▎ 摘　　要

A promising material for applications in near-field radiative heat transfer is graphene, due to large heat flux values and the capability to actively control the heat flux using various mechanisms such as applying a bias voltage. Theoretical studies have shown that a heat transfer coefficient as large as-1500 W/m2K can be modulated with a ratio of-100 for two graphene sheets at 300 K, free-standing in vacuum, with a gap of 100 nm. However, it is not clear how the heat transfer coefficient and the modulation ratio are affected in the presence of a substrate which needs to be used in practice. We study the effect of the presence of substrates on near-field radiative heat flux among two single-layer sheets of graphene. We determine the complex dielectric function that corresponds to maximal heat flux for an emitted electro-magnetic mode. We compute the heat flux and modulation ratio for 41 different substrates selected from common dielectric, metallic and semiconducting materials and show that the heat flux and the modu-lation ratio both reduce in the presence of a substrate. The dielectric substrates such as BaF2, KCl, NaF, RbCl and RbBr have the largest modulation ratio and heat flux among the selected substrates. The low-frequency and high-frequency dielectric functions of these substrates are closest to the free space, and their dispersion occurs at low frequencies far from the spectral location of the surface plasmon polari-tons of graphene. For low and high graphene sheet temperatures of 300 K and 400 K, respectively, and a separation gap of 100 nm, the largest heat coefficient ( = 1436 W/m2K) is obtained for BaF2 with a mod-ulation ratio of 20.3. The largest modulation ratio at the same temperatures and gap size is 22.5, which is obtained for NaF with a heat transfer coefficient of 1406 W/m2K.(c) 2023 Elsevier Ltd. All rights reserved.