Transient thermal conduction analysis of a rectangular plate with multiple insulated cracks by the alternating method

Chang, Chia-Ling; Ma, Chien‐Ching

doi:10.1016/s0017-9310(00)00292-1

Cited by 19 publications

(13 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The temperature distribution is compared with solutions for problems on an infinite strip and changing flux conditions. Chang and Ma [7] studied this problem under transient conditions. The solution in [7] is based on an iterative superposition of solutions combining the solutions for a finite plate with no cracks with those for an infinite plate with a crack.…”

Section: Digitalcommonsunledumentioning

confidence: 99%

“…In Section 5 we solve the transient heat conduction problem in a 2D plate with one or several stationary and non-intersecting cracks. We compare the results against finite element solutions (which use the classical heat equation) and other numerical solutions from the literature which also utilize the classical diffusion equation [3,7]. We then use the new formulation to solve transient heat transfer problems in bodies with evolving discontinuities, such as insulated cracks that intersect as they grow, and change the heat flow patterns, and in thermally heterogeneous material systems such as fiber-reinforced composites.…”

Section: Digitalcommonsunledumentioning

confidence: 99%

“…For the case of heat flow over multiple insulated cracks we refer to the solutions provided in [3] using the finite element alternating method and in [7] using the alternating method. We consider the same setup as the ones used in [3] and [7]: heat flow in a square plate (L = 2 cm, W = 2 cm) with two inclined insulated cracks as shown in Figure 19 (left).…”

Section: Example 4: Heat Transfer In a Plate With Multiple Insulated mentioning

confidence: 99%

“…We consider the same setup as the ones used in [3] and [7]: heat flow in a square plate (L = 2 cm, W = 2 cm) with two inclined insulated cracks as shown in Figure 19 (left). The initial temperature is 0 °C.…”

Section: Example 4: Heat Transfer In a Plate With Multiple Insulated mentioning

confidence: 99%

“…We run the test until t = 4.5 s to ensure that it reaches steady state conditions so that we can compare with the results for the classical model given in [7] and [3]. We employ δ = 13L/120 and 13L/240, and m = 6.5.…”

Section: Example 4: Heat Transfer In a Plate With Multiple Insulated mentioning

confidence: 99%

See 4 more Smart Citations

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

Bobaru

Duangpanya

2012

Journal of Computational Physics

250

142

View full text Add to dashboard Cite

We introduce a multidimensional peridynamic formulation for transient heat-transfer. The model does not contain spatial derivatives and uses instead an integral over a region around a material point. By construction, the formulation converges to the classical heat transfer equations in the limit of the horizon (the nonlocal region around a point) going to zero. The new model, however, is suitable for modeling, for example, heat flow in bodies with evolving discontinuities such as growing insulated cracks. We introduce the peridynamic heat flux which exists even at sharp corners or when the isotherms are not smooth surfaces. The peridynamic heat flux coincides with the classical one in simple cases and, in general, it converges to it in the limit of the peridynamic horizon going to zero. We solve test problems and compare results with analytical solutions of the classical model or with other numerical solutions. Convergence to the classical solutions is seen in the limit of the horizon going to zero. We then solve the problem of transient heat flow in a plate in which insulated cracks grow and intersect thus changing the heat flow patterns. We also model heat transfer in a fiber-reinforced composite and observe transient but steep thermal gradients at the interfaces between the highly conductive fibers and the low conductivity matrix. Such thermal gradients can lead to delamination cracks in composites from thermal fatigue. The formulation may be used to, for example, evaluate effective thermal conductivities in bodies with an evolving distribution of insulating or permeable, possibly intersecting, cracks of arbitrary shapes.

show abstract

Section: Digitalcommonsunledumentioning

confidence: 99%

Section: Digitalcommonsunledumentioning

confidence: 99%

Section: Example 4: Heat Transfer In a Plate With Multiple Insulated mentioning

confidence: 99%

Section: Example 4: Heat Transfer In a Plate With Multiple Insulated mentioning

confidence: 99%

Section: Example 4: Heat Transfer In a Plate With Multiple Insulated mentioning

confidence: 99%

See 3 more Smart Citations

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

Bobaru

Duangpanya

2012

Journal of Computational Physics

250

142

View full text Add to dashboard Cite

show abstract

Peridynamic Theory and Its Applications

Madenci

Öterkuş²

2014

621

840

View full text Add to dashboard Cite

show abstract

Peridynamic Thermal Diffusion

Madenci

Öterkuş

2013

Peridynamic Theory and Its Applications

View full text Add to dashboard Cite

This study presents the derivation of ordinary state-based peridynamic heat conduction equation based on the Lagrangian formalism. The peridynamic heat conduction parameters are related to those of the classical theory. An explicit time stepping scheme is adopted for numerical solution of various benchmark problems with known solutions. It paves the way for applying the peridynamic theory to other physical fields such as neutronic diffusion and electrical potential distribution.

show abstract

Transient thermal conduction analysis of a rectangular plate with multiple insulated cracks by the alternating method

Cited by 19 publications

References 15 publications

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities

Peridynamic Theory and Its Applications

Peridynamic Thermal Diffusion

Contact Info

Product

Resources

About