In a di erential equations course, one typically studies a few classes of problems for which there are closed form solutions, such as ordinary, linear di erential equations with constant coe cients. Most problems of interest in real world simulation problems are much more complex, however, involving domains of two or more dimensions or nonlinear e ects, yielding partial di erential equations or...

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This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. ...

In this paper, the three-dimensional hyperbolic effect subjected to a cosine heat flux boundary condition is carried out. Equations in rectangular coordinates are solved. Analytical solution with method of separation of variables is derived. The main aim of this paper is to obtain some possibly explicit analytical solution of the (1+3)-dimensional hyperbolic heat conduction equation for given i...

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

We look at a basic introduction to classical models of heat conduction, with a few examples including both finite and infinite systems, with techniques appropriate to each based on the boundary and initial conditions. Portions of the paper follow chapter 11 of Theoretical Mechanics of Particles and Continua [1], where I have attempted to expand the analysis in an attempt to provide clarity wher...

Heat conduction modelling ........................................................................................................................... 1 Case studies ........................................................................................................................................... 2 Analytical solutions.........................................................................

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux is prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. T...

Heat conduction in a ne scale mixture of two conductors is examined in the presence of a contact resistance between phases. The problem is studied rigorously in the context of periodic homogenization. Unlike the case of perfect heat transmission between phases, the temperature elds studied here may converge weakly in L to the homogenized temperature. The temperature gradients converge weakly as...