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The structure of divergence(s) in stationary state of irreversible heat conduction processes and their partial differential equations of elliptic type

AIP Conference Proceedings, 2002
Irreversible processes mean entropy production or simply energy dissipation. This is true for stationary states too. The Laplace’s equation for heat conduction as an elliptic linear second order partial differential equation does not express any energy dissipation in the conservative potential field according to the minimum principles.
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Error estimation for approximations of the solution of the one-dimensional stationary heat conduction equation on the basis of the governing principle of dissipative processes

International Journal of Engineering Science, 1975
Abstract On the basis of the Gyarmati's variational principle, a bound for the maximum difference between the approximation and the exact solution is established for the stationary heat conduction in a rigid bar.
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Boundary Value and Control Problems for the Stationary Magnetic Hydrodynamic Equations of Heat Conducting Fluid with Variable Coefficients

Journal of Dynamical and Control Systems
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Solving the heat equation with variable thermal conductivity

Applied Mathematics Letters, 2023
Bernard Deconinck, Bernard Deconinck
exaly  

Distributed control of nonlinear conductivity heat transfer equation in a thick functionally graded plate

International Communications in Heat and Mass Transfer, 2022
Amin Moosaie, Behrooz Rahmani
exaly  

Exact solutions of the stationary Navier – Stokes equations of a viscous heat-conducting gas for a flat jet from a linear source

Прикладная математика и механика, 2018
M. Brutyan, P. Krapivsky
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