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Solving transient energy transport is crucial for accurately predicting the behavior of materials and devices during thermal cycling, pulsed heating, and transient operational states where heat generation and dissipation rates vary over time. Traditional methods, like the finite difference and element methods, discretize space and time and update temperature values at each grid point iteratively over time steps. Its straightforward implementation makes it popular for solving heat transfer problems. However, when high temporal and spatial resolutions or prolonged heating durations are required, the computational demand rises significantly, leading to significantly greater resource consumption. To address this, in this work we develop a new method termed Complex-modeling with Fourier Transform (CFT) that enables rapid and efficient simulations of transient energy transport problems. The CFT method decomposes the periodical heating problem into a complex-temperature energy transport problem with a single harmonic heat source. 1D and 3D transient heat conduction problems (conjugated with hot carrier transfer) are solved using the CFT method to demonstrate its effectiveness. The CFT method produces similar or higher accuracy results compared with the finite difference method, while the computational speed is increased by more than two orders of magnitude. We also developed a new method termed Complex-modeling with Fourier and Heaviside Transforms (CFHT) that can solve any transient energy transport problems with orders of magnitude speed increase. The CFT and CFHT methods developed in this work are applicable to linear problems that could involve mechanical, thermal, optical, and electrical responses. 

Upon laser irradiation, 2D materials experience a cascading energy transfer from electrons to optical phonons (OPs) and then to acoustic phonons (APs), resulting in a significant thermal non-equilibrium among energy carriers. This non-equilibrium presents challenges for Raman-based thermal characterization, as Raman scattering measures only OP temperature rise, while APs are the primary energy carriers. Despite recent efforts to address this issue, OP–AP thermal non-equilibrium in supported 2D materials remains poorly resolved. Here, we develop a method to distinguish the OP and AP temperature rises based on their different temporal thermal responses under laser irradiation: the OP–AP temperature difference responds almost immediately (∼a few to tens of ps), while the AP temperature rise takes longer to establish (∼tens of ns). Using energy transport-state resolved Raman, we probe the transient thermal response of Si-supported nm-thick MoS₂from 20 to 100 ns. We find that the OP–AP temperature difference exceeds 120% of the AP temperature rise under ∼0.439 µm radius laser heating. The intrinsic interfacial thermal conductance of the samples, based on the true AP temperature rise, varies from 0.199 to 1.46 MW·m⁻²·K⁻¹, showing an increasing trend with sample thickness. 

Nafion, a widely used proton exchange membrane in fuel cells, is a representative perfluorosulfonic acid membrane consisting of a hydrophobic Teflon backbone and hydrophilic sulfonic acid side chains. Its thermal conductivity (k) is critical to fuel cell's thermal management. During fuel cell operation, water molecules inevitably enter Nafion and could strongly affect its k. In this work, we measure the k of Nafion of different water content (λ). Findings reveal that k is significantly low in a vacuum environment characterized as 0.110 W m−1 K−1, but at λ ∼1, a notable increase is observed, reaching 0.162 W m−1 K−1. Moreover, k at λ ≈ 6 is 60% higher than that of λ ∼1. This exceptional k increase is far beyond the theoretical prediction by the effective medium theory that only considers simply physical mixing. Rather this k increase is attributed to the formation of water clusters and channels with increased λ, creating thermal pathways through hydrogen bonding, thereby improving chemical connections within the Nafion structure and augmenting its k. Furthermore, it is observed that Nafion's k reaches the maximum value of 0.256 W m−1 K−1 at λ ≈ 6, with no further increase up to λ ≈ 10.5. This phenomenon is explained by the coalescence of water clusters at λ ≈ 6, forming channels that optimize heat transfer pathways and connections within the Nafion structure. Moreover, the free movement of water molecules within water channels (λ > 6) shows physical alterations in Nafion structure (significant volume increase), which have a lesser impact on k. 

This study investigates the structural effects on the cross-plane thermal conductivity of Li4Ti5O12-based anode active material. Three structures are investigated: a basic structure consisting of LiBr/LiCl/Li4Ti5O12, polyvinylidene difluoride, and Super P (sample #1); a structure without Li4Ti5O12 (sample #2); and a structure without LiBr/LiCl (sample #3). Despite its high porosity level (77%), sample #1 exhibits higher thermal conductivity than sample #3 (64% porosity) in both air and vacuum conditions, potentially due to the extra structural bonding provided by LiBr/LiCl. The observed difference in cross-plane thermal conductivity between air and vacuum conditions provides insights into the configuration of the anode's active material in the heat transfer direction. The lower limit corresponds to the parallel thermal circuit configuration of active material and air, which is the product of the sample's porosity and thermal conductivity of air. Our analysis suggests that in sample #2, the anode's active material and air inside the pores demonstrate a more serial configuration, while in sample #3, they exhibit a more parallel configuration in the heat transfer direction. However, the thermal conductivity difference observed for sample #1 falls below the theoretical lower bound indicating significant thermal radiation within the pores. Furthermore, the in-plane thermal conductivity is predominantly controlled by the copper foil. Sample #2 exhibits the lowest in-plane thermal conductivity. This is attributed to the severe oxidization of the copper foil by LiBr/LiCl, which is confirmed by structure characterization. 

Abstract Interfacial thermal resistance plays a crucial role in efficient heat dissipation in modern electronic devices. It is critical to understand the interfacial thermal transport from both experiments and underlying physics. This review is focused on the transient opto-thermal Raman-based techniques for measuring the interfacial thermal resistance between 2D materials and substrate. This transient idea eliminates the use of laser absorption and absolute temperature rise data, therefore provides some of the highest level measurement accuracy and physics understanding. Physical concepts and perspectives are given for the time-domain differential Raman (TD-Raman), frequency-resolved Raman (FR-Raman), energy transport state-resolved Raman (ET-Raman), frequency domain ET-Raman (FET-Raman), as well as laser flash Raman and dual-wavelength laser flash Raman techniques. The thermal nonequilibrium between optical and acoustic phonons, as well as hot carrier diffusion must be considered for extremely small domain characterization of interfacial thermal resistance. To have a better understanding of phonon transport across material interfaces, we introduce a new concept termed effective interface energy transmission velocity. It is very striking that many reported interfaces have an almost constant energy transmission velocity over a wide temperature range. This physics consideration is inspired by the thermal reffusivity theory, which is effective for analyzing structure-phonon scattering. We expect the effective interface energy transmission velocity to give an intrinsic picture of the transmission of energy carriers, unaltered by the influence of their capacity to carry heat.