3 years ago

# Applications of non-integer Caputo time fractional derivatives to natural convection flow subject to arbitrary velocity and Newtonian heating

Maryam Aleem, Ilyas Khan, M. A. Imran, Nehad Ali Shah

### Abstract

Unsteady time fractional natural convection flow of incompressible viscous fluid due to arbitrary velocity with radiation and Newtonian heating is investigated. By introducing dimensionless variables and functions, the resulting equations are solved by the Laplace transform technique. Exact solutions for temperature and velocity fields are obtained by Caputo time fractional derivatives in dimensionless form, and they are expressed in terms of Robotnov–Hartley function and Wright’s function. The rate of heat transfer on plate is obtained in terms of Nusselt number. Some known solutions from the existing literature are obtained as limiting case when $$\alpha = 1$$ . At the end, we have seen the significant influence of fractional parameter $$\alpha$$ on the temperature and velocity graphically and observed that it has shown an opposite behavior on temperature and velocity for small and large values of time t, respectively. This shows that how fractional parameter $$\alpha$$ affects the fluid flow.

DOI: 10.1007/s00521-016-2741-6

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