The Penny-Shaped Interface Crack With Heat Flow, Part 2: Imperfect Contact

1983 ◽  
Vol 50 (4a) ◽  
pp. 770-776 ◽  
Author(s):  
J. R. Barber ◽  
Maria Comninou
Keyword(s):  
Heat Flux ◽  
Thermal Contact ◽  
Closed Form Solution ◽  
Integral Equation Method ◽  
Form Solution ◽  
Heat Fluxes ◽  
Crack Face ◽  
Imperfect Contact ◽  
Penny Shaped Crack ◽  
Shaped Crack

The penny-shaped crack with heat flux is investigated for the case in which the heat flux is into the material with the lower distortivity. A harmonic potential function representation is used to reduce the problem to a boundary value problem which is solved by an integral equation method. If a sufficiently high tensile traction is applied, a solution is obtained involving a central circle of separation and surrounding annuli of imperfect and perfect thermal contact. For lower tractions, or higher heat fluxes, the crack closes completely and a closed-form solution is obtained in which the division of the crack face into imperfect and perfect contact regions is unaffected by further changes in heat flux or traction. Multiple solutions are obtained in an intermediate range.

The Penny-Shaped Interface Crack With Heat Flow, Part 1: Perfect Contact

1983 ◽  
Vol 50 (1) ◽  
pp. 29-36 ◽  
Author(s):  
C. J. Martin-Moran ◽  
J. R. Barber ◽  
M. Comninou
Keyword(s):  
Heat Flux ◽  
Heat Flow ◽  
Thermal Stresses ◽  
Contact Region ◽  
Thermal Contact ◽  
Dissimilar Materials ◽  
Contact Radius ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Shaped Crack

A solution is given for the thermal stresses due to a penny-shaped crack at the interface between dissimilar materials loaded in tension for the case where the heat flux is into the material with higher distortivity. Regions of separation and perfect thermal contact are developed at the crack faces. A harmonic potential function representation is used to reduce the problem to a three-part boundary value problem which is formulated as a pair of coupled Abel integral equations using the method of Green and Collins. These equations are further reduced to a single Fredholm equation which is solved numerically. Results are presented illustrating the effect of heat flux and applied tractions on the contact radius and the stress intensity factors for various combinations of material constants. The effect of heat flux is profoundly influenced by the relative signs of Dundurs constant β and a constant γ describing the mismatch of distortivities. If the more distortive material is also the more rigid, the contact region at the crack face is reduced by heat flow; otherwise it is increased. In the latter case, solutions involving separation are obtained even for applied compressive tractions if the latter is within a certain range. The solution also exhibits nonuniqueness in this range.

A Nondimensional Analysis of Boiling Dry a Vertical Channel with a Uniform Heat Flux

1981 ◽  
Vol 103 (4) ◽  
pp. 667-672 ◽  
Author(s):  
K. H. Sun ◽  
R. B. Duffey ◽  
C. Lin
Keyword(s):  
Heat Flux ◽  
Nuclear Power ◽  
Closed Form Solution ◽  
Vertical Channel ◽  
Form Solution ◽  
Uniform Heat Flux ◽  
Two Phase ◽  
Drift Flux ◽  
Rod Bundle ◽  
Uniform Heat

A thermal-hydraulic model has been developed for describing the phenomenon of hydrodynamically-controlled dryout, or the boil-off phenomenon, in a vertical channel with a spatially-averaged or uniform heat flux. The use of the drift flux correlation for the void fraction profile, along with mass and energy balances for the system, leads to a dimensionless closed-form solution for the predictions of two-phase mixture levels and collapsed liquid levels. The physical significance of the governing dimensionless parameters are discussed. Comparisons with data from single-tube experiments, a 3 × 3 rod bundle experiment, and the Three Mile Island nuclear power plant show good agreement.

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

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.

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

2015 ◽  
Vol 26 (5) ◽  
pp. 721-741 ◽  
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.

Exact Analytical Hyperbolic Temperature Profile in a Three-Dimensional Media Under Pulse Surface Heat Flux

2015 ◽  
Vol 32 (3) ◽  
pp. 339-347 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi ◽  
S. Bakhshandeh
Keyword(s):  
Heat Flux ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Biological Tissues ◽  
Form Solution ◽  
Hyperbolic Heat Conduction ◽  
Duhamel Integral

AbstractIn this paper three-dimensional hyperbolic heat conduction equation in a cubic media with rectangular cross-section under a pulsed heat flux on the upper side has been solved analytically using the method of separation of variables and the Duhamel integral. The closed form solution of both Fourier and non-Fourier profiles are introduced with both modes of steady and pulsed fluxes. The results show the considerable difference between the Fourier and Non-Fourier temperature profiles. Then the answer procedure is used for modeling of interaction of a cubical tissue under a short laser pulse heating. The effects of pulse duration and laser intensity are studied analytically. Furthermore the results can be applied as a verification branch for other numerical solutions or laser treatments of biological tissues.

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