The spectral formulation of the stochastic finite-element method is applied to the problem of heat conduction in a random medium. Specifically, the conductivity of the medium, as well as its heat capacity are treated as uncorrelated random processes with spatial random fluctuations. Using the spectral stochastic finiteelement method, this paper analyzes the sensitivity of heat conduction proble...

We define and analyze a linear transformation – the heat transform – that allows to map solutions of hyperbolic equations to solutions of corresponding parabolic equations. The inversion of this mapping can be used to transform an inverse problem for the heat equation to a similar problem for the wave equation. This work is motivated by problems of finding interfaces, boundaries and associated ...

The classical problem of heat conduction in one dimension on a composite ring is examined. The problem is formulated using the heat equation with periodic boundary conditions. We provide an explicit solution of this problem using the Method of Fokas. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumption of continuit...

Longitudinal heat conduction is an important parameter in the cryogenic field, especially in cryogenic heat exchangers. In the present work, the parasitic effect of tube wall longitudinal heat conduction on temperature measurement has been studied in cryogenic laminar hydrogen flow. The effects of various parameters such as wall cold end temperature, wall thermal conductivity, gas volumetric fl...

A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids is presented. The coupled thermo-mechanical boundary-value problem under consideration consists of the equilibrium problem for a deformable, inelastic and dissipative solid with the heat conduction problem appended in addition. The variational formulation allows for general dissipati...

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