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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 article, a similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a wedge with mixed thermal boundary conditions.
Abstract: A similarity analysis was performed to investigate the laminar free-convection boundary-layer flow in the presence of a transverse magnetic field over a wedge with mixed thermal boundary conditions. Boundary-layer velocity and temperature profiles were determined numerically for various values of the Prandtl number and the magnetic parameter. The results show that the magnetic field retards the velocity profiles and increases the skin friction. The temperature profiles were expanded with increasing values of the magnetic parameter resulting in higher surface temperatures. A transformation relating the similarity solutions of the boundary-layer velocity and temperature profiles associated with different values of the mixed thermal boundary condition parameter was obtained.
9 citations
TL;DR: In this paper, the Navier-Stokes equations for two-dimensional steady slip flow in microchannels are reduced to a nonlinear third-order differential equation by using similarity solution.
Abstract: In this paper, the two-dimensional steady slip flow in microchannels is investigated. Research on micro flow, especially on micro slip flow, is very important for designing and optimizing the micro electromechanical system (MEMS). The Navier-Stokes equations for two-dimensional steady slip flow in microchannels are reduced to a nonlinear third-order differential equation by using similarity solution. The variational iteration method (VIM) is used to solve this nonlinear equation analytically. Comparison of the result obtained by the present method with numerical solution reveals that the accuracy and fast convergence of the new method.
9 citations
TL;DR: In this article, the authors studied the onset of Marangoni instability of an evaporating liquid layer and applied linear stability analysis to obtain the critical wave number for the onset, and found that the most unstable mode shifts from a lower wave number to a higher wave number as time proceeds.
Abstract: The onset of Marangoni instability of an evaporating liquid layer is studied theoretically. By assuming the surface regression of the liquid layer is negligibly small and the surrounding gas phase is asymptotically steady, similarity solutions are obtained prior to the onset of instability. Linear stability analysis is then applied to obtain the critical Marangoni number for the onset of instability. The results indicate that : (1) The onset condition is a strong function of the initial temperature of the liquid layer with which the critical Marangoni number decreases. (2) As time proceeds, the thermal boundary layer thickness near the free surface becomes larger, and the liquid layer becomes more unstable. (3) For a liquid layer with a higher initial temperature (closer to the boiling point) the most unstable mode of the disturbance shifts from a lower wave number to a higher wave number.
9 citations
TL;DR: In this paper, scaling laws are used with the model data to predict the behavior of the large prototype to test the validity of the method, which is very close to the theoretically obtained response of the prototype.
Abstract: Problems associated primarily with structural similitude as applied to sandwich beams and columns are investigated. Similitude theory is employed to develop the necessary similarity conditions or scaling laws. Scaling laws provide the relationship between a full-scale structure (prototype) and its scaled down model. These relationships can be used to design the small-scale model and to extrapolate the experimental data of the model to predict the behavior of the large prototype. Note that scaled down models are inexpensive and easily tested. The developed methodology is demonstrated through analysis of the bending of sandwich beams subjected to transverse loads, and it is totally analytical. A small model is designed and theoretically analyzed. The theoretically obtained responsepredictions are treated as if they wereexperimentally obtained (from model testing ). Then, scaling laws are used with the model data to predict the behavior of the large prototype. Finally, these predictions are compared to the theoretically obtained response of the prototype to test the validity of the method. Predicted and theoretical response is very close, and therefore, the demonstration is successful. Both complete (satisfaction of all similarity conditions) and partial similarity are discussed. Nomenclature bwk = width of panel ck = thickness of the core dtk;dbk = thickness of the upper and the lower skin, respectively EAtk;EAbk = longitudinal rigidities of the upper and the lower face, respectively Eck; Gck = vertical modulus of elasticity of the core and its shear modulus, respectively EIk = e exural rigidity of beam EItk;EIbk = e exural rigidities of upper and lower faces, respectively k = p or m, where p refers to the prototype and m to the model
9 citations
TL;DR: The nonlinear effects on the macroscopic convection-diffusion equation are addressed in this article, where an exact similarity solution for the concentration distribution, to the Cauchy problem, is obtained.
Abstract: The nonlinear effects on the macroscopic convection-diffusion equation are addressed An exact similarity solution for the concentration distribution, to the Cauchy problem, is obtained The conditions for the existence of travelling wave solutions, expressed in terms of certain inequalities to be satisfied by the fitting parameters, are shown and discussed
9 citations