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Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.


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TL;DR: In this paper, the effect of minute quantities of entrained air on the shock similarity solution for water is investigated, using air void fraction as a fit parameter, and observed relaxation time data are analyzed to yield the levels of air that may have been present in various underwater explosive experiments.
Abstract: Similarity solutions developed from the equations of nonlinear acoustics [P. H. Rogers, J. Acoust. Soc. Am. 62, 1412–1419 (1977); B. E. McDonald and J. Ambrosiano, J. Acoust. Soc. Am. 84, 1497–1503 (1988)] have adequately accounted for the range dependence of overpressures in the propagation of underwater spherical shocks, while giving only fair to poor predictions for relaxation time constants at large ranges from the source. The relaxation time discrepancy seems to suggest an anomalously large nonlinearity coefficient at great distances from the source. The effect of minute quantities of entrained air on the shock similarity solution for water is investigated. It is well known that microbubbles can greatly increase the nonlinearity coefficient of water at ambient conditions. At high pressures, however, bubbles may collapse to the point of being dynamically unimportant. The equation of state for water is modified to account for ambient microbubble populations, and the resulting equations solved for self‐similar shock profiles. Using air void fraction as a fit parameter, observed relaxation time data are analyzed to yield the levels of entrained air that may have been present in various underwater explosive experiments.

2 citations

Journal ArticleDOI
TL;DR: In this article, a two-dimensional free convective mass transfer flow of an incompressible, viscous, and electrically conducting fluid past a continuously moving semi-infinite vertical porous plate with large suction in the presence of a magnetic field applied normal to the plate is studied.
Abstract: The problem of a two-dimensional free convective mass transfer flow of an incompressible, viscous, and electrically conducting fluid past a continuously moving semi-infinite vertical porous plate with large suction in the presence of a magnetic field applied normal to the plate is studied The non-linear partial differential equations governing the flow have been transformed by a set of similarity transformations into a system of non-linear ordinary differential equations The resulting system of the similarity equations are solved analytically adopting the perturbation technique The expressions for the velocity field, temperature field, concentration field, induced magnetic field, drag coefficient, and the coefficient of the rate of heat and mass transfer at the plate are obtained The results are discussed in details through graphs and tables to observe the effect of various physical parameters involved in the problem © 2013 Wiley Periodicals, Inc Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrarycom/journal/htj) DOI 101002/htj21097

2 citations

Proceedings ArticleDOI
22 Apr 2013
TL;DR: In this paper, the steady flow over a static plate immersed in a copper-water nanofluid with the bottom surface of the plate heated by convection is considered, and the results indicate that the inclusion of nanoparticles into the base fluid produces an increase in the skin friction coefficient and the heat transfer rate at the surface.
Abstract: The steady flow over a static plate immersed in a copper-water nanofluid with the bottom surface of the plate heated by convection is considered. Similarity solutions for the flow and the thermal fields are possible if the convective heat transfer from the hot fluid on the lower surface of the plate varies like x−1/2, where x is the distance from the leading edge. The governing partial differential equations are first transformed into a system of ordinary differential equations, before being solved numerically. The results indicate that the inclusion of nanoparticles into the base fluid produces an increase in the skin friction coefficient and the heat transfer rate at the surface.

2 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface.
Abstract: Abstract The current work attempts to investigate the existence of similarity solution for the natural convection boundary layer flow of a power-law fluid over a heated horizontal semi-infinite plate surface. Three types of surface temperature variation are considered, namely (i) constant surface temperature (CST), (ii) power-law variation of surface temperature (PST) and (iii) power-law variation of surface heat flux (PHF). A reduction of the governing partial differential equations is achieved by using a suitable similarity transformation. But, a careful mathematical verification confirms that the similarity solution does not exist in the CST case and for the PST case it exists only under a particular value of the wall temperature parameter r = 1/3. It also ensured the existence of similarity solution for the PHF case and this will happen only when the plate surface is held at a constant heat flux situation. A new fundamental parameter S arises from the dimensionless analysis which is reduced to the reciprocal of the usual Prandtl number Pr for Newtonian fluids. A novel result of this analysis is that the salient features of the Grashof number Gr which differentiates the thermal responses of the shear-thinning fluid (0 < n < 1) flows from the shear-thickening fluid (n > 1) flows while the Newtonian fluid (n = 1) flows remain unaffected by this parameter no matter what be the value of S.

2 citations

01 Jan 2010
TL;DR: In this paper, the effects of lateral mass flux, thermal radiation, transverse magnetic field and double diffusion on heat and mass transfer in a mixed convection boundary layer flow over a heated vertical surface embedded in Darcian porous media have been studied.
Abstract: The effects of lateral mass flux, thermal radiation, transverse magnetic field and double diffusion ( Soret and Dufour effects) on heat and mass transfer in a mixed convection boundary layer flow over a heated vertical surface embedded in Darcian porous media have been studied. The Rosseland approximation for the radiative heat flux is used in the energy equation. It is found that the similarity solution exists in the present case. The resulting set of coupled non-linear ordinary differential equations is solved numerically using shooting technique. Dimensionless velocity, temperature and concentration profiles are presented graphically against η for various values of the mixed convection parameter RP. The numerical values of local Nusselt number and local Sherwood number have been tabulated for various values of involved parameters and discussed in detail.

2 citations


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Metrics
No. of papers in the topic in previous years
YearPapers
202313
202238
202141
202045
201947
201850