Computational modeling of near-field radiative heat transfer between nanoparticles or surfaces is a critical area of research in nanoscale thermal science. This phenomenon, which occurs at sub-wavelength separations, can exceed the far-field blackbody limit by orders of magnitude due to the contribution of evanescent waves. The theoretical framework for understanding and predicting this behavior relies on fluctuational electrodynamics, dielectric function engineering, and numerical techniques to solve Maxwell's equations in the near-field regime. Applications in thermophotovoltaics further highlight the practical significance of this field.

The foundation of near-field radiative heat transfer lies in fluctuational electrodynamics, which extends classical electrodynamics to include thermal fluctuations in materials. According to this theory, thermally agitated charges in a material generate stochastic currents, which in turn produce fluctuating electromagnetic fields. These fields can couple with nearby objects, leading to enhanced energy transfer. The key quantity in this framework is the mean Poynting vector, which describes the radiative heat flux between two bodies. Computational approaches often involve solving the dyadic Green's function for the system, which relates the stochastic currents to the resulting electromagnetic fields. For planar geometries, the heat flux can be decomposed into propagating and evanescent waves, with the latter dominating at nanoscale gaps. Numerical methods such as the scattering matrix approach or the Fourier modal method are commonly employed to compute the heat transfer for complex geometries.

Dielectric function tuning plays a central role in controlling near-field radiative heat transfer. The dielectric properties of materials determine their ability to support surface modes, such as surface phonon polaritons or surface plasmon polaritons, which enhance the heat flux. For instance, polar dielectrics like silicon carbide (SiC) exhibit strong surface phonon polaritons in the infrared range, leading to significant near-field enhancement. Computational models incorporate the frequency-dependent dielectric function, often described by the Lorentz-Drude model, to capture these effects. By tailoring the dielectric function through material selection or nanostructuring, the spectral and spatial distribution of heat transfer can be optimized. For example, hyperbolic materials, which have anisotropic dielectric tensors, can support a high density of states for evanescent waves, further boosting the heat flux. Numerical simulations of such materials require careful treatment of their optical anisotropy and dispersion relations.

The computational modeling of near-field heat transfer between nanoparticles introduces additional complexities due to curvature effects and multiple scattering. Techniques such as the coupled dipole method or the T-matrix method are used to solve the multiple scattering problem in nanoparticle systems. These methods discretize the nanoparticles into dipoles or higher-order multipoles and compute their mutual interactions. The heat transfer between two spherical nanoparticles, for instance, depends on their size, separation, and material properties. Computational results show that the heat flux scales with the inverse of the separation distance at very small gaps, deviating from the far-field inverse square law. For larger nanoparticles, retardation effects and higher-order multipoles become significant, requiring full-wave numerical solutions.

Applications in thermophotovoltaics (TPV) leverage near-field radiative heat transfer to improve energy conversion efficiency. TPV systems convert thermal radiation into electricity using photovoltaic cells, and the near-field enhancement can significantly increase the power output. Computational models for TPV devices integrate near-field heat transfer with charge carrier generation in the photovoltaic material. Key parameters include the emitter and cell temperatures, the spectral matching between the thermal radiation and the cell bandgap, and the nanoscale gap between the emitter and the cell. Simulations demonstrate that near-field TPV systems can achieve power densities several orders of magnitude higher than far-field systems, with efficiencies approaching the thermodynamic limit. However, challenges such as maintaining nanoscale gaps in practical devices and minimizing parasitic losses require further computational exploration.

The numerical tools for modeling near-field radiative heat transfer include both analytical approaches and full-wave simulations. Analytical methods, such as the proximity approximation or the effective medium theory, provide quick estimates but are limited to simple geometries. For more complex systems, finite-difference time-domain (FDTD) or finite-element method (FEM) simulations are employed. These methods solve Maxwell's equations numerically and can handle arbitrary geometries and material properties. However, they are computationally expensive, especially for three-dimensional problems. Recent advances in computational techniques, such as the use of periodic boundary conditions or domain decomposition methods, have improved the efficiency of these simulations.

A critical aspect of computational modeling is the validation against experimental data. Near-field heat transfer measurements are challenging due to the difficulty of maintaining precise nanoscale gaps and isolating the near-field contribution. Nevertheless, several experiments have confirmed the predictions of fluctuational electrodynamics, such as the enhanced heat flux between parallel plates or between a tip and a surface. Computational models that incorporate realistic experimental conditions, including surface roughness and temperature gradients, provide better agreement with measurements.

In summary, computational modeling of near-field radiative heat transfer relies on fluctuational electrodynamics, dielectric function engineering, and advanced numerical techniques. The ability to predict and optimize heat transfer at the nanoscale has important implications for thermophotovoltaics and other energy applications. Continued development of computational methods, coupled with experimental validation, will further advance this field and enable the design of novel nanoscale thermal devices.