Topic
Hele-Shaw flow
About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.
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TL;DR: In this article, a weighted residual model (WRM) is derived and used to predict the combined effects of bottom waviness, heating, and permeability on the stability of the flow.
Abstract: The method of weighted residuals for thin film flow down an inclined plane is extended to include the effects of bottom waviness, heating, and permeability in this study. A bottom slip condition is used to account for permeability and a constant temperature bottom boundary condition is applied. A weighted residual model (WRM) is derived and used to predict the combined effects of bottom waviness, heating, and permeability on the stability of the flow. In the absence of bottom topography, the results are compared to theoretical predictions from the corresponding Benney equation and also to existing Orr-Sommerfeld predictions. The excellent agreement found indicates that the model does faithfully predict the theoretical critical Reynolds number, which accounts for heating and permeability, and these effects are found to destabilize the flow. Floquet theory is used to investigate how bottom waviness influences the stability of the flow. Finally, numerical simulations of the model equations are also conducted and compared with numerical solutions of the full Navier-Stokes equations for the case with bottom permeability. These results are also found to agree well, which suggests that the WRM remains valid even when permeability is included.
43 citations
TL;DR: In this article, the slow viscous flow past a rectangular array of parallel circular cylinders was studied and the method of eigenfunction expansions and matching between two domains was used to obtain the flow.
42 citations
42 citations
TL;DR: In this paper, the problem of steady, incompressible, viscous flow between two infinite concentric cylinders, the cross-sections of the inner and outer cylinders being circular and square respectively, was solved for Reynolds number in the range 1-1400 and for several values of the parameter B, defined as the ratio of the side of the square to the diameter of the circle.
Abstract: Numerical solutions have been obtained for the problem of steady, incompressible, viscous flow between two infinite concentric cylinders, the cross-sections of the inner and outer cylinders being circular and square respectively. The square cylinder is fixed and the flow is driven by the rotation of the circular cylinder. Solutions are given for Reynolds number in the range 1–1400 and for several values of the parameter B, defined as the ratio of the side of the square to the diameter of the circle.
42 citations
TL;DR: In this paper, a computational method for the calculation of the flow and heat transfer in a channel, with elements of various heights inducing a streamwise-periodic flow, is presented and evaluated.
Abstract: A computational method for the calculation of the flow and heat transfer in a channel, with elements of various heights inducing a streamwise-periodic flow, is presented and evaluated. The time-averaged conservation equations of mass, momentum, and energy were solved together using a finite-control-volume method. Reynolds stresses were obtained using a two-equation model, which solves the time-averaged equations of the turbulence kinetic energy and its dissipation rate. The calculated flow field is shown to be in satisfactory agreement with the experimental data. The results indicate that the local and overall heat loss parameters increase with increasing Reynolds and Prandtl numbers and element height and with decreasing spacing.
42 citations