Effect of variable thermal conductivity on a half-space under the fractional order theory of thermoelasticity

• We apply the fractional order theory of thermoelasticity to a half-space problem.
• We consider the thermal conductivity as a variable depending on the temperature.
• Almost all authors consider the thermal conductivity to be a constant.
• Our assumption is supported by actual experimental data.
• The fractional theory is compared with the generalized theory of thermoelasticity.

In this work, we consider the problem for a half-space formed of a material with variable thermal conductivity. The problem is within the context of the theory of fractional order theory of thermoelasticity. The boundary plane of the half-space is assumed to be traction free and subjected to a thermal shock that is a function of time. Laplace transform techniques are used. The inverse transforms are obtained by using a numerical method based on Fourier expansion techniques. The predictions of the theory are discussed and compared with those for the generalized theory of thermoelasticity. We also study the effect of the fractional derivative parameter on the behavior of the solution. Numerical results are represented graphically for the temperature, displacement and stress distributions.