## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Growth of N-dimensional spherical bubble within viscous, superheated liquid: Analytical solution

**ABSTRACT**

In this paper, we present the study of the bevaiour of spherical bubble in N-dimensions fluid. The fluid is a mixture of vapour and superheated liquid. The mathematical model is formulated in N-dimensions fluid on the basis of continuity and momentum equations, and solved its analytically. The variable viscosity is taken in an account problem. The obtained results show that the radius of bubble increases with the decreasing of the value of N-dimensions.

**KEYWORDS**

PAPER SUBMITTED: 2019-03-30

PAPER REVISED: 1970-01-01

PAPER ACCEPTED: 2019-09-22

PUBLISHED ONLINE: 2019-10-06

- Brujan E., Cavitation in Non-Newtonian Fluids, Biomedical and Bioengineering Applications, 2011th ed., Springer, 2010
- Klotz A. R., Hynynen K., Simulations of the Devin and Zudin modified Rayleigh-Plesset equations to model bubble dynamics in a tube, Electronic Journal of Technical Acoustics, 11 (2010), pp. 1-15
- Brujana E. A., Takahira H., Ogasawar T., Planar jets in collapsing cavitation bubbles, Experimental Thermal and Fluid Science, 101 (2019), pp. 48-61
- Mohammadein S. A., Abu-Bakr A. F., The growth of vapour bubble in a superheated liquid between two-phase turbulent flow, Canadian Journal of Physics 88 (2010), 5, pp. 317-324
- Rattner A. S., Garimella S., Simulation of Taylor flow evaporation for bubble-pump applications, International Journal of Heat and Mass Transfer 116 (2018), pp. 231-247
- Rayleigh L., On the pressure developed in a liquid during the collapse of a spherical cavity. Philosophical Magazine, 34 (1917), 200, pp. 94-98
- Plesset M., Zwick S., The Growth of vapour bubbles in superheated liquids, Journal of Applied Physics, 25 (1954), pp. 493-500
- Mohammadein S. A., Shalaby G. A., Abu-Bakr A. F., Abu-Nab A. K.. Analytical Solution of Gas Bubble Dynamics between Two-Phase Flow, Results in Physics, 7 (2017), pp. 2396-2403
- Olek S., Zvirin Z., Elias E.. Bubble growth predictions by the hyperbolic and parabolic heat conduction equations, Waerme Stoffuebertragung, 25 (1990), pp. 17-26
- Kudryashov N. A., Sinelshchikov D. I., Analytical solutions for problems of bubble dynamics, Physics Letters A, 379 (2015), pp. 798-802
- Kudryashov N. A., Sinelshchikov D.I., Analytical solutions of the Rayleigh equation for empty and gas-filled bubble, Journal of Physics A: Mathematical and Theoretical, 47 (2014), 405202
- Prosperetti A., Plesset M. S., Vapour-bubble growth in a superheated liquid, Journal of Fluid Mechanics, 85 (1978), 2, pp. 349-368
- Abu-Bakr A. F., Abourabia A.M., The Cole-Hopf transformation for solving Rayleigh-Plesset equation in bubble dynamics. Advances in Modeling and Analysis A, 55 (2018), 2, pp. 82-87
- Obreschko D., Bruderer M., Farhat M., Analytical approximations for the collapse of an empty spherical bubble, Physical Review E, 85 (2012), 066303
- Robert A., Gorder V., Dynamics of the Rayleigh_Plesset equation modelling a gas-filled bubble immersed in an incompressible fluid, Journal of Fluid Mechanics, 807 (2016), pp. 478-508.
- Fan J., Jiang S., Ni G., On regularity criteria for the N-dimensional Navier-Stokes equations in terms of the pressure, Journal Differential Equations 244 (2008) pp. 2963-2979
- Zhou Y., Pokorny M., On the regularity of the solutions of the Navier-Stokes equations via one velocity component, Nonlinearity. 23 (2010), 5, pp. 1097
- Zwick S. A,, Plesset M. S., On the Dynamics of Small Vapor Bubbles in Liquids. Journal Mathematics and Physics 33 (1954). pp. 308-330
- Haar, L., Gallagher, J. S. and Kell G. S. NBS/NRC Steam Tables, New York: Hemisphere Publishing, 1984
- Forster H. K., Zuber N., Growth of a Vapor Bubble in a Superheated Liquid, Journal of Applied Physics 25 (1954), 4, pp. 474 - 478
- Bosnakovic F., Verdampfung and Flusigkeitsuberhizung.Technology Mechances Thermo-Dynanamics. BERL, 1 (1930), 358