Model of fractional heat conduction in a thermoelastic thin slim strip
with temperature-dependent thermal conductivity and thermal shock
In this work, the fractional order thermoelasticity theory is used to
investigate the thermoelastic problem of a thin slim strip considering
the thermal conductivity is to be variable. The theory of thermal
stresses based on the heat conduction equation with the Caputo
time-fractional derivative of order α is used. The surface of the strip
is subjected to a thermal shock and assumed to be traction free. By
using the Laplace transform and numerical Laplace inversion, the
governing equations are solved. The inverse of the Laplace transform is
done numerically using a method based on Fourier expansion techniques.
Numerical calculations for the considered variables are performed and
the results obtained have been presented graphically. The effects of
fractional order parameter and the variation of thermal conductivity on
temperature, stress, and displacement are investigated.