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.

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.

Nonlocal Analytical Solutions for Multilayered One-Dimensional Quasicrystal Nanoplates

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Natalie Waksmanski ◽  
Ernian Pan
Keyword(s):  
Coupling Effect ◽  
Nonlocal Parameter ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mode Shapes ◽  
One Dimensional ◽  
Vibrational Response ◽  
Homogeneous Crystal ◽  
Traction Boundary Conditions

An exact closed-form solution for the three-dimensional static deformation and free vibrational response of a simply supported and multilayered quasicrystal (QC) nanoplate with the nonlocal effect is derived. Numerical examples are presented for a homogeneous crystal nanoplate, homogenous QC nanoplate, and sandwich nanoplates with various stacking sequences. Induced by traction boundary conditions, extended displacements and stresses reveal the important role that the nonlocal parameter plays in the structural analysis of nanoquasicrystals (nano-QCs). The natural frequencies and the corresponding mode shapes of the nanoplates further show the influence of stacking sequence and phonon–phason coupling effect. This exact solution is useful for it provides benchmark results to assess the accuracy of finite element nano-QC models and can assist engineers in tuning their quasicrystal nanoplate design.

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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