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For most solids, thermal expansion is proportional to the change in temperature: Thus, the change in either the strain or temperature can be estimated by: = where = is the difference of the temperature between the two recorded strains, measured in degrees Fahrenheit, degrees Rankine, degrees Celsius, or kelvin, and is the linear coefficient of ...
Apart from modelling melting of solids, Stefan problem is also used as a model for the asymptotic behaviour (in time) of more complex problems. For example, Pego [10] uses matched asymptotic expansions to prove that Cahn-Hilliard solutions for phase separation problems behave as solutions to a non-linear Stefan problem at an intermediate time ...
A heating due to Ohmic losses may also induce mechanical stress via thermal expansion. This changes the birefringence of the optical element according to the photoelastic effect and hence may influence the optical behavior. JCMsuite can solve linear problems of continuum mechanics. The equations governing linear elasticity follow from the ...
Thus in 2D and 3D negative thermal expansion in close-packed systems with pair interactions is realized even when the third derivative of the potential is zero or even negative. Note that one-dimensional and multidimensional cases are qualitatively different. In 1D thermal expansion is caused by anharmonicity of interatomic potential only ...
It discretizes the space into smaller elements for which basis functions are assigned to their nodes or edges. Basis functions are linear or higher order polynomials. Applying the differential equation and the boundary conditions of the problem to the basis functions, a system of equations is formulated using either the Ritz or Galerkin method.
Temperature gradients, thermal expansion or contraction and thermal shocks are things that can lead to thermal stress. This type of stress is highly dependent on the thermal expansion coefficient which varies from material to material. In general, the greater the temperature change, the higher the level of stress that can occur.
Increased thermal vibrations produce thermal expansion characterized by the coefficient of thermal expansion (CTE) that is the gradient of the graph of dimensional change versus temperature. CTE depends upon thermal transitions such as the glass transition. CTE of the glassy state is low, while at the glass transition temperature (Tg) increased ...
A direct practical application of the heat equation, in conjunction with Fourier theory, in spherical coordinates, is the prediction of thermal transfer profiles and the measurement of the thermal diffusivity in polymers (Unsworth and Duarte). This dual theoretical-experimental method is applicable to rubber, various other polymeric materials ...