The present analysis proposes a novel theory of generalized thermoelasticity, taking into account the general heat conduction law, which depends on thermomass motion. This is defined as the equivalent mass of phonon gas in dielectrics, according to Einstein’s mass–energy relation, involving the inertia effect on the temporal and spatial variations of heat flux and temperature. The constitutive equation is formulated using nonlocal stress theory proposed by Eringen. The governing equations have been solved for a thermoelastic rod, where the boundaries are traction-free and the left boundary of the rod is subjected to ramp-type heating, while on the right boundary, there is no temperature. Invoking the Laplace integral transform, the solution of the present problem is achieved. In order to capture the solutions in real space-time domain, a viable simulation has been carried out for the numerical inversion of the Laplace transform using the method of Zakian. The findings illustrate the differences between various kernel functions in the heat transport process. Moreover, the impact of the present revolutionary thermoelastic model is also reported. How various effective parameters, such as the nonlocal parameter and the time delay parameters influence each of the physical fields, have also been analyzed.
AlvarezFXJouDSellittoA. Phonon hydrodynamics and phonon-boundary scattering in nanosystems. J Appl Phys2009; 105: 014317.
12.
TiwariR.SaeedA. M.AbouelregalA.SinghalA.SalemM. G.Nonlocal thermoelastic waves inside nanobeam resonator subject to various loadings. Mech Based Design of Struct Mach2022; 52(1): 215–238. https://doi.org/10.1080/15397734.2022.2104312
13.
TiwariRSaeedAMKumarR, et al. Memory response on generalized thermoelastic medium in context of dual phase lag thermoelasticity with non-local effect. Arch Mech2022; 74(2–3): 69–88.
14.
FourierJ. Analytical theory of heat. New York: Dover Publications, 1955.
15.
GuoZY. Movement and transport of thermomass and thermon gas. J Eng Thermophys2006; 27(4): 631–634.
16.
EringenAC. Nonlocal continuum field theories. New York: Springer, 2002.
17.
EdelenDGBLawsN. On the thermodynamics of systems with nonlocality. Arch Ration Mech Anal1971; 43(1): 24–35.
18.
KarličićDMurmuTAdhikariS, et al. Non-local structural mechanics. Hoboken, NJ: Wiley, 2016.
19.
PodlubnyI. Fractional differential equations. New York: Academic Press, 1999.
20.
WangJLLiHF. Surpassing the fractional derivative: concept of the memory-dependent derivative. Comput Math Appl2011; 62: 1562–1567.
21.
AbouelregalAETiwariR. Computational analysis of thermoelastic vibrations of functionally graded nonlocal nanobeam excited by thermal shock. J Vibr Control2024; 30(13–14): 3105–3116.
22.
AbouelregalAETiwariRNofalTA. Modeling heat conduction in an infinite media using the thermoelastic mgt equations and the magneto-seebeck effect under the influence of a constant stationary source. Arch Appl Mech2023; 93: 2113–2128.
23.
MondalSSurA. Thermo-hydro-mechanical interaction in a poroelastic half-space with nonlocal memory effects. Int J Appl Comput Math2024; 10: 68.
24.
SurA. Magneto-photo-thermoelastic interaction in a slim strip characterized by hereditary features with two relaxation times. Mech Time Dep Mater2024; 28: 1465–1490.
25.
SurA. Moore-Gibson-Thompson generalized heat conduction in a thick plate. Ind J Phys2024; 98: 1715–1726.
26.
SurA. Photo-thermoelastic inter action in a semiconductor with cylindrical cavity due to memory-effect. Mech Time Dep Mater2024; 28: 1219–1243.
27.
HalstedDJBrownDE. Zakian’s technique for inverting Laplace transforms. The Chem Engrng J1972; 3: 312–313.
28.
WangHD. Theoretical and experimental studies on non-Fourier heat conduction based on thermomass theory. Berlin and Heidelberg: Springer, 2014.
29.
GuoZYCBWangM. General heat conduction equations based on the thermomass theory. Front Heat Mass Transf2010; 1(1): 1–8.
30.
DongYGuoZ. Entropy analyses for hyperbolic heat conduction based on the thermomass model. Int J Heat Mass Trans2011; 54(9–10): 1924–1929.
31.
DongYCaoBYGuoZY. Generalized heat conduction laws based on thermomass theory and phonon hydrodynamics. J Appl Phys2011; 110(6): 063504.
32.
YoussefHMAl-LehaibiEAN. General generalized thermoelasticity theory (GGTT). J Therm Anal Calorim2023; 148: 5917–5926.
33.
EringenAC. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys1983; 54: 4703–4710.
34.
MondalSSurA. Thermal waves based on the thermomass model due to mechanical damage with memory. Applied Physics A2025; 131: 4.
35.
MondalSSurA. Studies on piezoelectric vibrations in thermoelasticmicrobeam resonator with memory and nonlocal effects. J Strain Anal Eng Design2024; 60: 180–195.
36.
SurA. Fractal theory of thermoelasticity in non-integer dimension space. J Appl Math Mech2025; 105: e202401301.
37.
YuYJHuWTianXG. A novel generalized thermoelasticity model based on memory-dependent derivative. Int J Engrg Sci2014; 81: 123–134.
38.
EzzatMAEl-KaramanyASEl-BaryAA. Electro-thermoelasticity theory with memory-dependent derivative heat transfer. Int J Engrng Sci2016; 99: 22–38.
39.
EzzatMAEl-BaryAA. Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature. J Mech Sci Tech2015; 29: 4273–4279.
40.
EzzatMAEl-KaramanyASEl-BaryAA. Generalized thermoelasticity with memory-dependent derivatives involving two temperatures. Mech Adv Mater Struct2016; 23: 545–553.
41.
EzzatMAEl-KaramanyASEl-BaryAA. Modeling of memory-dependent derivative in generalized thermoelasticity. Euro Phys J Plus2016; 131: 372.
42.
SurA. Thermo-hydro-mechanical nonlocal response on porous deep-sea sediments under vibration of mining vehicle. Int J Comput Mater Sci Eng2024; 13: 2350030.
43.
SurA. Elasto-thermodiffusive nonlocal responses for a spherical cavity due to memory effect. Mech Time Dep Mater2024; 28: 1395–1419.
44.
YoussefHMAl-LehaibiEA. State-space approach of two-temperature generalized thermoelasticity of one-dimensional problem. Int J Solids Struct2007; 44: 1550–1562.
