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Entropy generation minimization in transient heat conduction processes PART II – Transient heat conduction in solids

Kolenda Z. S., Szmyd J. S.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2014

Vol. 62, nr 4

883--887

Formulation and solution of the initial boundary-value problem of heat conduction in solids have been presented when an entropy generation minimization principle is imposed as the arbitrary constraint. Using an entropy balance equation and the Euler-Lagrange variational approach a new form of the heat conduction equation (non-linear partial difference equation) is derived.

An variational approach and mathematical model for nonlinear mechanics of elastic systems

Burak Y., Moroz H.

Journal of Applied Computer Science

2004

Vol. 12, nr 2

23-34

A variational formulation of initial-boundary value problems for the nonlinear elasticity theory of couple stresses is formulated using Hamilton functional. The local model equations are obtained. It is considered the model variants for theories of dynamical uncouple stress, quasistatic couple and uncouple stress elasticity as particular cases. The partial Hamilton functional is specified for the linear couple stress elasticity theory.

Some properties of a 3-D solution to the heat equation

Fetecau C., Fetecau G.

International Journal of Applied Mechanics and Engineering

2001

Vol. 6, no 4

999-1004

In this note, we construct a 3-D solution to the heat equation by means of the Fourier sine transform. If there exists no source of heat and the initial inner temperature of the body is zero our solution depends on x, y, z and t only by the similarity variables _ , _ and _ . Moreover, the corresponding 2-D and 1-D solutions appear as limiting cases for _ or _ and _ .