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This work concerns the strain gradient theory of thermoelasticity with dual-phase-lag model. We obtain the Galerkin-type representation solution of the field equations. The strain gradient scale-length parameter plays an essential role in the material response. Therefore, we analyze the microstructural effect through the scale-length parameter on an isotropic thermoelastic half-space. We formulate the problem with a suitable boundary condition. The solution of the different field variables such as temperature, displacement, stresses, and double stresses is obtained in the Laplace transform domain. Then, we apply a numerical method for Laplace inversion to find the solution for different fields in the physical domain. The results are displayed in graphical form to show the microstructural effect through the scale-length parameter.

Being a most sensitive organ of the human body, eyes are significantly affected from the environmental/thermal changes. Therefore, mathematical modelling of the heat transport inside the human eye has become a topic of immense interest for the scientific community. The current article establishes a new mathematical model to observe the impact of the temperature distributions inside each part of the human eye. A bio-heat transfer model concerning two relaxation times (dual phase lag) is taken into account for the study of the heat flux in the eye. Closed-form solutions are determined by adopting a normal model analysis approach. Quantitative results are evaluated in the space and the time domain. Influences of the prominent parameters such as porosity parameter, activation energy, blood perfusion quantity and ambient temperature are observed on the temperature distributions for each part of the human eye. Influences of the phase lag parameters on the temperature distributions are obtained inside different layers of eye. Advantages of the present heat transfer model are established by comparing the present numerical results with the corresponding results under the theory of the old established bio heat transfer model having one relaxation parameter (LS model) and classical theory of heat transfer (CTE model) without relaxation time.