We consider an axisymmetric inverse heat conduction problem of determining the surface temperature from a fixed location inside a cylinder. This problem is ill-posed; the solution if it exists does not depend continuously on the data. A special project method—dual least squares method generated by the family of Shannon wavelet is applied to formulate regularized solution. Meanwhile, an order op...

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.........................................................................

small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. non-fourier heat transfer overcomes some shortcomings of fourier heat tran...

In many applications, such as the heat conduction and hydrology, there is a need to recover the (possibly discontinuous) diffusion coefficient a from boundary measurements of solutions of a parabolic equation. The complete inverse problem is ill posed and nonlinear, so numerical solution is quite difficult, and we linearize the problem around constant a. We study and solve numerically the linea...

A numerical method for the solution of inverse heat conduction problems in two-dimensional rectangular domains is established and its performance is demonstrated by computational results. The present method extends Beck's' method to two spatial dimensions and also utilizes future times in order to stabilize the ill-posedness of the underlying problems. The approach relies on a line approximatio...

A 3-D finite element method (FEM) formulation for the prediction of unknown boundary conditions in linear steady thermoelastic continuum problems is presented. The present FEM formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-spec...

The deterioration of the performance of a cross flow heat exchanger with condensation due to the longitudinal conduction was investigated. For a relatively small change of wall temperature along the flow directions which was shown to be common in many applications, the energy equations were solved numerically. An iterative method was used to solve the resulting equations of the finite differenc...