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To find the solutions to the equations containing non-linear terms is a very tough task for the researchers. Even it becomes more challenging when someone wants to find the exact solutions. The exact solutions play a vital role which can be used as a benchmark for numerical and empirical solutions. Therefore, the present article aims to investigate the amalgamated effect of viscous dissipation and joule heating on the electro-osmotic flow of generalized Maxwell nanofluid along with heat transfer in a channel. Nanofluid is formed by the uniform dispersion of ultra-fine nano-sized solid particles of clay in concrete which is considered as a base fluid. The classical model of the Maxwell nanofluid is generalized by using the new definition of the Atangana-Baleanu time-fractional derivative. Fourier sine transform and the Laplace transform techniques are used to evaluate the exact expressions for the velocity and temperature distributions. The impact of various embedded parameters such as fractional parameter, Maxwell fluid parameter, volume fraction parameter, zeta potential parameters, electro-kinetic parameter, Brinkman number, joule heating parameter and Prandtl number on velocity and temperature profiles are drawn and illustrated graphically. It is interesting to see that by using nano-clay in concrete the rate of heat transfer increases with 25.5%.

Exact Analysis of Non-Linear Electro-Osmotic Flow of Generalized Maxwell Nanofluid: Applications in Concrete Based Nano-Materials