engineering), 16(4): 354-362 (2009).
[29] Hao X., Yang X., Peng C., Yao Z., Heat Transfer between Rotating Sphere and Spherical-Surface Heat Sink, Journal of Thermal Analysis and Calorimetry, 141(1): 413-420 (2020).
[30] Zhang J., Zhen Q., Liu J., Lu W.-Q., Effect of Spacing on Laminar Natural Convection Flow and Heat Transfer from Two Spheres in Vertical Arrangement, International Journal of Heat and Mass Transfer, 134: 852-865 (2019).
[31] Nigam S.D., Note on the Boundary Layer on a Rotating Sphere, Zeitschrift für angewandte Mathematik und Physik ZAMP, 5(2): 151-155 (1954).
[32] Singh S.N., Heat Transfer by Laminar Flow from a Rotating Sphere, Applied Scientific Research, 9(1): 197 (1960).
[33] Samad A., Garrett S.J., On the Laminar Boundary-Layer Flow over Rotating Spheroids, International Journal of Engineering Science, 48(12): 2015-2027 (2010).
[34] Kreith F., Roberts L.G., Sullivan J.A., Sinha S.N., Convection Heat Transfer and Flow Phenomena of Rotating Spheres, International Journal of Heat and Mass Transfer, 6(10): 881-895 (1963).
[35] Feng Z.-G., Direct Numerical Simulation of Forced Convective Heat Transfer from a Heated Rotating Sphere in Laminar Flows, Journal of Heat Transfer, 136(4): (2014).
[36] Gutiérrez G., Fehr C., Calzadilla A., Figueroa D., Fluid Flow up the Wall of a Spinning Egg, American Journal of Physics, 66(5): 442-445 (1998).
[37] Martinez J., Polatdemir E., Bansal A., Yifeng W., Shengtao W., Fluid Flow up a Spinning Egg and the Coriolis Force, European Journal of Physics, 27(4): 805 (2006).
[38] Safarzadeh S., Rahimi A.B., Numerical Investigation of Flow and Heat Transfer from a Rotating Sphere with Constant Angular Velocity around Vertical Axis Floating in Stationary Fluid, Journal of Heat Transfer, 144(2): (2021).
[39] Hirt C.W., Nichols B.D., Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries, Journal of Computational Physics, 39(1): 201-225 (1981).
[40] Kohama Y., Kobayashi R., Boundary-Layer Transition and the Behaviour of Spiral Vortices on Rotating Spheres, Journal of Fluid Mechanics, 137: 153-164 (1983).
[41] Garrett S.J., Peake N., The Stability and Transition of the Boundary Layer on a Rotating Sphere, Journal of Fluid Mechanics, 456: 199-218 (2002).
[42] Brackbill J.U., Kothe D.B., Zemach C., A Continuum Method for Modeling Surface Tension, Journal of Computational Physics, 100(2): 335-354 (1992).
[43] Du W., Feng D., Xu J., Wei W., Computational Fluid Dynamics Modeling of Gas-Liquid Two-Phase Flow around a Spherical Particle, Chemical Engineering & Technology, 36(5): 840-850 (2013).
Iranian Journal of Chemistry and Chemical Engineering
Volume 42, Issue 4 - Serial Number 126
April 2023
Pages 1329-1342

Files

Share

How to cite

Statistics