Reflection and transmission of thermo-diffusive viscoelastic waves with variable thermal conductivity at an imperfect interface
Amr M.Y. Abdelaty,Khaled Lotfy,Saurav Sharma,Rajneesh Kumar,Fulin Shang,Alaa A. El-Bary,Lotfi Jlali,Ibrahim S. Elshazly
Abstract
This paper presents an analytical investigation of the reflection and transmission of elastic waves at an imperfect interface separating an elastic half-space and a bio-thermo-diffusive viscoelastic half-space, with particular emphasis on the role of temperature-dependent thermal conductivity. Unlike conventional interface-wave models that assume constant thermal conductivity, the present formulation incorporates variable thermal conductivity into the bioheat equation, leading to a more physically realistic description of thermo-mechanical coupling in viscoelastic media. The resulting nonlinearity is treated analytically using the Kirchhoff transformation, allowing closed-form normal-mode solutions to be obtained. Reflection and transmission coefficients, together with the associated energy ratios, are derived for both longitudinal (P) and shear vertical (SV) wave incidences by enforcing mechanical, thermal, and diffusive boundary conditions at a mechanically imperfect interface. Numerical results demonstrate that variable thermal conductivity significantly alters wave attenuation and energy redistribution by enhancing thermodiffusive coupling, particularly near critical angles of incidence. Blood perfusion is shown to act as an additional damping mechanism that suppresses oscillatory energy exchange and accelerates energy dissipation, with these effects being markedly amplified in the presence of viscoelasticity. Furthermore, SV-wave incidence exhibits higher sensitivity to thermal conductivity variations and perfusion effects than P-wave incidence, reflecting stronger coupling between shear deformation and thermo-diffusive processes. The proposed model extends existing thermoelastic and viscoelastic interface theories and provides new insight into energy partition mechanisms in coupled thermo-diffusive viscoelastic media.
Key Words
energy ratios; imperfect interface; reflection and transmission; thermo-diffusive coupling; variable thermal conductivity; viscoelastic waves
Address
Amr M.Y. Abdelaty — Department of Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 1142, Riyadh 12373, Saudi Arabia
Khaled Lotfy — Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt
Saurav Sharma — Cullen College of Engineering, University of Houston, 7900 Cambridge Street, #7-2G, Houston, Texas, 77054, USA
Rajneesh Kumar — Department of Mathematics, Kurukshetra University, Kurukshetra, 136119, Haryana, India
Fulin Shang — Department of Engineering Mechanics, Xi'an Jiaotong University, Xian-Ning West Road 28, Xi'an, 710049, China
Alaa A. El-Bary — Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Alexandria, Egypt
Lotfi Jlali — Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Ibrahim S. Elshazly — Department of Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 1142, Riyadh 12373, Saudi Arabia
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