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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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58 citations
TL;DR: In this article, two phase natural convection adjacent to a heated, vertical surface in a permeable medium is treated using boundary-layer approximations for conditions under which the vapor layer adjacent to the heated surface is thin.
58 citations
TL;DR: In this article, the small-time asymptotic solution for a penny-shaped fluid-driven fracture is obtained semianalytically, showing that the portion of the fracture that is filled with fluid increases with time according to a power law.
Abstract: The small-time asymptotic solution for a penny-shaped fluid-driven fracture is obtained semianalytically. Scaling considerations indicate that the portion of the fracture that is filled with fluid increases with time according to a power law. The problem is shown to be self-similar at the length scale of the small fluid-filled region and to depend on only the mean fluid pressure at the length scale of the fracture. This similarity solution is unusual as the two length scales of the problem — the radius of the fracture and the radius of the fluid front — evolve according to two different power laws of time.
58 citations
TL;DR: In this paper, the stability analysis of the boundary-layer flow and heat transfer of a nanofluid past a moving surface in an external uniform free stream with leading edge accretion or ablation is studied theoretically.
58 citations
TL;DR: In this paper, the boundary layer flow characteristics of magnetic generalized Newtonian fluid due to a paraboloid revolution under bioconvection and chemical reactive species were analyzed numerically and graphically.
Abstract: This article gives brief summary about the boundary layer flow characteristics of magnetic generalized Newtonian fluid due to a paraboloid revolution under bioconvection and chemical reactive species. The nanofluid model utilized in this work includes the behavior of Brownian motion and thermophoresis. The differential equations can be determined by a similarity solution. The determined ordinary differential equations have been solved numerically by fifth order Runge–Kutta Fehlberg method-based shooting technique. The behavior of different physical controlling dimensionless parameters on the base flow velocity, temperature, concentration, skin friction heat and mass transfer rates are analyzed numerically and graphically. We observed that the velocity, temperature and concentration profile reduce for increasing values of Hartmann number, Weissenberg number, wall thickness, stretching index, bioconvection, Prandtl number, Lewis number and Brownian motions whilst behavior is noticed for power law index. Moreover, for increases the values of Brownian and thermophoresis parameter the temperature profile shown increasing behavior. Comparison has been with represents date and found that the results have good agreement.
58 citations