Abstract
Drilling fluids are significant in the drilling methods of oils and gases from rocks and land. To improve the performance of drilling fluid clay nanoparticles, play a vital rule. When clay nanoparticles are added to the drilling fluids, the thermal conductivity, viscosity levels, and boiling point of the fluid boost which provide resistant to high temperatures and control the fluid cost. Bearing in mind the substantial rule of clay nanoparticles in drilling fluid, this article demonstrates the convection heat transfer in drilling nanofluid. More exactly, clay nanoparticles are suspended in three different based fluids (water, kerosene, and engine oil). The mathematical expressions of Maxwell-Garnett and Brinkman for the effective thermophysical properties of clay nanofluids are utilized, whereas the flow phenomenon is governed by a set linear PDEs with physical initial and boundary conditions. The Laplace transform technique is applied to obtain exact analytical solutions for velocity and temperature profiles. The skin friction and Nusselt number are computed and presented in tabular forms. To insight the influence of various flow parameters, the obtained solutions are computed using Mathcad and plotted in different figures. The results show that the Nusselt number is significantly increased with increasing values of volume concentration.