Closed-form solution for a circular nano-inhomogeneity with interface effects in an elastic plane under uniform remote heat flux

Thermal and Fluid Dynamic Model for Capillary-Driven Heat Pipe With Closed-Form Solution

Volume 1B, Symposia: Fluid Measurement and Instrumentation; Fluid Dynamics of Wind Energy; Renewable and Sustainable Energy Conversion; Energy and Process Engineering; Microfluidics and Nanofluidics; Development and Applications in Computational Fluid Dynamics; DNS/LES and Hybrid RANS/LES Methods ◽

10.1115/fedsm2017-69441 ◽

2017 ◽

Author(s):

Jesse Maxwell

Keyword(s):

Boundary Condition ◽

Heat Flux ◽

Closed Form ◽

Heat Pipe ◽

Closed Form Solution ◽

Constant Heat Flux ◽

Form Solution ◽

Constant Heat ◽

Micro Channels ◽

Flow Through

A model is derived for the steady state performance of capillary-driven heat pipes on the basis treating fluid flow through miniature- and micro-channels and applied as bulk properties to a large aspect ratio quasi-one-dimensional two-phase system. Surface tension provides the driving force based on an equivalent bulk capillary radius while laminar flow through micro-channels and the vapor core are treated. Heat conduction is accounted for radially while isothermal advection is treated along the axis. A closed-form solution is derived for a steady state heat pipe with a constant heat flux boundary condition on the evaporator as well as a constant heat flux or a convective boundary condition along the condenser. Two solution methods are proposed, and the result is compared to empirical data for a copper-water heat pipe. The components of the closed-form solution are discussed as contributors to driving or frictional forces, and the existence of an optimal pore radius is demonstrated.

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Closed-form solution of a thermocapillary free-film problem due to Pukhnachev

European Journal of Applied Mathematics ◽

10.1017/s095679251500008x ◽

2015 ◽

Vol 26 (5) ◽

pp. 721-741 ◽

Cited By ~ 1

Author(s):

BRIAN R. DUFFY ◽

MATTHIAS LANGER ◽

STEPHEN K. WILSON

Keyword(s):

Heat Flux ◽

Closed Form ◽

Closed Form Solution ◽

Critical Value ◽

Form Solution ◽

Free Fluid ◽

Parametric Solution ◽

Free Film ◽

Film Version ◽

Flux Parameter

We consider the steady two-dimensional thin-film version of a problem concerning a weightless non-isothermal free fluid film subject to thermocapillarity, proposed and analysed by Pukhnachev and co-workers. Specifically, we extend and correct the paper by Karabut and Pukhnachev (J. Appl. Mech. Tech. Phys. 49, 568–579, 2008), in which the problem is solved numerically, and in which it is claimed that there exists a unique solution for any value of a prescribed heat-flux parameter in the model. We present a closed-form (parametric) solution of the problem, and from this show that, on the contrary, solutions exist only when the heat-flux parameter is less than a critical value found numerically by Karabut and Pukhnachev, and that when this condition is satisfied there are in fact two solutions, one of which recovers that obtained numerically by Karabut and Pukhnachev, the other being new.

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Green’s functions for soft materials containing a hard line inhomogeneity

Mathematics and Mechanics of Solids ◽

10.1177/1081286519850225 ◽

2019 ◽

Vol 24 (11) ◽

pp. 3614-3631 ◽

Cited By ~ 2

Author(s):

Pengyu Pei ◽

Guang Yang ◽

Cun-Fa Gao

Keyword(s):

Thermal Expansion ◽

Heat Source ◽

Closed Form ◽

Hilbert Problem ◽

Closed Form Solution ◽

Soft Materials ◽

Form Solution ◽

Soft Material ◽

Elastic Plane ◽

Rigid Line

The linear elastic plane deformation of a soft material containing a rigid line inhomogeneity subjected to a concentrated force, a concentrated moment, and a point heat source was studied. Distinct from the existing rigid line inhomogeneity model which neglects the deformation of the inhomogeneity induced by both the mechanical stresses and thermal expansion, the current model allows for the thermal expansion-induced stretch and rotation of the inhomogeneity. In this context, we derive the closed-form solution for the full stress field in the soft material by solving the corresponding Riemann–Hilbert problem. In particular, our solution can serve as the Green’s function to establish other analytical solutions for more practical and complicated problems in this area. Several numerical examples are presented to illustrate our closed-form solution corresponding to the thermal loading. It is found that the presence of the heat source contributes significantly to the rigid rotation of inhomogeneity, and the thermal expansion-induced stretch of the inhomogeneity has a great impact on the stress intensity factors at the inhomogeneity tips.

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