The conjugate heat transfer in mixtures of a fluid and single granular clusters is studied in this paper using a novel lattice Boltzmann method (LBM) programmed for parallel computation on the graphics processing unit (GPU). The LBM is validated for heat conduction by finite volume method (FVM) in a one dimensional geometry of multi-layer composites, and also in a three dimensional (3D) geometry of air filled cube with the central solid sphere. Then the LBM is employed to study the influence of stationary interstitial fluid on the effective thermal conductivity (ETC) of various mixtures containing clusters of different number of particles and particle configurations. The clusters are randomly extracted from a discrete element method (DEM) generated packed bed. Our results reveal how the ETC strongly depends on the number of contacts, which can boost the ETC by 40 percent. In addition, our results show as the ratio of solid to fluid conductivity goes below 5, the ETC rises several folds. On the other hand, it slightly decreases when that ratio stretches from 5 to 50. (c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )