Exact Analytical Hyperbolic Temperature Profile in a Three-Dimensional Media Under Pulse Surface Heat Flux

2015 ◽  
Vol 32 (3) ◽  
pp. 339-347 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi ◽  
S. Bakhshandeh
Keyword(s):  
Heat Flux ◽  
Numerical Solutions ◽  
Rectangular Cross Section ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Biological Tissues ◽  
Form Solution ◽  
Hyperbolic Heat Conduction ◽  
Duhamel Integral

AbstractIn this paper three-dimensional hyperbolic heat conduction equation in a cubic media with rectangular cross-section under a pulsed heat flux on the upper side has been solved analytically using the method of separation of variables and the Duhamel integral. The closed form solution of both Fourier and non-Fourier profiles are introduced with both modes of steady and pulsed fluxes. The results show the considerable difference between the Fourier and Non-Fourier temperature profiles. Then the answer procedure is used for modeling of interaction of a cubical tissue under a short laser pulse heating. The effects of pulse duration and laser intensity are studied analytically. Furthermore the results can be applied as a verification branch for other numerical solutions or laser treatments of biological tissues.

Three-dimensional stress state in inclined backfilled stopes obtained from numerical simulations and new closed-form solution

2018 ◽  
Vol 55 (6) ◽  
pp. 810-828 ◽  
Author(s):  
Abtin Jahanbakhshzadeh ◽  
Michel Aubertin ◽  
Li Li
Keyword(s):  
Stress State ◽  
Closed Form ◽  
Numerical Solutions ◽  
Hanging Wall ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Solid Waste Disposal ◽  
Inclination Angles ◽  
Backfilled Stopes

Backfill is commonly used world-wide in underground mines to improve ground stability and reduce solid waste disposal on the surface. Practical solutions are required to assess the stress state in the backfilled stopes, as the stress state is influenced by the fill settlement that produces a stress transfer to the adjacent rock walls. The majority of existing analytical and numerical solutions for the stresses in backfilled openings were developed for two-dimensional (plane strain) conditions. In reality, mine stopes have a limited extension in the horizontal plane so the stresses are influenced by the four walls. This paper presents recent three-dimensional (3D) simulations results and a new 3D closed-form solution for the vertical and horizontal stresses in inclined backfilled stopes with parallel walls. This solution takes into account the variation of the stresses along the opening width and height, for various inclination angles and fills properties. The numerical results are used to validate the analytical solution and illustrate how the stress state varies along the opening height, length, and width, for different opening sizes and inclination angles of the footwall and hanging wall. Experimental results are also used to assess the validity of the proposed solution.

Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source

2016 ◽  
Vol 33 (1) ◽  
pp. 65-75 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction

AbstractThis paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

Conduction of Heat across Rectangular Cellular Enclosures

1981 ◽  
Vol 103 (3) ◽  
pp. 591-595 ◽  
Author(s):  
J. Eftekhar ◽  
G. Darkazalli ◽  
A. Haji-Sheikh
Keyword(s):  
Heat Flux ◽  
Analytical Model ◽  
Thermal Conduction ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Numerical Data ◽  
Form Solution ◽  
Geometrical Configuration ◽  
Conduction Model ◽  
One Dimensional

A simplified analytical model for the computation of thermal conduction across rectangular-celled enclosures based on the assumption of quasi-one-dimensional conduction in the cell partitions is presented. The rectangular enclosures may contain solid or liquid for which the conduction is two or three-dimensional depending on the geometrical configuration. Additional assumptions concerning radiation interchange between participating surfaces are necessary when the enclosure contains a stagnant gas. This analytical model leads to a closed form solution for temperature distribution in the partitions and the multidimensional conductive region. A parametric study of heat flux is presented. The numerical data define a range of parameters for which a one-dimensional conduction model is satisfactory.

scholarly journals An augmented Lagrangian method for solving total variation (TV)-based image registration model

2020 ◽  
Vol 14 ◽  
pp. 174830262097353
Author(s):  
Noppadol Chumchob ◽  
Ke Chen
Keyword(s):  
Image Registration ◽  
Augmented Lagrangian ◽  
Numerical Solutions ◽  
Augmented Lagrangian Method ◽  
Closed Form Solution ◽  
Numerical Algorithms ◽  
Lagrangian Method ◽  
Form Solution ◽  
The Other ◽  
Other Hand

Variational methods for image registration basically involve a regularizer to ensure that the resulting well-posed problem admits a solution. Different choices of regularizers lead to different deformations. On one hand, the conventional regularizers, such as the elastic, diffusion and curvature regularizers, are able to generate globally smooth deformations and generally useful for many applications. On the other hand, these regularizers become poor in some applications where discontinuities or steep gradients in the deformations are required. As is well-known, the total (TV) variation regularizer is more appropriate to preserve discontinuities of the deformations. However, it is difficult in developing an efficient numerical method to ensure that numerical solutions satisfy this requirement because of the non-differentiability and non-linearity of the TV regularizer. In this work we focus on computational challenges arising in approximately solving TV-based image registration model. Motivated by many efficient numerical algorithms in image restoration, we propose to use augmented Lagrangian method (ALM). At each iteration, the computation of our ALM requires to solve two subproblems. On one hand for the first subproblem, it is impossible to obtain exact solution. On the other hand for the second subproblem, it has a closed-form solution. To this end, we propose an efficient nonlinear multigrid (NMG) method to obtain an approximate solution to the first subproblem. Numerical results on real medical images not only confirm that our proposed ALM is more computationally efficient than some existing methods, but also that the proposed ALM delivers the accurate registration results with the desired property of the constructed deformations in a reasonable number of iterations.

A Nondimensional Analysis of Boiling Dry a Vertical Channel with a Uniform Heat Flux

1981 ◽  
Vol 103 (4) ◽  
pp. 667-672 ◽  
Author(s):  
K. H. Sun ◽  
R. B. Duffey ◽  
C. Lin
Keyword(s):  
Heat Flux ◽  
Nuclear Power ◽  
Closed Form Solution ◽  
Vertical Channel ◽  
Form Solution ◽  
Uniform Heat Flux ◽  
Two Phase ◽  
Drift Flux ◽  
Rod Bundle ◽  
Uniform Heat

A thermal-hydraulic model has been developed for describing the phenomenon of hydrodynamically-controlled dryout, or the boil-off phenomenon, in a vertical channel with a spatially-averaged or uniform heat flux. The use of the drift flux correlation for the void fraction profile, along with mass and energy balances for the system, leads to a dimensionless closed-form solution for the predictions of two-phase mixture levels and collapsed liquid levels. The physical significance of the governing dimensionless parameters are discussed. Comparisons with data from single-tube experiments, a 3 × 3 rod bundle experiment, and the Three Mile Island nuclear power plant show good agreement.

Analytical and Numerical Studies of a Thick Anisotropic Multilayered Fiber-Reinforced Composite Pressure Vessel

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Isaiah Ramos ◽  
Young Ho Park ◽  
Jordan Ulibarri-Sanchez
Keyword(s):  
Finite Element ◽  
Pressure Vessel ◽  
Structural Damage ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Analytical Results ◽  
Composite Pressure Vessel

In this paper, we developed an exact analytical 3D elasticity solution to investigate mechanical behavior of a thick multilayered anisotropic fiber-reinforced pressure vessel subjected to multiple mechanical loadings. This closed-form solution was implemented in a computer program, and analytical results were compared to finite element analysis (FEA) calculations. In order to predict through-thickness stresses accurately, three-dimensional finite element meshes were used in the FEA since shell meshes can only be used to predict in-plane strength. Three-dimensional FEA results are in excellent agreement with the analytical results. Finally, using the proposed analytical approach, we evaluated structural damage and failure conditions of the composite pressure vessel using the Tsai–Wu failure criteria and predicted a maximum burst pressure.

scholarly journals SOLUTION OF THE MULTIDIMENSIONAL DIFFUSION EQUATION USING LIE SYMMETRIES: SIMULATION OF POLLUTANT DISPERSION IN THE ATMOSPHERE

2005 ◽  
Vol 4 (2) ◽  
Author(s):  
J. R. Zabadal ◽  
C. A. Poffal
Keyword(s):  
Differential Operators ◽  
Hybrid Methods ◽  
Formal Solution ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Pollutant Dispersion ◽  
Form Solution ◽  
Lie Symmetries ◽  
Advection Equation ◽  
Mean Values

Several analytical, numerical and hybrid methods are being used to solve diffusion and diffusion advection problems. In this work, a closed form solution of the three-dimensional diffusion advection equation in a Cartesian coordinate system is obtained by applying rules, based on the Lie symmetries, to manipulate the exponential of the differential operators that appear in its formal solution. There are many advantages of applying these rules: the increase in processing velocity so that the solution may be obtained in real time, the reduction in the amount of memory required to perform the necessary tasks in order to obtain the solution, since the analytical expressions can be easily manipulated in post-processing and also the discretization of the domain may not be necessary in some cases, avoiding the use of mean values for some parameters involved. These rules yield good results when applied to obtain solutions for problems in fluid mechanics and in quantum mechanics. In order to show the performance of the method, a one-dimensional scenario of the pollutant dispersion in a stable boundary layer is simulated, considering that the horizontal component of the velocity field is dominant and constant, disregarding the other components. The results are compared with data available in the literature.

Induction Proof for a General Exponential Integral Formula

1995 ◽  
Vol 80 (2) ◽  
pp. 424-426
Author(s):  
Frank O'Brien ◽  
Sherry E. Hammel ◽  
Chung T. Nguyen
Keyword(s):  
Closed Form ◽  
Integral Formula ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Probability Method ◽  
Exponential Integral ◽  
Need To Evaluate ◽  
Three Dimensional Space

The authors' Poisson probability method for detecting stochastic randomness in three-dimensional space involved the need to evaluate an integral for which no appropriate closed-form solution could be located in standard handbooks. This resulted in a formula specifically calculated to solve this integral in closed form. In this paper the calculation is verified by the method of mathematical induction.

scholarly journals SOLUTION OF THE MULTIDIMENSIONAL DIFFUSION EQUATION USING LIE SYMMETRIES: SIMULATION OF POLLUTANT DISPERSION IN THE ATMOSPHERE

2005 ◽  
Vol 4 (2) ◽  
pp. 197
Author(s):  
J. R. Zabadal ◽  
C. A. Poffal
Keyword(s):  
Differential Operators ◽  
Hybrid Methods ◽  
Formal Solution ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Pollutant Dispersion ◽  
Form Solution ◽  
Lie Symmetries ◽  
Advection Equation ◽  
Mean Values

Several analytical, numerical and hybrid methods are being used to solve diffusion and diffusion advection problems. In this work, a closed form solution of the three-dimensional diffusion advection equation in a Cartesian coordinate system is obtained by applying rules, based on the Lie symmetries, to manipulate the exponential of the differential operators that appear in its formal solution. There are many advantages of applying these rules: the increase in processing velocity so that the solution may be obtained in real time, the reduction in the amount of memory required to perform the necessary tasks in order to obtain the solution, since the analytical expressions can be easily manipulated in post-processing and also the discretization of the domain may not be necessary in some cases, avoiding the use of mean values for some parameters involved. These rules yield good results when applied to obtain solutions for problems in fluid mechanics and in quantum mechanics. In order to show the performance of the method, a one-dimensional scenario of the pollutant dispersion in a stable boundary layer is simulated, considering that the horizontal component of the velocity field is dominant and constant, disregarding the other components. The results are compared with data available in the literature.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

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