Our study investigates the motion, temperature and volume fraction of a nanofluid that flows at a vertical channel exposed to natural and forced (mixed) convection heat transfer. The distribution function for temperature and volume fraction on the channel's wall is exponential. Nanofluid governing equations have been solved using the radial basis function method. Various parameters, including Grashof number, Brownian motion, thermophoresis parameter, plus distinct states for temperature and volume fraction functions for the channel's wall, have been probed. The results show that increasing the Grashof number by 50% will increase the fluid velocity and temperature by about 41% and 5.7% and decrease the volume fraction by 22%. In addition, it has been proved that doubling the Brownian motion parameter improves the fluid temperature and velocity by 67% and 66% and lowers the volume fraction by 53%. Moreover, increasing the thermophoresis parameter has a similar effect to the Brownian motion parameter. Finally, it has been seen that velocity, temperature and volume fraction functions strongly depend on temperature and volume fraction distribution functions on the channel's wall.
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