Topic
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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8 citations
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TL;DR: In this article, the authors investigated theoretically the problem of three-dimensional, magnetohydrodynamic, boundary layer flow of a Jeffrey fluid with heat transfer in the presence of thermal radiation over an exponentially stretching surface.
Abstract: This study investigated theoretically the problem of three-dimensional, magnetohydrodynamic, boundary layer flow of a Jeffrey fluid with heat transfer in the presence of thermal radiation over an exponentially stretching surface. Highly nonlinear coupled partial differential equations are obtained using boundary layer approach. These equations are reduced to a set of ordinary differential equations using appropriate similarity transformations. The solution of the problem is found with the help of homotopy analysis method along with optimal homotopy analysis method to find optimal/best value for the convergence control parameter appearing in a series solution. The solution behaviors, for different emerging parameters, of velocity profiles (along $$x$$
and $$y$$
direction) as well as temperature profile are investigated and the effect of these parameters are explained through graphs. Moreover, for the present study, effective Prandtl number is used in the description of temperature profile. The skin friction coefficients along $$x$$
-axis and $$y$$
-axis are also discussed through graphs. The tabulated values of dimensionless heat transfer coefficient, Nusselt number, is presented.
8 citations
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TL;DR: In this paper, the similarity solution of cylindrical Korteweg-de Vries equation given by Tian and Gao in their Comment on our paper can be obtained by the group analysis method using the same generators given in the paper by Sahu and Roychoudhury.
Abstract: It is shown that the similarity solution of cylindrical Korteweg–de Vries equation given by Tian and Gao in their Comment on our paper can be obtained by the group analysis method using the same generators given in the paper by Sahu and Roychoudhury.
8 citations
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TL;DR: In this article, a one-dimensional shock reflection problem is discussed for the two-dimensional shallow water equations with cylindrical symmetry, and the differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankine-Hugoniot shock relations.
Abstract: A one-dimensional shock (bore) reflection problem is discussed for the two-dimensional shallow water equations with cylindrical symmetry. The differential equations for a similarity solution are derived and solved numerically in conjunction with the Rankine-Hugoniot shock relations.
8 citations
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TL;DR: In this article, a phase-plane method is proposed to model flow fields bounded by constant-velocity detonation waves propagating in TNT charges, where similarity transformations are used to formulate the problem in the phase plane of non-dimensional sound speed Z versus nondimensional velocity F, resulting in two coupled ordinary differential equations that are solved simultaneously.
Abstract: A phase-plane method is proposed to model flow fields bounded by constant-velocity detonation waves propagating in TNT charges. Similarity transformations are used to formulate the problem in the phase plane of non-dimensional sound speed Z versus non-dimensional velocity F. The formulation results in two coupled ordinary differential equations that are solved simultaneously. The solution corresponds to an integral curve Z(F) in the phase plane, starting at the Chapman-Jouguet (CJ) point and terminating at the singularity A, which is the sonic point within the wave. The system is closed by computing thermodynamic variables along the expansion isentrope passing through the CJ point, forming, in effect, the complete equation of state of the thermodynamic system. The CJ condition and isentropic states are computed by the Cheetah thermodynamic code. Solutions are developed for planar, cylindrical, and spherical detonations. Species profiles are also computed; carbon graphite is found to be the predominant component (≈10 mol/kg). The similarity solution is used to initialize a 1D gas-dynamic simulation that predicts the initial expansion of the detonation products and the formation of a blast wave in air. Such simulations provide an insight into the thermodynamic states and species concentrations that create the initial optical emissions from TNT fireballs.
8 citations