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Clay nanoparticles are hanging in three different based fluids (water, kerosene, and engine oil). The exact terminologies of Maxwell-Garnett and Brinkman for the current thermophysical properties of clay nanofluids are used, while the flow occurrence is directed by a set linear PDE with physical initial and boundary conditions. The classical governing equations are extended to non-integer order hybrid fractional derivative which is introduced in . Analytical solutions for temperature anddoi:10.2298/tsci20343a fatcat:zixqvlhurjhjdis2imjy2jweha