Multiscale mathematical models for nanoscale heat transport phenomena
M. Thamizhsudarthamizhsudar@avit.ac.inDepartment of Humanities and ScienceAarupadai Veedu Institute of TechnologyVinayaka Mission’s Research Foundation (Deemed to be University)Paiyanoor, Tamil Nadu, 603104, IndiaView full profile → , *Satya Ranjan DasCorresponding authorsatyadas@soa.ac.inDepartment of Computer Science and EngineeringInstitute of Technical Education and ResearchSiksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , Manisha Chandnamanisha.chandna.orp@chitkara.edu.inCentre of Research Impact and Outcome (CRIO)Chitkara UniversityRajpura, Punjab, 140417, IndiaView full profile → , Saurabh Guptasguptaaec@gmail.comDepartment of Mechanical EngineeringIndira College of Engineering & ManagementPune, Maharashtra, 410506, IndiaView full profile → , Tanya Singhdean.academics@niu.edu.inSchool of Engineering and TechnologyNoida International UniversityGreater Noida, Uttar Pradesh, 201312, IndiaView full profile → , D. Prakasa Raodprakashrao@gmail.comDepartment of Electrical & Electronics EngineeringPragati Engineering CollegeSurampalem, Andhra Pradesh, 533437, IndiaView full profile → , Angajala Rama Krishnadean_admissions@adityauniversity.inDepartment of PhysicsAditya UniversitySurampalem, Andhra Pradesh, 533437, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 27 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2808
- Pages:
- 2917–2928
Abstract
Multiscale mathematical models offer a mathematically sound basis to study heat transport phenomena in the nanoscale range for which classical continuum-based models are not applicable. In this study, a full mathematical formulation is introduced that combines Fourier heat conduction, Boltzmann Transport Equation, dual-phase-lag and hyperbolic heat conduction, as well as molecular dynamics approaches to account for the thermal behavior at various spatial and temporal scales. The numerical solution algorithms are used to investigate heat propagation, temperature evolution and phonon transport phenomena at the nanoscale. The proposed framework enhances the ability to predict the heat transfer, which is represented by both ballistic and diffusive heat transfer, while retaining the computational efficiency. The convergence is shown to be better compared to the conventional single-scale approach, while the stability is improved and the thermal prediction error is smaller than those of existing methods, through a comparative numerical evaluation. The resulting multiscale mathematical model provides a sound theoretical basis for the design of nanoscale electronic devices, thermoelectric systems, advanced materials and novel technologies for thermal management.
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References
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