Unsteady Flow of Non-Newtonian Visco-Elastic Fluid in Dual-Porosity Media with the Fractional Derivative

Fractional time-dependent Bingham model for muddy clay

“…The starting point of the fractional derivative model of a non-Newtonian fluid is also a classical differential equation which is modified by replacing the time derivative of an integer order by the fractional calculus operators. Shan et al [21] used the fractional order derivative to establish the relaxation models for non-Newtonian viscoelastic fluids in dual porous media to research the seepage flow. Ezzat [22] constructed a new mathematical model for thermoelectric MHD non-Newtonian fluid with fractional order.…”

A space fractional constitutive equation model for non-Newtonian fluid flow

“…Fractional-derivative models were recently suggested by several studies as a promising tool to characterize non-Newtonian fluids, because fractional calculus can well characterize a physical system with long-term memory and spatial non-locality [15,17,18,19]. For example, the time fractionalderivative based constitutive equation, which can well describe the history dependency in fluid dynamics, was proposed to characterize different types of time-dependent non-Newtonian fluids [17].…”

“…For example, the time fractionalderivative based constitutive equation, which can well describe the history dependency in fluid dynamics, was proposed to characterize different types of time-dependent non-Newtonian fluids [17]. This equation was further applied to analyze the various dynamic processes of muddy clay [17], seepage flow in dual-porosity media [18], blood viscosity [19], and the behavior of Sesbania gel and xanthan gum [20]. Previous studies of fractional-derivative models for non-Newtonian fluids, however, are mainly from the rheology viewpoint.…”

A volume deformation model for brittle rock based on fractional order calculus

“…For example, a series of researches on viscoelastic dampers have been finished by Park [21], Lewandowski [22] and Rossikhin [23][24][25][26]. In other cases, for a viscoelastic fluid, Shan [27], Ezzat [28] and Mahmood [29] have employed fractional calculus in their studies. However, these efforts were more focused on the stress-strain-time relationship and until now it is still unclear whether fractional calculus can be used to represent the volume strain.…”