Transient Conduction From Parallel Isothermal Cylinders

2012 ◽  
Vol 134 (12) ◽  
Author(s):  
Rajai S. Alassar
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Energy Equation ◽  
Transient Heat Conduction ◽  
Infinite Medium ◽  
Basis Functions ◽  
Cylindrical Coordinates ◽  
Transient Conduction ◽  
Isothermal Cylinders

The transient heat conduction from two parallel isothermal cylinders is studied using the naturally fit bipolar cylindrical coordinates system. The energy equation is expanded in a Fourier series using appropriate basis functions to eliminate one of the physical coordinates. The resulting modes of the expansion are solved using a finite difference scheme. It is shown that, as is the case with a single isothermal cylinder in an infinite medium, steady states for two isothermal cylinders are not possible and heat transfer changes indefinitely with time.

Simple Explicit Equations for Transient Heat Conduction in Finite Solids

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
A. G. Ostrogorsky
Keyword(s):  
Fourier Series ◽  
Heat Conduction ◽  
Biot Number ◽  
Series Solution ◽  
Transient Heat Conduction ◽  
Simple Equation ◽  
Lower Error ◽  
Transient Conduction ◽  
The One ◽  
Cylinders And Spheres

Abstract Based on the one-term Fourier series solution, a simple equation is derived for low Biot number transient conduction in plates, cylinders, and spheres. In the 0<Bi<0.3 range, the solution gives approximately three times less error than the lumped capacity solution. For asymptotically low values of Bi, it approaches the lumped capacity solution. A set of equations valid for 0<Bi<1 is developed next. These equations are more involved but give approximately ten times lower error than the lumped capacity solution. Finally, a set of broad-range correlations is presented, covering the 0<Bi<∞ range with less than 1% error.

scholarly journals 1-D heat conduction in a fractal medium: A solution by the local fractional Fourier series method

2013 ◽  
Vol 17 (3) ◽  
pp. 953-956 ◽  
Author(s):  
Yuzhu Zhang ◽  
Aimin Yang ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Series Method ◽  
Heat Transfer Mechanism ◽  
Basic Properties ◽  
Fractal Medium ◽  
Fourier Series Method

In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.

EVALUATION OF COMBINED DELAUNAY TRIANGULATION AND REMESHING FOR FINITE ELEMENT ANALYSIS OF CONDUCTIVE HEAT TRANSFER

2004 ◽  
Vol 27 (4) ◽  
pp. 319-339 ◽  
Author(s):  
Sutthisak Phongthanapanich ◽  
Pramote Dechaumphai
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Heat Conduction ◽  
Steady State ◽  
Delaunay Triangulation ◽  
Transient Heat Conduction ◽  
Conductive Heat ◽  
Element Analysis ◽  
Adaptive Remeshing ◽  
Solution Accuracy

A finite element method is combined with the Delaunay triangulation and an adaptive remeshing technique to solve for solutions of both steady-state and transient heat conduction problems. The Delaunay triangulation and the adaptive remeshing technique are explained in detail. The solution accuracy and the effectiveness of the combined procedure are evaluated by heat transfer problems that have exact solutions. These problems include steady-state heat conduction in a square plate subjected to a highly localized surface heating, and a transient heat conduction in a long plate subjected to a moving heat source. The examples demonstrate that the adaptive remeshing technique with the Delaunay triangulation significantly reduce the number of the finite elements required for the problems and, at the same time, increase the analysis solution accuracy as compared to the results produced using uniform finite element meshes.

scholarly journals An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Ryoichi Chiba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Differential Equations ◽  
Transfer Coefficient ◽  
Transient Heat Conduction ◽  
External Boundary ◽  
Composite Slab ◽  
Composite Slabs

An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of n layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at n-1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

Nonlinear Inverse Heat Conduction With a Moving Boundary: Heat Flux and Surface Recession Estimation

1999 ◽  
Vol 121 (3) ◽  
pp. 708-711 ◽  
Author(s):  
V. Petrushevsky ◽  
S. Cohen
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Fourier Series ◽  
Heat Conduction ◽  
Moving Boundary ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Variable Order ◽  
Inverse Heat Conduction ◽  
One Dimensional

A one-dimensional, nonlinear inverse heat conduction problem with surface ablation is considered. In-depth temperature measurements are used to restore the heat flux and the surface recession history. The presented method elaborates a whole domain, parameter estimation approach with the heat flux approximated by Fourier series. Two versions of the method are proposed: with a constant order and with a variable order of the Fourier series. The surface recession is found by a direct heat transfer solution under the estimated heat flux.

Conservation laws and associated Lie point symmetries admitted by the transient heat conduction problem for heat transfer in straight fins

Open Physics ◽  
2013 ◽  
Vol 11 (8) ◽  
Author(s):  
Partner Ndlovu ◽  
Rasselo Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Conduction ◽  
Conservation Laws ◽  
Linear Function ◽  
Power Law ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Lie Point Symmetries ◽  
Transient Heat Conduction Problem

AbstractSome new conservation laws for the transient heat conduction problem for heat transfer in a straight fin are constructed. The thermal conductivity is given by a power law in one case and by a linear function of temperature in the other. Conservation laws are derived using the direct method when thermal conductivity is given by the power law and the multiplier method when thermal conductivity is given as a linear function of temperature. The heat transfer coefficient is assumed to be given by the power law function of temperature. Furthermore, we determine the Lie point symmetries associated with the conserved vectors for the model with power law thermal conductivity.

scholarly journals Analytic transient solutions of a cylindrical heat equation

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2617-2628
Author(s):  
K.Y. Kung ◽  
Man-Feng Gong ◽  
H.M. Srivastava ◽  
Shy-Der Lin
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Conduction ◽  
Heat Equation ◽  
Heat Conduction Equation ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Transient Temperature ◽  
Transient Solutions

The principles of superposition and separation of variables are used here in order to investigate the analytical solutions of a certain transient heat conduction equation. The structure of the transient temperature appropriations and the heat-transfer distributions are summed up for a straight mix of the results by means of the Fourier-Bessel arrangement of the exponential type for the investigated partial differential equation.

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