The time nonlocal generalization of the classical Fourier law with the “Long-tail” power kernel can be interpreted in terms of fractional calculus and leads to the time fractional heat conduction equation. The solution to the fractional heat conduction equation under a Dirichlet boundary condition with zero temperature and the physical Neumann boundary condition with zero heat flux are obtained by integral transform. Thermal deflection has been investigated in the context of fractional-order heat conduction by quasi-static approach for a thin hollow circular disk. The numerical results for temperature distribution and thermal deflection using thermal moment are computed and represented graphically for copper material.

In the present scenario, the whole world struggling with COVID-19 which affects highly transmittable and pathogenic viral infection that rose by a newly discovered coronavirus and believed to be originated in China. The more serious effects of the virus occur for the people who are under medical problems as diabetes, chronic respiratory diseases, cancer, and cardiovascular diseases also in older persons. Because of the unavailability of proper vaccine, medical facility and medical experts the current situation becomes worst and uncontrollable for many countries. Hence, in order to overcome and reduce the spread of infection there is a necessity to prepare the predictive mathematical model due to prevention factor and suitability conditions. Enlightened by the coronavirus, the present study deals with a novel mathematical model of COVID-19 to investigate the impact of S-I-R-M model due to the influence of prevention factor and suitability conditions. Numerical calculation for infectious rate, recovery rate and mortality rate have been discussed and displayed graphically. Moreover, some comparisons have been shown in figure to estimate the effect of prevention factor.

The present work is concerned with the solution of a fractional-order thermoelastic problem of a two-dimensional infinite half space under axisymmetric distributions in which lower surface is traction free and subjected to a periodically varying heat source. The thermoelastic displacement, stresses and temperature are determined within the context of fractional-order thermoelastic theory. To observe the variations of displacement, temperature and stress inside the half space, the authors compute the numerical values of the field variables for copper material by utilizing Gaver-Stehfast algorithm for numerical inversion of Laplace transform. The effects of fractional-order parameter on the variations of field variables inside the medium are analyzed graphically. The paper aims to discuss these issues. Integral transform technique and Gaver-Stehfast algorithm are applied to prepare the mathematical model by considering the periodically varying heat source in cylindrical co-ordinates. This paper studies a problem on thermoelastic interactions in an isotropic and homogeneous elastic medium under fractional-order theory of thermoelasticity proposed by Sherief (Ezzat and El-Karamany, 2011b). The analytic solutions are found in Laplace transform domain. Gaver-Stehfast algorithm (Ezzat and El-Karamany, 2011d; Ezzat, 2012; Ezzat, El Karamany, Ezzat, 2012) is used for numerical inversion of the Laplace transform. All the integrals were evaluated using Romberg’s integration technique (El-Karamany et al., 2011) with variable step size. A mathematical model is prepared for copper material and the results are presented graphically with the discussion on the effects of fractional-order parameter. Constructed purely on theoretical mathematical model by considering different parameters and the functions. The system of equations in this paper may prove to be useful in studying the thermal characteristics of various bodies in real-life engineering problems by considering the time fractional derivative in the field equations. In this problem, the authors have used the time fractional-order theory of thermoelasticity to solve the problem for a half space with a periodically varying heat source to control the speed of wave propagation in terms of heat and elastic waves for different conductivity like weak conductivity, moderate conductivity and super conductivity which is a new and novel contribution.

In this paper, analytical solutions are presented for temperature and thermal behavior of a thermosensitive multilayered annular disc due to point heat source. Convective heating is applied to both the innermost and outermost layers. The nonlinearity of the thermal diffusivity equation is dealt...

This study examines the thermoelastic behavior of an isotropic, homogeneous thick plate with copper material with a height of 2h and infinite lateral dimensions with boundary conditions for temperature distribution θ (r, ±h, t) = θ 0 (r) sint − cost + e −t. The coordinate system is centred at the mid-plane of the plate, with the z-axis serving as the axis of symmetry. Employing cylindrical polar coordinates (r, ϕ, z), the analysis focuses on the transient temperature distribution T (r, z, t), assuming axial symmetry with respect to time t. To explore the coupled thermal and mechanical responses under various stress and boundary conditions, both analytical and numerical approaches are utilized. The analytical solution is derived using Laplace and Hankel transforms, providing insights into the temperature field and deformation characteristics. Additionally, numerical simulations are carried out to validate and complement the analytical results, offering a comprehensive understanding of the thermoelastic dynamics within the thick plate.