A thermal lattice Boltzmann model for investigating the flow and heat transfer process of the mixtures of the pure liquid and nanoparticles (nanofluids) in the microchannel has been developed. The external and internal forces, such as buoyancy, gravity, drag and Brownian force, and the mechanical and thermal interactions among the nanoparticles and their impact on the equilibrium velocity have been introduced. Along with a Gauss white noise model for Brownian motion, the double-distribution-function (DDF) approach is used to derive the velocities and temperatures of nanofluids in a microchannel. Some numerical computations of this model have been performed and several results have been provided in this paper. It has been found that the temperature distribution of the nanofluids in the microchannel is quite different from that of pure water flowing through a channel. Due to the random motion of the suspended nanoparticles under the action of various forces, the temperature distribution of the nanofluids seems to be irregular and the temperature distribution in the vertical direction becomes flatter compared to that for pure water in a channel. The distribution morphology and the volume fraction of the nanoparticles play a vital role in enhancing the heat transfer of the nanofluids. Numerical results also demonstrate that the distribution of the suspended nanoparticles leads to a fluctuation of the Nusselt number of the nanofluids in the direction of the main flow. Nusselt number also increases with an increase in the inlet Reynolds number.

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