Axisymmetric problem in modified couple stress thermoelastic with void, diffusion and phase lags

The present work is focused on investigating the axisymmetric deformation in a thick circular plate with a heat source in modified couple stress thermoelastic (MCT) under void, diffusion, and phase lags impacts. The new set of governing equations is formulated and solved by using Laplace and Hankel transform techniques after converting the system of equations into dimensionless form and using the potential functions. The plate is subjected to a ramp-type heat source along with a thermal source, mass concentration source, and source over volume fraction field of voids (SVFV). For application, particular types of sources are taken to demonstrate the utility of the problem. The physical quantities like displacements, temperature field, mass concentration, chemical potential, and volume fraction field are determined analytically in the closed form. A numerical mathematical technique is employed to determine the resulting quantities for the original region and displayed in form of graphs to examine the different physical effects. The problem is validated by comparing results with those obtained by different authors. The results provide a motivation to investigate thermal conducting modified couple stress elastic solid under the physical impact of mass diffusion, porosity and phase lags as a new class of material. The present work is very much expected to be useful for various deformation and vibration problems in geophysics, material science, engineering, and biothermoelastic materials.

Automated summary

The present work investigates the axisymmetric deformation in a thick circular plate with a heat source under void, diffusion, and phase lags impacts using modified couple stress thermoelastic (MCT). New set of governing equations is formulated and solved using Laplace and Hankel transform techniques in dimensionless form and using potential functions. Analytical closed-form solutions for physical quantities such as displacements, temperature field, mass concentration, chemical potential, and volume fraction field are obtained, and numerical techniques are employed to analyze different physical effects. The results provide motivation to study thermal conducting modified couple stress elastic solid under the physical impact of mass diffusion, porosity, and phase lags as a new class of material. This work has significant importance for various deformation and vibration problems in geophysics, material science, engineering, and biothermoelastic materials.