
Green's Function for Heat Conduction in Annuli R15Phi00 and R51Phi00 with Type 1 and Type 5 Boundary Conditions
16 Oct 2014  Papers  Contributor(s): Donald E. Amos
Abstract The Green’s function is the principal tool in construction of the general solution to the classical heat conduction problem. The solution is presented in terms of the internal heat generation, initial temperature and integrals which reflect the physical influence of the boundary. In the current literature ( http://Exact.unl.edu ) the common boundary conditions are presented as Types 1,2,3,4, and 5 ranging from specified temperature (Type 1) to the most general form (Type 5)...

Green's Function for Heat Conduction in an Annulus R55Phi00 with Type 5 Boundary Conditions
14 Oct 2014  Papers  Contributor(s): Donald E. Amos
Abstract The Green’s function is the principal tool in construction of the general solution to the classical heat conduction problem. The solution is presented in terms of the internal heat generation, initial temperature and integrals which reflect the physical influence of the boundary. In the current literature ( http://Exact.unl.edu ) the common boundary conditions are presented as Types 1,2,3,4, and 5 ranging from specified temperature (Type 1) to the most general form (Type 5)...

Green's Function for Heat Conduction in an Infinite Hollow Cylinder R50 with a Type 5 Boundary Condition
05 May 2014  Papers  Contributor(s): Donald E. Amos
The Green’s function is the principal tool in construction of the general solution to the classical heat conduction problem. The solution is presented in terms of the internal heat generation, initial temperature and integrals which reflect the physical influence of the boundary. In the current literature ( http://Exact.unl.edu ) the common boundary conditions are presented as Types 1,2,3,4, and 5 ranging from specified temperature (Type 1) to the most general form (Type 5) where …

Green's Function for Heat Conduction in a Semiinfinite Medium X50 with a Type 5 Boundary Condition
01 May 2014  Papers  Contributor(s): Donald E. Amos
The Green's function is the principal tool in construction of the general solution to the classical heat conduction problem. The solution is presented in terms of the internal heat generation, initial temperature and integrals which reflect the physical influence of the boundary. In the current literature ( http://Exact.unl.edu ) the common boundary conditions are presented as Types 1,2,3,4, and 5 ranging from a specified temperature (Type 1) to the most general form (Type 5) where input...

Green's Function for Heat Conduction in a Hollow Cylinder R55 with Type 5 Boundary Conditions
25 Mar 2014  Papers  Contributor(s): Donald E. Amos
Abstract The Green's function is the principal tool in construction of the general solution to the classical heat conduction problem. The solution is presented in terms of the internal heat generation, initial temperature and integrals which reflect the physical influence of the boundary. In the current literature ( http://Exact.unl.edu ) the common boundary conditions are presented as Types 1,2,3,4, and 5 ranging from specified temperature (Type 1) to the most general form (Type 5)...

Green's Function for Heat Conduction in a Slab X55 with Type 5 Boundary Condtions
10 Mar 2014  Papers  Contributor(s): Donald E. Amos
The Green's function is the principal tool in construction of the general solution to the classical heat conduction problem. The solution is presented in terms of the internal heat generation, initial temperature and integrals which reflect the physical influence of the boundary. In the current literature ( http://Exact.unl.edu ) the common boundary conditions are presented as Types 1,2,3,4, and 5 ranging from a specified temperature (Type 1) to the most general form (Type 5) where input energy …

Heat Conduction in a Hollow Cylinder R55T0 and Subcases
08 Mar 2014  Papers  Contributor(s): Donald E. Amos
A hollow cylinder is heated on both surfaces with known fluxes which are partly dissipated by conduction into the cylinder, partly lost to the exterior media, and partly stored in boundary layers with only heat capacity. This description of each boundary condition is known as a Type 5 condition and in the current literature is labeled R55. The initial temperature of the cylinder is zero (T0).
The motivation for considering the R55T0 case is to solve several interesting subcases in one …

Heat Conduction in a Slab X55T0 and Subcases
05 Mar 2014  Papers  Contributor(s): Donald E. Amos
A slab is heated on both faces with known fluxes which are partly dissipated by conduction into the slab, partly lost to the exterior media, and partly stored in a boundary layer with only heat capacity. This description of each boundary condition is known as a Type 5 condition and in the current literature is labeled X55. The initial temperature of the slab is zero (T0).
The motivation for considering the X55T0 case is to solve several interesting subcases in one formula. By specializing …

Theory of Heat Conduction with Type 5 Boundary Condition
19 Feb 2014  Papers  Contributor(s): Donald E. Amos
In the classical theory, the general solution of the heat conduction problem is expressed in terms of the Green's function. Terms which take into account volumetric heat generation, an initial temperature distribution and boundary conditions can be identified. In the current literature ( http://Exact.unl.edu ) a numbering system is used to describe a large set of possible problems arising from a variety of physical conditions and geometries. In this system, the classical boundary Types 1 …

Green's Function For Radial Heat Conduction in TwoRegion Composite Cylinders With Imperfect Boundary Contact
31 Jul 2013  Papers  Contributor(s): Donald E. Amos
This paper presents the derivation of the Green's function for composite cylinders 0a with contact resistance on the surface r=a.

Green's Function For Radial Heat Conduction in TwoRegion Composite Cylinders With Perfect Boundary Contact
20 Mar 2013  Papers  Contributor(s): Donald E. Amos
This paper presents the derivation of the Green's function for composite cylinders 0<r<a and r>a in perfect contact on the surface r=a. Because the source function can be in either region, there are two pairs of functions which define the Green's function. Each pair is the solution to a tworegion conduction problem with zero initial temperatures and continuity of temperature and flux on the cylinder r=a.

1D Green's Functions For Heat Conduction Between Semiinfinite Slabs With Perfect and Imperfect Boundary Contact
17 Jan 2013  Papers  Contributor(s): Donald E. Amos
This document presents two derivations for 1D Green's functions
for semiinfinite slabs in contact along the boundary x=0. The case of
imperfect contact with a heat transfer coefficient h is derived and the case
of perfect contact is obtained by taking h to infinity. The two dimensional
case with source point (x',y') is reduced to the one dimensional case by
applying a constant source in the y' direction. Because the twodimensional
source solutions have complex …

Handbook of Integrals Related to Heat Conduction and Diffusion
03 May 2012  Papers  Contributor(s): Donald E. Amos
This handbook is presented in four parts. Chapter 1 presents a Table of Integrals with references to Chapter 2 where the main formulae are presented in handbook format. Formulae presented in Chapter 2 reference Chapter 3 where the derivations are presented in full detail in subsections called Folders. The Table of Contents of Chapter 3 lists the titles of 29 Folders along with a brief summary of the results of each Folder. Chapter 4 is devoted to the description of files containing FORTRAN...

Theory of Heat Conduction for Two Region Problems Using Green's Functions
03 Apr 2012  Papers  Contributor(s): Donald E. Amos
This paper derives equations which describe transient temperature distributions in adjacent regions which share a common boundary. These regions consist of materials with distinct, constant physical properties. The theory is developed for two types of boundary contact. The first formula is developed for perfect contact where there is continuity of both temperature and flux. The second formula allows for a thermal resistance at the boundary which retains continuity of flux, but causes a …

Green's Functions For Heat Conduction in Adjacent Materials
11 Mar 2012  Papers  Contributor(s): Donald E. Amos
This paper considers classical linear, transient heat conduction problems set in Regions 1 and 2 defined by the half planes x>0 and x

Transient Heat Conduction in Adjacent Quadrants Separated by a Thermal Resistance
19 Jan 2012  Papers  Contributor(s): Donald E. Amos, James Vere Beck, Filippo de Monte
Abstract Two linear, transient heat conduction problems set in quadrants 1 and 2 of the (x,y) plane are solved. In each problem, the quadrants have distinct, constant physical properties and are separated by an infinitely thin thermal resistance along the yaxis. Each region is initially at zero temperature. In Problem I, constant fluxes are specified along the xaxis boundaries to complete the problem definition; while in Problem II, constant temperatures are specified.
An attempt at a …

Transient Heat Conduction in Adjacent Materials Heated on Part of the Common Boundary
01 Nov 2011  Papers  Contributor(s): Donald E. Amos
This paper considers a classical linear, transient heat conduction problem set in Regions 1 and 2 defined by the half planes x>0 and x