A class of similarity solutions for the nonlinear thermal conduction problem

Mayer, F. J.; Mcgrath, Joseph F.; Steele, J W

doi:10.1088/0305-4470/16/14/031

Cited by 20 publications

(14 citation statements)

References 2 publications

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“…In this case the constant of integration c can, for example, be determined by the conserved load E. In passing, we notice that the exact solution Eq. (11) corresponds to the known Zeldovich-Raizer solution in the context of nonlinear heat conduction [4,5]. We show the various scaling solutionsh(ỹ) of Eq.…”

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confidence: 90%

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Anomalous scaling and solitary waves in systems with nonlinear diffusion

2011

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We study a nonlinear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a nonlinear diffusion predicts the existence of fronts as well as shock fronts. Despite the absence of memory effects, solutions in the case of pure nonlinear diffusion exhibit an anomalous subdiffusive scaling. Due to a balance between nonlinear diffusion and convection we, in particular, show that solitary waves appear. For large times they merge into a single solitary wave exhibiting a topological stability. Even though our results concern a specific equation, numerical simulations support the view that anomalous diffusion and the solitary waves disclosed will be general features in such nonlinear convective-diffusive dynamics.

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confidence: 90%

“…Even though the nonlinear diffusion-convection equation that we study has its origins in the dynamics of wetting films, related equations appear in other contexts like nonlinear heat conduction [4,5]. Wetting films have, in their own right, received much attention recently due to their relevance for flows in porous media (see, e.g., Ref.…”

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confidence: 99%

Anomalous scaling and solitary waves in systems with nonlinear diffusion

2011

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“…[9] differentiates the equation with respect to K and gets its expression, but we think it is more reasonable to differentiate the equation with respect to a because K is a constant while a is the parameter in FEM, then the first relation of K-a is got.…”

Section: Physical Model Of the Interior Corner Flowmentioning

confidence: 99%

Interior corner flow theory and its application to the satellite propellant management device design

Wei

Chen

Huang

2011

Sci. China Technol. Sci.

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The interior corner flow theory is fundamental for liquid management in space. In this paper, the interior corner flow theory is modified by correction of the curvature and shape parameters based on geometry relationship, so that it can be extended to a wide range of applications including different dihedral angles and contact angles. This modification is validated with the data provided by the references using capillary tube and drop tower. Besides, the errors between the theory and experiment value are analyzed for the case of small viscosity and the long-time flow, finding that the main reason causing the error is the transformation of the flow resistance along the flow path. At last, the theory of interior corner flow is applied to the primary design of the Propellant Management Device in satellite tank, and optimum design of the vanes is given in terms of maximum flow rate.interior corner flow, capillary flow, drop tower, propellant management device Citation:Wei Y X, Chen X Q, Huang Y Y. Interior corner flow theory and its application to the satellite propellant management device design.

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“…This equation was first addressed by Mayer et al (1983) for nonlinear heat conduction problems. In this formulation however,F(η) is related to the dimensionless meniscus profile h(z, t), andη is the invariant similarity parameter.…”

Section: Introductionmentioning

confidence: 99%

Compound Capillary Flows in Complex Containers: Drop Tower Test Results

Bolleddula

Chen

Semerjian

et al. 2010

Microgravity Sci. Technol.

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Drop towers continue to provide unique capabilities to investigate capillary flow phenomena relevant to terrestrial and space-based capillary fluidics applications. In this study certain 'capillary rise' flows and the value of drop tower experimental investigations are briefly reviewed. A new analytic solution for flows along planar interior edges is presented. A selection of test cell geometries are then discussed where compound capillary flows occur spontaneously and simultaneously over local and global length scales. Sample experimental results are provided. Tertiary experiments on a family of asymmetric geometries that isolate the global component of such flows are then presented along with a qualitative analysis that may be used to either avoid or exploit such flows. The latter may also serve as a design tool with which to assess the impact of inadvertent container asymmetry.

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A class of similarity solutions for the nonlinear thermal conduction problem

Cited by 20 publications

References 2 publications

Anomalous scaling and solitary waves in systems with nonlinear diffusion

Anomalous scaling and solitary waves in systems with nonlinear diffusion

Interior corner flow theory and its application to the satellite propellant management device design

Compound Capillary Flows in Complex Containers: Drop Tower Test Results

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