Intrinsic verification and a heat conduction database

Cole, Kevin D.; Beck, James V.; Woodbury, Keith A.; Monte, Filippo de

doi:10.1016/j.ijthermalsci.2013.11.002

Cited by 54 publications

(26 citation statements)

References 13 publications

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“…Then, according to the numbering system devised in [12,Chap. 2], [13], the above problem may be denoted by X62B10T11. In particular, this number denotes a transient heat conduction problem concerning a 1D rectangular finite body (by the X), subject to a boundary condition of the sixth kind at the surface x=0 (by the 6 in X62) with a constant applied heat flux (by the B1), and having an insulated boundary at x=L (type 2 boundary condition by the 2 in X62, and zero heat flux by the 0 in B10); also, T11 denotes a nonzero uniform initial temperature for both layers.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Effect of Heat Source and Imperfect Contact on Simultaneous Estimation of Thermal Properties of High‐Conductivity Materials

D'Alessandro

Monte

Amos

2019

Mathematical Problems in Engineering

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In the current paper a novel methodology accounting for both the heater heat capacity and the imperfect thermal contact between a thin heater and a specimen is proposed. In particular, the volumetric heat capacity of the heater is considered by modelling it as a lumped capacitance body, while the imperfect thermal contact is considered by means of a contact resistance. Thus, the experimental apparatus consisting of three layers (specimen-heater-specimen) is reduced to a single finite layer (sample) subject to a “nonclassical” boundary condition at the heated surface, known as sixth kind. Once the temperature solution is derived analytically using the Laplace transform method, the scaled sensitivity coefficients are computed analytically at the interface between the heater and the sample (heater side and sample side) and at the sample backside. By applying the proposed methodology to a lab-controlled experiment available in the specialized literature, a reduction of the thermal properties values of about 1.4% is observed for a high-conductivity material (Armco iron).

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Section: Mathematical Formulationmentioning

confidence: 99%

Effect of Heat Source and Imperfect Contact on Simultaneous Estimation of Thermal Properties of High‐Conductivity Materials

D'Alessandro

Monte

Amos

2019

Mathematical Problems in Engineering

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“…Therefore, the solution after performing the spatial integration becomes Notice that this step has eliminated the heat flux term q and the total heat addition rate at the single point of heating, Q, has appeared, now that the differential element for area has been integrated out. Next, although performing the time integration is not simple, it can be shown that 2 where K o is the Bessel function and E n is Exponential Integral function as defined in Reference [7].…”

Section: F Two-dimensional Point-heating Solution Formulationmentioning

confidence: 99%

“…Moreover, the method prescribed there lends itself to straightforward solutions for two or three-dimensional problems using the principle of superposition. Many combinations of boundary conditions and geometries have been cataloged using a numbering system with solutions generated for future use as described by Cole et al [2]. This reference provides a number of examples for other applications for analytical solutions as well.…”

Section: Introductionmentioning

confidence: 99%

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Diffusion Penetration Time for Transient Conduction

McMasters

Monte

Beck

et al. 2015

45th AIAA Thermophysics Conference

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The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations since the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for five geometries including one-dimensional cases for Cartesian, cylindrical and spherical coordinates. The fourth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in radial coordinates. A sixth case is also mentioned, which is the only two-dimensional configuration discussed, having to do with point heating on a flat plate.For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a non-heated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case showing the relationships between the temperature rise of interest and the amount of time required to reach that temperature. Nomenclature A Number of significant figures in solution (integer) E nExponential Integral Function G R One-dimensional Green's function along r (m -1 ) G X One-dimensional Green's function along x (m -1 ) J 0 Bessel function of the first kind, zeroth order (dimensionless) J 1 Bessel function of the first kind, first order (dimensionless) k Thermal conductivity (Wm -1 K -1 ) K o Modified Bessel function of the second kind, zeroth order (dimensionless) p Geometric index (unitless) Q Heat addition rate (W) q Heat flux (Wm -2 ) R Radius of cylinder or sphere (m) R 1 Inner radius of hollow cylinder (m) R 2 Outer radius of hollow cylinder (m) R Dimensionless outer radius of cylinder r Radial spatial variable (m) r Dimensionless radial spatial variable r/R Downloaded by UNIVERSITY OF TENNESSEE on August 17, 2015 | http://arc.aiaa.org |

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“…In order to solve this problem the concept of intrinsic verification of analytical solutions of heat conduction problems found in books or another databases was describes in Ref. [9].…”

Section: Introductionmentioning

confidence: 99%