Nanofluid flow and MHD mixed convection inside a vertical annulus with moving walls and transpiration considering the effect of Brownian motion and shape factor

In the present study, the exact solution of a nanofluid flow and mixed convection within a vertical cylindrical annulus with suction/injection, which is adjacent to the radial magnetic field, is presented with regard to the motion of cylinders’ walls. The impact of Brownian motion and shape factor on the thermal state of CuO–water nanofluid is also considered. The influence of such parameters as Hartmann number, mixed convection parameter, suction/injection, volume fraction of nanoparticles and motion of cylinders’ walls on flow and heat transfer is probed. The results show that the shape of the nanoparticles could change the thermal behavior of the nanofluid and when the nanoparticles are used in the shape of a platelet, the highest Nusselt number is obtained (about 2.5% increasement of Nusselt number on internal cylinders’ wall comparison to spherical shape). The results shed light on the fact that if, for example, the external cylinder is stationary and the internal cylinder moves in the direction of z axis, the maximum and minimum heat transfer take place on the walls of internal and external cylinders, respectively (for η?=?300, about 15% increasement of Nusselt number on internal cylinders’ wall). Furthermore, the enhancement of radius ratio between two cylinders increases the rate of heat transfer and decreases the shear stress on the internal cylinder’s wall.