Sinusoidal oscillations radiating from a cylindrical source in thermal conduction or groundwater flow: Closed‐form solutions |
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| Authors: | Antoine Saucier Clément Frappier Robert P Chapuis |
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| Institution: | 1. Ecole Polytechnique de Montréal, Department of Mathematics and Industrial Engineering, C.P. 6079, succ. centre‐ville, Montreal (Quebec), Canada H3C 3A7;2. Ecole Polytechnique de Montréal, Department of Civil, Geological and Mining Engineering, C.P. 6079, succ. centre‐ville, Montreal (Quebec), Canada H3C 3A7 |
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| Abstract: | The diffusion equation governs thermal conduction and groundwater flow phenomena. In this paper, we study the two‐dimensional radial propagation of a sinusoidal perturbation radiating from a cylindrical source within an infinite slab of homogeneous material. The solution of this problem has several applications. For instance, it can be used to determine the hydraulic diffusivity of the subsurface based on measurements of the hydraulic head around a vertical well during its development. For thermal problems, it can be used to determine the thermal diffusivity based on measurements of the temperature distribution around a cylindrical heat source generating a sinusoidal power per unit length. In this paper, we present a comprehensive analytical solution of this problem and we compare these solutions with numerical solutions. Two approximate analytical solutions, which can be relevant in practice, are also presented. Finally, we give an upper bound for the survival time of the transient part of the solution and we provide an estimate of the radius of influence of the sinusoidal solicitation. Copyright © 2010 John Wiley & Sons, Ltd. |
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| Keywords: | boundary value problem diffusion equation ground water flow sinusoidal oscillations radiating from a cylindrical source thermal conduction monitoring well |
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