Document Type : Research Note


Department of Mechanical Engineering, Payame Noor University, Iran


In this experimental study, we investigate the freezing of water in cylindrical stagnation flow, using a device. The water impinges vertically on a cold flat plate while the water outlet section is cylindrical. The water starts to freeze when the substrate plate is sufficiently cold. The effects of distance between the outlet and the substrate plate, magnitude of the flow strain, water temperature, and the plate involved in ice formation, and most importantly, the final thickness of the ice have been investigated. We are also looking for a way to determine the flow regime in stagnation flow. Results are compared for validation with those of a numerical solution. The results show a good agreement in the middle of the ice thickness curve. As a result, the speed of ice formation is very high at first, and declines sharply with a steep slope. Also, a particular definition is employed for achieving the regimes (laminar, turbulent, or transitional) in stagnation flow. According to the results, the ice thickness in laminar flow is more than in turbulent one.


1. Stefan, J. “About the theory of ice formation, in particular on the ice formation in polar seas”, (Uber die theorie der eisbildung, insbesondere uber die eisbildung in polarmaere), A. Phys. Chem. 42, pp. 269-286 (1891).
2. Goodrich, L. E. “Efficient numerical technique for one dimensional thermal problems with phase change”,  Int. Journal of Heat Mass Transfer, 21, pp. 615-621 (1978).
3. Sparrow, J. W. Ramsey and Harris S. ”The transition from natural convection controlled freezing to conduction controlled freezing”, Journal of Heat Transfer, 103, pp. 7-13 (1983).
4. Lacroix, M. “Computation of heat transfer during melting of a pure substance from an isothermal wall”, Numer. Heat Transfer B, 15, pp. 191-210 (1989).
5. Yeoh, G. H., Behnia, M. and De Vah Davis, G. et al. "A numerical study of three-dimensional natural convection during freezing of water", Int. J. Numer. Mech. Engng., 30, pp. 899-914 (1990).
6. Hadji, L. and Schell, M. “Interfacial pattern formation in the presence of solidification and thermal convection”,  Phy., Rev. A, 41, pp. 863-873 (1990).
7. Hanumanth, G. S., “Solidification in the presence of natural convection”, Int, Comm. Heat Mass Transfer, 17, pp. 283-292 (1990).
8. Curtic, M. Oldenburg and Frank, J. Spera, “Hybrid model for solidification and convection”, Numer, Heat Transfer B, 21, pp. 217-229 (1992).
9. Trapaga, G., Matthys, E. F. and Valecia, J. J. et al. “Fluid Flow, heat transfer and solidification of molten metal droplets impinging on substrates: comparison of numerical and experimental results”, Metall. Trans. B, 23B, pp. 701-718 (1992).
10. Watanabe, T. I. and Kuribayashi, and Honda, T. and Kanzawa, A., “Deformation and solidification of a droplet on a cold substrate”, Cham. Engng, 47, pp. 3059-3065 (1992).
11. Marchi, C. San and Liu, H. et al. “Numerical analysis of the deformation and solidification of a single droplet impinging on to a flat substrate”,  Journal Mater, 28, pp. 3313-3321 (1993).
12. Weidman, P. D., and Mahalingam, S., "Axisymmetric Stagnation-Point Flow Impinging on a Transversely Oscillating Plate with Suction", J. Engineering Mathematics, 31, pp. 305-318 (1997).
13. Shokrgozar Abbasi, A., and Rahimi, A.B., "Non-axisymmetric three-dimensional stagnation-point flow and heat transfer on a flat plate", Trans. ASME J. Fluids Engineering131(7), pp. 074501–074505 (2009).
14. Shokrgozar Abbasi, A., and Rahimi, A.B., "Three-dimensional stagnation-point flow and heat transfer on a flat plate with transpiration", J. Thermophys. Heat Transfer, 23(3), pp. 513-521 (2009).
15. Shokrgozar Abbasi, A., Rahimi, A.B., and Niazmand, H., "Exact Solution of Three-Dimensional Unsteady Stagnation Flow on a Heated Plate". J. Thermophys. Heat Transfer, 25(1), pp. 55-58 (2011).
16. Shokrgozar Abbasi, A., and Rahimi, A.B., "Investigation of two-dimensional unsteady stagnation flow and heat transfer impinging on an accelerated flat plate," Trans. ASME J. Heat Transfer, 134(6), pp. 064501-064505 (2012).
17. Shokrgozar Abbasi, A., Rahimi A.B. and Mozayyeni, H., "Investigation of three-dimensional axisymmetric unsteady stagnation-point flow and heat transfer impinging on an accelerated flat plate", J. Applied Fluid Mechanics (JAFM), 9(1), pp. 451-461 (2016).
18. Brattkus, k. and Davis, S. H., “Flow induced morphological instabilities: stagnation-point flows”, Journal of Crystal Growth, 89, pp. 423-427 (1988).
19. Rangel, R. H. and Bian, X., “The inviscid stagnation-flow solidification problem”, Int. Journal of Heat Mass Transfer, 39(8), pp. 1591-1602 (1994).
20. Lambert, R. H. and  Rangel, R. H., “Solidification of a supercooled liquid in stagnation-point flow”, Int. Journal of Heat Mass Transfer, 46,  pp. 4013-4021 (2003).
21. Yoo, J.S., “Effect of viscous plane stagnation flow on the freezing of fluid”, Int. Journal of Heat and Fluid Flow, 121, pp. 735-739 (2000).
22. Shokrgozar Abbasi, A. and Rahimi, A.B., “Solidification of Two-Dimensional Viscous, Incompressible Stagnation Flow” Int. Journal of Heat Transfer, 135, pp. 072301-072308 (2013).
23. Shokrgozar Abbasi, A., “Three-Dimensional Axisymmetric Solidification of a Viscous Incompressible Flow in the Stagnation Point Region", J. Applied Fluid Mechanics (JAFM), 10(1), pp. 413-420 (2017).
24. Alizadeh, R, Rahimi, A.B. and Najafi, M., "Non-axisymmetric stagnation-point flow and heat transfer of a viscous fluid on a stationary cylinder", Scientia Iranica, B, 23(5), pp. 2238-2246 (2016).
25- Adil, M.S., “MHD Stagnation Point Flow of Nanofluid on a Plate with Anisotropic Slip”, Symmetry, 11(2), 132 (2019).
26- Imtiaz, M., Nazar, H. and Hayat et al. “Effect of Porous Medium in Stagnation Point Flow of Ferrofluid Due to a Variable Convected Thicked Sheet”,  J. Heat Transfer,  141(11), pp. 112602-112611, 2019.
27. Rahimi, A.B. and Mozayeni, H., "Similarity Solutions of Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous, Boussinesq-Related Density Fluid on a Moving Flat Plate", Scientia Iranica, B, 21(4), pp. 1440-1450 (2018).
28. Waini, I., Ishak, A. and Pop, I. "Hybrid nanofluid flow towards a stagnation point on a stretching/shrinking cylinder", Scientific Reports10, 9296 (2020).
29. Shokrgozar Abbasi, A. and Ghayeni, M., "Water Vapor Solidification of Saturated Air in Two-Dimensional Stagnation Flow", Journal of Mechanical Engineering, Transaction of  Scientia Iranica, B, 27(2), pp. 693-703 (2020).
30. Narender, G., Govardhan, K. and Sreedhar, G.S., "Magnetohydrodynamic stagnation point on a Casson nanofluid flow over a radially stretching sheet", Beilstein J. Nanotechnol.  11, pp. 1303–1315 (2020). 
31. Maqbool, R.,  Ijaz, M.K. and Qayyum, S. et al.  "Numerical modeling and MHD stagnation point flow of ferrofluid (non-Newtonian) with Ohmic heating and viscous dissipation", International Journal of Modern Physics B, 34(28), 2050265 (2020).