Unsteady natural convection boundary layer flow and heat transfer past a vertical flat plate with novel constitution models

Seeking proper and reasonable constitutive relations to study the characteristics of flow and heat transfer of viscoelastic fluid is a hot topic in recent years. In this work, a new distributed order time fractional constitution model is put forward to analyse the unsteady natural convection boundary layer flow and heat transfer, in which the magnetic field effect is considered. The mid-point quadrature method is applied to approach the distributed order integrals and the L1-formula is employed to discrete the time fractional derivatives. The influences of different involved parameters on the velocity and temperature distributions and the comparisons of the distributions with different constitution models are presented by graphical illustrations and discussed in detail.