Analysis of Marangoni boundary layer flow and heat transfer with novel constitution relationships

Abstract Based on traditional constitutive relationships of Maxwell fluid flow and Cattaneo heat transfer, a modified model of unsteady Marangoni convective boundary layer flow and heat transfer behavior is constructed, which introduces the distributed fractional-order derivative. The governing equations and the corresponding initial and boundary conditions are derived, in which the finite difference method with L1 scheme is used to solve the obtained equations and the solvability is analysed. Afterwards, a pair of source terms are added into the momentum equation and energy equation respectively to facilitate obtaining the exact solution, and the validity of the numerical scheme is verified by comparing with the exact solution. The influences of the physical parameters on the thickness of the velocity and temperature boundary layer and rheological characteristics with the flow and heat transfer mechanism are discussed and analysed in detail.