Similarity solution

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

Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate

Abstract: General formulation and solution of Navier–Stokes and energy equations are sought in the study of two-dimensional unsteady stagnation-point flow and heat transfer impinging on a flat plate when the plate is moving with variable velocity and acceleration toward main stream or away from it. As an application, among others, this accelerated plate can be assumed as a solidification front which is being formed with variable velocity. An external fluid, along z-direction, with strain rate a impinges on this flat plate and produces an unsteady two-dimensional flow in which the plate moves along z-direction with variable velocity and acceleration in general. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. Velocity and pressure profiles, boundary layer thickness, and surface stress-tensors along with temperature profiles are presented for different examples of impinging fluid strain rate, selected values of plate velocity, and Prandtl number parameter.

Multiple solutions for hydromagnetic flow of a second grade fluid over a stretching or shrinking sheet

Abstract: We study a class of fourth-order nonlinear differential equations arising in the hydromagnetic flow of a second grade fluid over a stretching or shrinking sheet. Explicit exact solutions are obtained. Furthermore we show that the differential equation may admit zero or one or two physically meaningful solutions depending on the values of the physical parameters of the model. As a special case, we recover the single or the dual solutions and compare them with the available results in the literature. Also, the obtained multiple solutions for several sets of values of the parameters are presented through tables and graphs, and the qualitative behaviors are discussed.

Numerical modeling of Glauert type exponentially decaying wall jet flows of nanofluids using Tiwari and Das’ nanofluid model

Abstract: Purpose The purpose of this study is to present a simple analytic solution to wall jet flow of nanofluids. The concept of exponentially decaying wall jet flows proposed by Glauert (1956) is considered. Design/methodology/approach A proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved analytically. Findings Dual solutions are found and a stability analysis has been done. These solutions show that the first solution is physically realizable, whereas the second solution is not practicable. Originality/value The present results are original and new for the study of fluid flow and heat transfer over a static permeable wall, as they successfully extend the problem considered by Glauert (1956) to the case of nanofluids.

A slender rivulet of a power-law fluid driven by either gravity or a constant shear stress at the free surface

Abstract: Similarity solutions that describe the flow of a slender non-uniform rivulet of non-Newtonian power-law fluid down an inclined plane are obtained. Rivulets driven by either gravity or a constant shear stress at the free surface are investigated, and in both cases solutions are obtained for both weak and strong surface-tension effects. We find that, despite the rather different physical mechanisms driving the flow, the solutions for gravity-driven and shear-stress-driven rivulets are qualitatively similar. When surface-tension effects are weak there is a unique similarity solution in which the transverse rivulet profile has a single global maximum. This solution represents both a diverging and shallowing sessile rivulet and a converging and deepening pendent rivulet. On the other hand, when surface-tension effects are strong there is a one-parameter family of similarity solutions in which the transverse profile of a diverging and shallowing rivulet has one global maximum, while that of a converging and deepening rivulet has either one global maximum or two equal global maxima. We also show how the present similarity solutions can be modified to accommodate a fixed-contact-angle condition at the contact line by incorporating sufficiently strong slip at the solid/fluid interface into the model.