Transient heat conduction in a medium with multiple spherical cavities

Gordeliy, Elizaveta; Crouch, Steven L.; Mogilevskaya, Sofia G.

doi:10.1002/nme.2430

Cited by 20 publications

(33 citation statements)

References 26 publications

(60 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The temperature contours were shown for t = 1, 10 and 100 in the neighborhood of the heated cavity. From a comparison of Figure 7(c) of the present work and Figure 5(b) of [33], it can be seen that even though the pattern of the contours is similar in two and three dimensions, in the two-dimensional problem (i) the heat from the heater flows faster through the matrix, (ii) the effect of the heater reaches further into the matrix, and (iii) the temperature in the matrix raises from the zero initial value to higher values than in the three-dimensional problem. These observations demonstrate the dimensionality effect.…”

Section: Comparison With a Companion Three-dimensional Problemmentioning

confidence: 92%

“…For the present problem the algorithm has been implemented similarly as done in our previous work [33]. This algorithm has proved to be efficient and accurate for a certain class of functions [32], and it can be shown that the transformed quantitiesT (x, s),…”

Section: Solution In the Time Domainmentioning

confidence: 98%

“…For more explanation, see [32]. [33].) The Lopez-Fernandez and Palencia algorithm also allows for an automatic choice of the number of quadrature points (i.e.…”

Section: Solution In the Time Domainmentioning

confidence: 99%

See 2 more Smart Citations

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Gordeliy¹,

Mogilevskaya²,

Crouch³

2009

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYA two-dimensional transient heat conduction problem of multiple interacting circular inhomogeneities, cavities and point sources is considered. In general, a non-perfect contact at the matrix/inhomogeneity interfaces is assumed, with the heat flux through the interface proportional to the temperature jump. The approach is based on the use of the general solutions to the problems of a single cavity and an inhomogeneity and superposition. Application of the Laplace transform and the so-called addition theorem results in an analytical transformed solution. The solution in the time domain is obtained by performing a numerical inversion of the Laplace transform. Several numerical examples are given to demonstrate the accuracy and the efficiency of the method. The approximation error decreases exponentially with the number of the degrees of freedom in the problem. A comparison of the companion two-and threedimensional problems demonstrates the effect of the dimensionality.

show abstract

Section: Comparison With a Companion Three-dimensional Problemmentioning

confidence: 92%

Section: Solution In the Time Domainmentioning

confidence: 98%

See 1 more Smart Citation

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Gordeliy¹,

Mogilevskaya²,

Crouch³

2009

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…11,17,[26][27][28][29][30][31][32][33][34] At first sight, it would seem highly improbable that anything novel can be added to such a well-established subject. Indeed, strictly speaking, we do not believe that we have added anything really new to the subject that was not known already to experts in the field, in the sense that everything that we have presented is somehow implicitly contained in earlier work.…”

Section: A Comparison With the Existing State-of-the-artmentioning

confidence: 99%

“…In recent years, it has again become the subject of intense research activity following the seminal work of Greengard and co-workers on so-called fast multipole moments. This theory has now been developed for conductors, 11,[26][27][28] for dielectric media, [29][30][31][32] for the steady-state 33 and the time-dependent heat equation, 34 for molecular dynamics, 26,35 and in numerous other applications. It is remarkable that the recent flurry of activity in applying image-charge concepts to dielectric media [29][30][31][32] comes more than 130 years after the basic ideas were originally published.…”

Section: Introductionmentioning

confidence: 99%

Competitive effects between stationary chemical reaction centres: A theory based on off-center monopoles

Biello

Samson

2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

The subject of this paper is competitive effects between multiple reaction sinks. A theory based on off-center monopoles is developed for the steady-state diffusion equation and for the convection-diffusion equation with a constant flow field. The dipolar approximation for the diffusion equation with two equal reaction centres is compared with the exact solution. The former turns out to be remarkably accurate, even for two touching spheres. Numerical evidence is presented to show that the same holds for larger clusters (with more than two spheres). The theory is extended to the convection-diffusion equation with a constant flow field. As one increases the convective velocity, the competitive effects between the reactive centres gradually become less significant. This is demonstrated for a number of cluster configurations. At high flow velocities, the current methodology breaks down. Fixing this problem will be the subject of future research. The current method is useful as an easy-to-use tool for the calibration of other more complicated models in mass and/or heat transfer.

show abstract

Combining Maxwell’s methodology with the BEM for evaluating the two-dimensional effective properties of composite and micro-cracked materials

Mogilevskaya

Crouch

2012

Comput Mech

View full text Add to dashboard Cite

Transient heat conduction in a medium with multiple spherical cavities

Cited by 20 publications

References 26 publications

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Transient heat conduction in a medium with multiple circular cavities and inhomogeneities

Competitive effects between stationary chemical reaction centres: A theory based on off-center monopoles

Combining Maxwell’s methodology with the BEM for evaluating the two-dimensional effective properties of composite and micro-cracked materials

Contact Info

Product

Resources

About