Boundary value problems of heat conduction

Asynchronous phase field fracture model for porous media with thermally non-equilibrated constituents

Desde mediados del Siglo XX en adelante ha habido un gran interes en problemas relacionados con la industria alimentaria. La conservacion de alimentos ha sido importante para los humanos desde la antiguedad, cuando se utilizaban tecnicas tradicionales como la desecacion, el curado, la salazon, el encurtido, el ahumado, etc. La industria alimentaria se desarrollo cuando se produjo el desplazamiento masivo de la poblacion al medio urbano, ya que era preciso contar con un sumin istro masivo de alimentos en condiciones de consumo adecuadas. De esta manera se pudo prolongar la vida util de los alimentos, garantizar tratamientos a gran escala y mejorar aspectos logisticos como el transporte, la distribucion y el almacenamiento . Muchos de los metodos clasicos utilizados para la conservacion de los alimentos consisten en la aplicacion de tratamientos termicos, como por ejemplo la pasteurizacion, esterilizacion y congelacion. El problema de estos tratamientos es que pueden suponer una reduccion importante de las propiedades organolepticas y nutricionales del alimento. Por ello, ya que hoy en dia no solo importa alargar la vida util de los alimentos, sino que tambien se pretende que sean de buena calidad, se estan desar

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Mathematical models in food engineering

In this study, we propose a meshless and boundary-type numerical method, namely the homotopy method of fundamental solutions (HMFS), to solve the steady-state nonlinear heat conduction problems in two dimensions. The HMFS is composed by the homotopy analysis method (HAM) and the method of fundamental solutions (MFS). In the solution procedure, the Kirchhoff transformation is employed to transform the nonlinear governing partial differential equation into the Laplace equation with nonlinear boundary conditions. Sequentially, the HAM is applied to convert the Laplace equation with nonlinear boundary conditions into a sequence of the Laplace equation with linear boundary conditions, which can be solved by the MFS. In order to solve strongly nonlinear problems, a convergence control parameter is introduced to ensure the solution convergence of the prescribed sequence of problems. Several numerical experiments were carried out to validate the proposed method. In addition, a multiple-precision computing is performed to demonstrate the exponential convergence of the HMFS in both the spatial and homotopy coordinates for solving nonlinear heat conduction problems. Finally, bi-material and irregular-domain problems are also considered.

Homotopy method of fundamental solutions for solving nonlinear heat conduction problems

Nonlinear anisotropic temperature distribution in a wedge

This paper deals with the construction of mean square analytic-numerical solution of parabolic partial differential problems where both initial condition and coefficients are stochastic processes. By using a random Fourier transform, an infinite integral form of the solution stochastic process is firstly obtained. Afterwards, explicit expressions for the expectation and standard deviation of the solution are obtained. Since these expressions depend upon random improper integrals, which are not computable in an exact manner, random Gauss-Hermite quadrature formulae are introduced throughout an illustrative example.

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Boundary value problems of heat conduction

Citations

Asynchronous phase field fracture model for porous media with thermally non-equilibrated constituents

Mathematical models in food engineering

Homotopy method of fundamental solutions for solving nonlinear heat conduction problems

Nonlinear anisotropic temperature distribution in a wedge

Analytic-numerical solution of random parabolic models: A mean square Fourier transform approach

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