An analytic approach to the unsteady heat conduction processes in one-dimensional composite media

Monte, Filippo de

doi:10.1016/s0017-9310(01)00226-5

Cited by 129 publications

(48 citation statements)

References 9 publications

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“…The exact solution, to these equations, is developed by applying the method of separation of variables in each region and then applying the interface and boundary conditions (Tittle 1965;de Monte 2000de Monte , 2002. In order to this end, we assume the following product solutions:…”

Section: Exact Solutionmentioning

confidence: 99%

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Analytical Modeling of Soil Solution Monitoring by Diffusion in Porous Cups

et al. 2009

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There is increasing interest toward in situ solution monitoring of soil chemicals for agricultural, industrial, and ecological purposes. Rather than extracting soil solution, a series of laboratory experiments was conducted to evaluate a diffusion equilibration technique, providing for real time in situ soil solution nitrate concentration via UV absorption spectroscopy. Experiments allowed for diffusion of nitrate from an outside reservoir into a porous cup. The experimental data were compared with model predictions using three different analytical solutions: (i) an exact solution (EX model) assuming radial symmetry that includes a porous cup with a porous wall and a finite size outside reservoir, (ii) an approximate solution (RC model) that assumes an infinitely large supply reservoir with a porous cup wall that does not influence ion diffusion, and (iii) and a model based on an electric circuit analog (ECA model). The results indicate that the ECA solution provides the best match overall to the experimental data.

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Section: Exact Solutionmentioning

confidence: 99%

“…However, closely related functions can be defined that are orthogonal with respect to z (Tittle 1965;de Monte 2000de Monte , 2002 and which enable the constants a n to be calculated. These functions, denoted as δ n , are listed below.…”

Section: Exact Solutionmentioning

confidence: 99%

Analytical Modeling of Soil Solution Monitoring by Diffusion in Porous Cups

et al. 2009

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“…Transient heat transfer in multilayered composite plates, cylinders and spheres are of great interest in a number of engineering applications [4,5,6,7,8,9,10,11,12]. The use of composite media is necessary when the thermal and mechanical properties of a single layer is not sufficient as to fulfill both thermal and mechanical requirements.…”

Section: Introductionmentioning

confidence: 99%

Lumped models for transient thermal analysis of multilayered composite pipeline with active heating

2015

Applied Thermal Engineering

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“…The analytical and numerical method of solutions of unsteady heat conduction problems are presented in many papers, see for example Refs. [5][6][7][8][9][10]. In this paper a mixed in time nonstationary problem of heat conduction for a homogeneous nondeformable half-space is considered.…”

Section: Introductionmentioning

confidence: 99%