scholarly journals Heat Convection Equation with Nonhomogeneous Boundary Condition

2010 ◽  
Vol 53 (2) ◽  
pp. 213-229 ◽  
Author(s):  
Hiroko Morimoto
Keyword(s):  
Boundary Condition ◽  
Heat Convection ◽  
Nonhomogeneous Boundary Condition ◽  
Nonhomogeneous Boundary ◽  
Convection Equation

scholarly journals An Analytical Solution for Radiofrequency Ablation with a Cooled Cylindrical Electrode

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Ricardo Romero-Méndez ◽  
Enrique Berjano
Keyword(s):  
Boundary Condition ◽  
Radiofrequency Ablation ◽  
Analytical Solution ◽  
Separation Of Variables ◽  
Transcendental Equation ◽  
Functional Dependencies ◽  
Cylindrical Electrode ◽  
Electrical Currents ◽  
Nonhomogeneous Boundary Condition ◽  
Nonhomogeneous Boundary

We present an analytical solution to the electrothermal mathematical model of radiofrequency ablation of biological tissue using a cooled cylindrical electrode. The solution presented here makes use of the method of separation of variables to solve the problem. Green’s functions are used for the handling of nonhomogeneous terms, such as effect of electrical currents circulation and the nonhomogeneous boundary condition due to cooling at the electrode surface. The transcendental equation for determination of eigenvalues of this problem is solved using Newton’s method, and the integrals that appear in the solution of the problem are obtained by Simpson’s rule. The solution obtained here has the possibility of handling different functional dependencies of the source term and nonhomogeneous boundary condition. The solution provides a tool to understand the physics of the problem, as it shows how the solution depends on different parameters, to provide mathematical tools for the design of surgical procedures and to validate other modeling techniques, such as the numerical methods that are frequently used to solve the problem.

scholarly journals Inverse Source Problem for a Multiterm Time-Fractional Diffusion Equation with Nonhomogeneous Boundary Condition

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
L. L. Sun ◽  
X. B. Yan
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Source Function ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Inverse Source Problem ◽  
Nonhomogeneous Boundary Condition ◽  
Nonhomogeneous Boundary ◽  
Time Fractional Diffusion Equation ◽  
Continuation Technique

This paper is devoted to identify a space-dependent source function in a multiterm time-fractional diffusion equation with nonhomogeneous boundary condition from a part of noisy boundary data. The well-posedness of a weak solution for the corresponding direct problem is proved by the variational method. We firstly investigate the uniqueness of an inverse initial problem by the analytic continuation technique and the Laplace transformation. Then, the uniqueness of the inverse source problem is derived by employing the fractional Duhamel principle. The inverse problem is solved by the Levenberg-Marquardt regularization method, and an approximate source function is found. Numerical examples are provided to show the effectiveness of the proposed method in one- and two-dimensional cases.

Dynamic Programming and a Distributed Parameter Maximum Principle

1968 ◽  
Vol 90 (2) ◽  
pp. 152-156 ◽  
Author(s):  
W. L. Brogan
Keyword(s):  
Dynamic Programming ◽  
Maximum Principle ◽  
Programming Approach ◽  
Distributed Parameter ◽  
Programming Technique ◽  
Nonhomogeneous Boundary Condition ◽  
The Maximum Principle ◽  
Dynamic Programming Approach ◽  
Nonhomogeneous Boundary ◽  
Definition Of

A proof of a distributed parameter maximum principle is given by using dynamic programming. An example problem involving a nonhomogeneous boundary condition is also treated by using the dynamic programming technique and by extending the definition of the differential operator. It is thus demonstrated that for linear systems the dynamic programming approach is just as powerful as the variational approach originally used to derive the maximum principle.

The Study of Thermal Boundary Condition for CFRP Pressure Vessel with Metallic Liner during Manufacture Process

2008 ◽  
Vol 575-578 ◽  
pp. 1483-1488
Author(s):  
Zhao Hui Hu ◽  
Rong Guo Wang ◽  
Li Ma ◽  
Shan Yi Du
Keyword(s):  
Boundary Condition ◽  
Theoretical Calculation ◽  
Pressure Vessel ◽  
Thermal Boundary Condition ◽  
Heat Convection ◽  
Maximum Temperature ◽  
Convection Coefficient ◽  
Calculated Temperature ◽  
Metallic Liner ◽  
Temperature Test

The heat convection was considered the main heat exchange type in the autoclave where CFRP pressure vessel was cured in this analysis. To determine the heat convection coefficient, it needed the combination of theoretical calculation and temperature test. In the theoretical calculation, the determination of the heat convection coefficient was considered as an inversion problem of thermal conduction. By adjusting convection coefficient value in the finite element calculation, optimization method was employed to obtain a good agreement between calculated temperature and measured temperature. In the temperature test, the metallic liner of CFRP pressure vessel was used as test component to record temperature data which was compared with the calculated temperature. The calculated results reveal that the maximum value in convection coefficient sequence is 19.87 W/m2/K; the minimum value is 0.16 W/m2/K; the maximum temperature deviation between calculation and test is 1.67 °C. The results present the equivalent thermal boundary condition for the simulation of curing process of CFRP pressure vessel.

scholarly journals Multiple solutions for an inclusion quasilinear problem with nonhomogeneous boundary condition through Orlicz–Sobolev spaces

2017 ◽  
Vol 19 (03) ◽  
pp. 1650031 ◽  
Author(s):  
Rodrigo C. M. Nemer ◽  
Jefferson A. Santos
Keyword(s):  
Sobolev Spaces ◽  
Point Theory ◽  
Neumann Condition ◽  
Generalized Gradient ◽  
Inclusion Problems ◽  
Nonhomogeneous Boundary Condition ◽  
Nonhomogeneous Boundary ◽  
Locally Lipschitz Functional ◽  
Locally Lipschitz ◽  
Quasilinear Problem

In this work, we study multiplicity of nontrivial solution for the following class of differential inclusion problems with nonhomogeneous Neumann condition through Orlicz–Sobolev spaces, [Formula: see text] where [Formula: see text] is a domain, [Formula: see text] and [Formula: see text] is the generalized gradient of [Formula: see text]. The main tools used are Variational Methods for Locally Lipschitz Functional and Critical Point Theory.

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