Effects of conjugate buoyant generalized heat transport in water-based nanofluids with different nanoparticles are studied. The nanofluid flows in an infinite vertical annular channel with differently heated cylindrical surfaces. The generalized Cattaneo law of thermal flux is formulated in terms of time-fractional Caputo derivative. The annulus space is formed by a solid annular wall heated on the inner surface and an isothermal exterior cylindrical tube.Analytical solutions in the Laplace domain for the temperature in the solid wall, nanofluid temperature, and nanofluid velocity are determined. The solutions in the real domain are obtained using the numerical inversion algorithm for the Laplace transforms. The results corresponding to fractional models are compared with those of the ordinary models described by the classical Cattaneo law. It has found that the heat flux given by the fractional equation leads to the decrease of heat transfer in the solid wall because the values of the temperature gradient are attenuated by the weight function in the heat flux expression. The temperature in the nanofluid has a different evolution concerning the fractional parameter. In the area close to the solid wall, the temperature increases concerning the fractional parameter. The temperature decreases with the thermal memory parameter in the region close to the outer wall. For large values of time, it is observed that the fractional model leads to an improvement of heat transfer.

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