Drilling fluids execute a dominant role in the extraction of oil and gas from the land and rocks. To enhance the efficiency of drilling fluid, clay nanoparticulate has been utilized. The inclusion of clay nanomaterial to drilling fluids significantly elevate their viscosity and thermal conductivity. Therefore, the present investigation is focused on the analysis of time-fractional free convective electro-osmotic flow of Brinkman-type drilling nanofluid with clay nanoparticles. The heat generation and chemical reaction characteristics and influence of the transverse magnetic field have also been taken into an account. The local mathematical model is formulated in terms of coupled PDEs along with appropriate physical conditions. The dimensional governing equations have been non-dimensionalized by using relative similarity variables to encounter the units and reduce the variables. Further, the non-dimensional local model has been artificially converted to a generalized model by utilizing the definition of time-fractional Caputo-Fabrizio derivative with the exponential kernel. The graphical results are analyzed via computational software Mathematica, to study the flow behavior against inserted parameters. From graphical analysis it has been observed qualitatively that the velocity field has been raised against the greater magnitude of electro-osmosis parameter [Formula: see text]. Numerical table for Nusselt number is calculated from the obtained exact solutions. From the analysis 11.83% elevation in the rate of energy transition of drilling nanofluid has been reported in response of clay nanoparticles.
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