A MINLP approach to improve heat transfer in flat plates through the optimal distribution of nanoparticles

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In this work, the thermal effect of deploying nanoparticles on the steady-state two-dimensional heat transfer behavior on a square plate is presented. The aim is to strengthen process intensification through efficient energy use. The approach of this work is to present a general methodology to obtain the optimal configuration of the nanoparticles and the base fluid respectively in the system. Here, the objective function is maximizing the heat transfer of the system considering that the performance of the nanofluids depends on the distribution of the nanoparticles. A general model is presented that allows solving the two-dimensional heat equation for the nanoparticles and the base fluid independently. The mathematical formulation is presented as a problem of Mixed-Integer Non-linear Programming (MINLP) model. The system under consideration is a mixture of metallic nano-sized particles and conventional heat-transferring fluid. In addition, it is also considered that there is heat generation inside the base fluid and as well the thermal conductivity of the flat plate is assumed to vary as a linear function of the temperature. The results indicate that improved heat transfer can be achieved through optimal fluid location. However, in few cases this behavior was not observed and the explanation of this issue is linked to the the nonconvex MINLP problem rendering only optimal local solutions. In order to show the applicability of the proposed methodology, two parametric case studies are presented.