Different types of nanomaterials are used these days. Among them, clay nanoparticles are the one of the most applicable and affordable options. Specifically, clay nanoparticles have numerous applications in the field of medical science for cleaning blood, water, etc. Based on this motivation, this article aimed to study entropy generation in different drilling nanoliquids with clay nanoparticles. Entropy generation and natural convection usually occur during the drilling process of oil and gas from rocks and land, wherein clay nanoparticles may be included in the drilling fluids. In this work, water, engine oil and kerosene oil were taken as base fluids. A comparative analysis was completed for these three types of base fluid, each containing clay nanoparticles. Numerical values of viscosity and effective thermal conductivity were computed for the nanofluids based on the Maxwell–Garnett (MG) and Brinkman models. The closed-form solution of the formulated problem (in terms of partial differential equations with defined initial and boundary conditions) was determined using the Laplace transform technique. Numerical facts for temperature and velocity fields were used to calculate the Bejan number and local entropy generation. These solutions are uncommon in the literature and therefore this work can assist in the exact solutions of a number of problems of technical relevance to this type. Herein, the effect of different parameters on entropy generation and Bejan number minimization and maximization are displayed through graphs.
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