Solution of Unsteady Flow in a Confined Aquifer Interacting with a Stream with Exponentially Decreasing Stream Stage

Saeedpanah, Iraj; Azar, Ramin Golmohamadi

doi:10.1061/(asce)he.1943-5584.0001758

J. Hydrol. Eng.

2019

DOI: 10.1061/(asce)he.1943-5584.0001758

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Solution of Unsteady Flow in a Confined Aquifer Interacting with a Stream with Exponentially Decreasing Stream Stage

Iraj Saeedpanah

Ramin Golmohamadi Azar

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2023

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The Laplace Transform Shortcut Solution to a One-Dimensional Heat Conduction Model with Dirichlet Boundary Conditions

Tao

Ren

2023

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When using the Laplace transform to solve a one-dimensional heat conduction model with Dirichlet boundary conditions, the integration and transformation processes become complex and cumbersome due to the varying properties of the boundary function f(t). Meanwhile, if f(t) has a complex functional form, e.g., an exponential decay function, the product of the image function of the Laplace transform and the general solution to the model cannot be obtained directly due to the difficulty in solving the inverse. To address this issue, operators are introduced to replace f(t) in the transformation process. Based on the properties of the Laplace transform and the convolution theorem, without the direct involvement of f(t) in the transformation, a general theoretical solution incorporating f(t) is derived, which consists of the product of erfc(t) and f(0), as well as the convolution of erfc(t) and the derivative of f(t). Then, by substituting f(t) into the general theoretical solution, the corresponding analytical solution is formulated. Based on the general theoretical solution, analytical solutions are given for f(t) as a commonly used function. Finally, combined with an exemplifying application demonstration based on the test data of temperature T(x, t) at point x away from the boundary and the characteristics of curve T(x, t) − t and curve 𝜕T(x, t)/𝜕t − t, the inflection point and curve fitting methods are established for the inversion of model parameters.

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The Laplace Transform Shortcut Solution to a One-Dimensional Heat Conduction Model with Dirichlet Boundary Conditions

Tao

Ren

2023

Axioms

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show abstract

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Solution of Unsteady Flow in a Confined Aquifer Interacting with a Stream with Exponentially Decreasing Stream Stage

Cited by 1 publication

References 25 publications

The Laplace Transform Shortcut Solution to a One-Dimensional Heat Conduction Model with Dirichlet Boundary Conditions

The Laplace Transform Shortcut Solution to a One-Dimensional Heat Conduction Model with Dirichlet Boundary Conditions

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