Heat conduction with fractional Cattaneo-Christov upper-convective derivative flux model

•Fractional Cattaneo-Christov flux model is suggested in the investigation of heat conduction.•Formulated equation is solved numerically, where space fractional derivative is characterized by weight coefficient.•The concave and convex forms of temperature distribution profiles versus fractional parameters are discussed.

Fractional order derivatives are global operators for which the time fractional order derivative possesses memory character while the space ones reflects non-local behavior. In this paper, a new time and space fractional Cattaneo-Christov upper-convective derivative flux heat conduction model is suggested where the space fractional derivative is characterized by the weight coefficient of forward versus backward transition probability. Governing equation is formulated and solved by L1-approximation and shifted Grünwald formula. Results show that the fractional parameters, time and location parameters, relaxation parameter, weight coefficient and convection velocity have remarkable impacts on heat transfer characteristics. Temperature distribution profiles are monotonically decreasing in a concave form versus time fractional parameter with existing of relaxation parameter, while in a convex form with space fractional parameter evolution under three special conditions, i.e., the right region, the larger weight coefficient (γ ≥ 0.5) and smaller convection parameter u.