3D transient heat conduction in multilayer systems – Experimental validation of semi-analytical solution

Simões, N.; Simões, I.; Tadeu, A.; Vasconcellos, Carlos Alexandre Bastos de; Mansur, Webe João

doi:10.1016/j.ijthermalsci.2012.02.007

Cited by 23 publications

(13 citation statements)

References 21 publications

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“…It is possible to model multilayer transient heat conduction problems as various layers of composite slab geometry as is shown in Fig 1A . The eigenvalues of the composite slab are analyzed and estimated using the transient temperature data measured at two points along the direction of heat flux on the material plate as shown in Fig 1B , α 1 is approximately determined by the enamel layer[ 24 , 26 – 29 ], and within the dentine layer α 2 is calculated by Using the values of L 2 = 2.5mm and L 1 = 1.6mm, and the measured thermal diffusivities α of the enamel and dentine materials are 4.2×10 -7 m 2 s -1 and 2.6 ×10 -7 m 2 s -1 , corresponding to the thermal conductivities of enamel and dentine are 0.81 Wm -1 K -1 and 0.48 Wm -1 K -1 .…”

Section: Resultsmentioning

confidence: 99%

Heat Transfer Behavior across the Dentino-Enamel Junction in the Human Tooth

et al. 2016

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During eating, the teeth usually endure the sharply temperature changes because of different foods. It is of importance to investigate the heat transfer and heat dissipation behavior of the dentino–enamel junction (DEJ) of human tooth since dentine and enamel have different thermophysical properties. The spatial and temporal temperature distributions on the enamel, dentine, and pulpal chamber of both the human tooth and its discontinuous boundaries, were measured using infrared thermography using a stepped temperature increase on the outer boundary of enamel crowns. The thermal diffusivities for enamel and dentine were deduced from the time dependent temperature change at the enamel and dentine layers. The thermal conductivities for enamel and dentine were calculated to be 0.81 Wm-1K-1 and 0.48 Wm-1K-1 respectively. The observed temperature discontinuities across the interfaces between enamel, dentine and pulp-chamber layers were due to the difference of thermal conductivities at interfaces rather than to the phase transformation. The temperature gradient distributes continuously across the enamel and dentine layers and their junction below a temperature of 42°C, whilst a negative thermal resistance is observed at interfaces above 42°C. These results suggest that the microstructure of the dentin-enamel junction (DEJ) junction play an important role in tooth heat transfer and protects the pulp from heat damage.

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Section: Resultsmentioning

confidence: 99%

Heat Transfer Behavior across the Dentino-Enamel Junction in the Human Tooth

et al. 2016

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“…Notar que cuando las dimensiones geométricas de la generación de calor son despreciables (con respecto a las dimensiones geométricas del cuerpo) entonces es razonable considerar al cuerpo como un medio infinito. Los resultados analíticos obtenidos con esta hipótesis han sido validados experimentalmente [30][31][32][33], lo cual demuestra que esta hipótesis puede usarse (bajo las condiciones adecuadas) para modelar correctamente muchos casos relevantes para la ingeniería. Con el propósito de evidenciar la validez de esta hipótesis y resaltar la versatilidad de las técnicas analíticas, los resultados obtenidos en este trabajo (que están basados en la hipótesis de medio infinito) se han comparado con los resultados numéricos obtenidos tomando un cuerpo finito, cuyas dimensiones geométricas son mucho mayores que las dimensiones de la generación de calor (ver Sección IV).…”

Section: Marco Teóricounclassified

Solución Analítica de la Distribución de Temperaturas en un Medio Homogéneo Debido a un Cable Eléctrico con Forma de Onda Rectangular

Diestra-Cruz¹,

Brunet²,

Santos-Sánchez³

et al. 2020

Proceedings of the 18th LACCEI International Multi-Conference for Engineering, Education, and Technology: Engineering, Integrat

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Due to the limited amount of oil reserves, it is essential to ensure the efficient use of available energy, which is closely linked to the optimal design of electrical devices. Because these devices work with electrical energy, they cannot avoid having discrete heat generating sources and their design depends on the precise determination of the temperature field in the body. In this work, the integral method of Green's functions is used to determine the three-dimensional temperature distribution of a homogeneous medium due to a rectangular waveshaped heat generation source. The geometry of the heat generation has been selected in such a way that it has the typical shape of the commercially available flexible electric heaters. The solution obtained is exact and mathematically simple. To demonstrate the versatility of the results, this analytical solution has been compared with the purely numerical solution obtained using a computer package widely used in engineering (COMSOL Multiphysics). The analytical and numerical results coincide well in all the evaluated ranges. Using the equation obtained in this work, a procedure is proposed to determine the effective thermal conductivity of a material from the experimental data of temperature and position. The results of this research offer a simple way to calculate the thermal conductivity of a material and can be applied in the design of thermo-optical devices, flexible electric heaters or thermo-adjustable microfluidic devices.

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“…Simoes et al [18] developed an experimental validation of 2D and 2.5D BEM solutions for transient heat conduction in systems containing heterogeneities. They also presented an experimental validation of a semi-analytical solution for transient heat conduction in multilayer systems [19]. Alifanov and Nenarokomov [20] described an algorithm to process the data of unsteady-state thermal experiments and find the surface heat flux and temperature as functions of spatial coordinates and time.…”

Section: Introductionmentioning

confidence: 99%

The PCGM for Cauchy inverse problems in 3D potential

Zhou¹,

Bian²,

Cheng³

et al. 2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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The preconditioned conjugate gradient method (PCGM) in combination with the boundary element method (BEM) is developed for reconstructing the boundary conditions in 3-D potential. Morozov's discrepancy principle is employed to select the iteration step. The semi-analytical integral algorithm is proposed to treat the nearly singular integrals when the interior points are very close to the boundary. The numerical results confirm that the PCGM produces convergent and stable numerical solutions with respect to decreasing the amount of noise added into the input data. The numerical solutions are sensitive to the locations of the interior points when these points are distributed near the boundary without boundary conditions. The results are more accurate when these points are closer to the boundary.

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3D transient heat conduction in multilayer systems – Experimental validation of semi-analytical solution

Cited by 23 publications

References 21 publications

Heat Transfer Behavior across the Dentino-Enamel Junction in the Human Tooth

Heat Transfer Behavior across the Dentino-Enamel Junction in the Human Tooth

Solución Analítica de la Distribución de Temperaturas en un Medio Homogéneo Debido a un Cable Eléctrico con Forma de Onda Rectangular

The PCGM for Cauchy inverse problems in 3D potential

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