Abstract
In this article, we consider the transient free convection flow of nanofluids between two vertical parallel plates in the presence of radiation and damped thermal flux. The generalized Fourier's law is considered in thermal flux constitutive equation with a weakly memory. The integral transform technique is used for finding the exact solutions of the fractional governing differential equations for fluid temperature and velocity field. The solutions are presented in the term of the time-fractional derivative of the Wright function and Robotnov and Hartley function. Solutions to the ordinary fluid, corresponding to the fractional parameter equal to unit, are obtained as a particular case of the fractional problem. Numerical calculations are carried out and results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with thermal memory and the ordinary fluid is made.
•The generalized Fourier's law is considered in thermal flux constitutive equation.•Solutions are presented in term of Wright function, Robotnov and Hartley function.•Solutions to the ordinary fluid are obtained from the fractional problem.•Physical parameters on temperature and velocity fields are graphically underline.•A comparison between the fluid with thermal memory and the ordinary fluid is made.