Postdoc renewal seminar of Dr. Komal Jagid on Semi-analytical solution of the Boltzmann Transport Equation for 1-D models with interface of two dissimilar materials.
Venue:
F24, ME Department
March 19, 2025
Description of the talk
Title: Semi-analytical solution of the Boltzmann Transport Equation for 1-D models with interface of two dissimilar materials
Date/Time: 19th March, 3 PM to 3:45 PM
Venue: F24, ME Department
Abstract: Interfaces play a critical role in determining how effectively heat is dissipated in electronic nano-devices, which can directly impacti their performances and reliability. Proper thermal management in nano-electronics depends on accurately designing and understanding interfacial thermal resistance. In this study, we present a comprehensive analysis of temperature profiles, heat flux, and thermal boundary resistance (TBR) by solving the Boltzmann transport equation (BTE). Specifically, we address the steady-state one-dimensional frequency-dependent BTE for a double-layer(material) structure with a sharp interface. Our approach incorporates frequency-dependent interfacial conditions in terms of reflection and transmission of phonons at the interface which ensures accurate transmission of heat flux across the full spectrum of transport regimes, from diffusive to ballistic. To solve the BTE, we use the method of degenerate kernels, also known as the Fourier series expansion method. This method enables us to solve the complex problem efficiently while maintaining accuracy. We validate our results by comparing the BTE temperature and heat-flux profiles of Silicon-Germanium interface with the profiles obtained by nonequilibrium molecular dynamics (NEMD) simulations under different boundary temperature and length conditions. Our BTE results show good agreement with prior studies based on NEMD simulations and other BTE solutions and provide useful insights into improving the thermal properties of nanoelectronic devices. We also hope to propose nonlocal constitutive laws for heat conduction to explain nonlinear temperature profile obtained for NEMD and BTE solutions. We would also like to semi-analytically solve the coupled electron-phonon BTE. Finally, we are currently investigating the homogenized solutions for coupled charge and heat flux in thermoelectric materials.
About the speaker: Dr. Jangid obtained her PhD from Applied Mathematics, IIT BHU in Dec 2023 under the supervision of Prof. Santwana Mukhopadhyay. Her PhD thesis topic was "Mathematical Modeling on Thermoelasticity and Poro-Thermoelasticity". She has working as a postdoctoral scholar at IIT Bombay from April 2024 onward. Her list of publications is as follows:
1. Komal Jangid, Bhagwan Singh and Santwana Mukhopadhyay. "Legendre wavelet collocation method for investigating thermo-mechanical responses on biological tissue during laser irradiation." Mathematics and Computers in Simulation 219, 404-423 (2024)
2. Bhagwan Singh, Komal Jangid and Santwana Mukhopadhyay. "Implementation of Legendre wavelet method for the size dependent bending analysis of nano beam resonator under nonlocal strain gradient theory." Computers and Mathematics with Applications 153, 94-107 (2023)
3. Komal Jangid and Santwana Mukhopadhyay. "Application of Legendre wavelet collocation method to the analysis of poro-thermoelastic coupling with variable thermal conductivity." Computers and Mathematics with Applications 146, 1-11 (2023)
4. Komal Jangid and Santwana Mukhopadhyay. "Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source." Zeitschrift für angewandte Mathematik und Physik 73, 196 (2022)
5. Manushi Gupta, Komal Jangid and Santwana Mukhopadhyay. "Domain of influence results of dual-phase-lag thermoelasticity theory for natural stress–heat-flux problem. Zeitschrift für angewandte Mathematik und Physik 73, 169 (2022)
6. Komal Jangid and Santwana Mukhopadhyay. "Variational principle and continuous dependence results on the generalized poro-thermoelasticity theory with one relaxation parameter." Continuum Mechanics and Thermodynamics 34, 867–881 (2022)
7. Komal Jangid, Manushi Gupta and Santwana Mukhopadhyay. "On propagation of harmonic plane waves under the Moore- Gibson-Thompson thermoelasticity theory." Waves in Random and Complex Media (2021)
8. Komal Jangid and Santwana Mukhopadhyay. "A domain of influence theorem under MGT thermoelasticity theory." Mathematics and Mechanics of Solids 26(2), 285-295 (2021)
9. Komal Jangid and Santwana Mukhopadhyay. "A domain of influence theorem for a natural stress–heat-flux problem in the Moore–Gibson–Thompson thermoelasticity theory." Acta Mechanica 232, 177–187 (2021)
10. Komal Jangid and Santwana Mukhopadhyay. "Variational and reciprocal principles on the temperature-rate dependent two-temperature thermoelasticity theory." Journal of Thermal Stresses 43(7), 816-828 (2020)
2. Bhagwan Singh, Komal Jangid and Santwana Mukhopadhyay. "Implementation of Legendre wavelet method for the size dependent bending analysis of nano beam resonator under nonlocal strain gradient theory." Computers and Mathematics with Applications 153, 94-107 (2023)
3. Komal Jangid and Santwana Mukhopadhyay. "Application of Legendre wavelet collocation method to the analysis of poro-thermoelastic coupling with variable thermal conductivity." Computers and Mathematics with Applications 146, 1-11 (2023)
4. Komal Jangid and Santwana Mukhopadhyay. "Thermoelastic interactions on temperature-rate-dependent two-temperature thermoelasticity in an infinite medium subjected to a line heat source." Zeitschrift für angewandte Mathematik und Physik 73, 196 (2022)
5. Manushi Gupta, Komal Jangid and Santwana Mukhopadhyay. "Domain of influence results of dual-phase-lag thermoelasticity theory for natural stress–heat-flux problem. Zeitschrift für angewandte Mathematik und Physik 73, 169 (2022)
6. Komal Jangid and Santwana Mukhopadhyay. "Variational principle and continuous dependence results on the generalized poro-thermoelasticity theory with one relaxation parameter." Continuum Mechanics and Thermodynamics 34, 867–881 (2022)
7. Komal Jangid, Manushi Gupta and Santwana Mukhopadhyay. "On propagation of harmonic plane waves under the Moore- Gibson-Thompson thermoelasticity theory." Waves in Random and Complex Media (2021)
8. Komal Jangid and Santwana Mukhopadhyay. "A domain of influence theorem under MGT thermoelasticity theory." Mathematics and Mechanics of Solids 26(2), 285-295 (2021)
9. Komal Jangid and Santwana Mukhopadhyay. "A domain of influence theorem for a natural stress–heat-flux problem in the Moore–Gibson–Thompson thermoelasticity theory." Acta Mechanica 232, 177–187 (2021)
10. Komal Jangid and Santwana Mukhopadhyay. "Variational and reciprocal principles on the temperature-rate dependent two-temperature thermoelasticity theory." Journal of Thermal Stresses 43(7), 816-828 (2020)