New insight into the nano-fluid flow in a channel with tempered fractional operators

While studying time fractional fluid flow problems it is typical to consider the Caputo derivative, however, these models have limitations including a singular kernel and an infinite waiting time from a random walk perspective. To help remedy this problem, this paper considers a tempered Caputo derivative, giving the system a finite waiting time. Initially, a fast approximation to a generalised tempered diffusion problem is developed using a sum of exponential approximation. The scheme is then proven to be unconditionally stable and convergent. The convergence properties are also tested on a sample solution. The fast scheme is then applied to a system of coupled tempered equations which describes the concentration, temperature and velocity of a nanofluid under the Boussinesq approximation. The most notable finding is that increasing both the fractional and tempering parameters reduces the heat transfer ability of the nanofluid system.