A Transient Flow of a Non-Newtonian Fluid Modelled by a Mixed Time-Space Derivative: An Improved Integral-Balance Approach

  • Jordan HristovEmail author
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 24)


Transient flow of second-grade fluid, modelled by mixed time-space derivative, due to sudden change of the boundary condition (Stokes first problem) has been solved by an improved integral-balance method utilizing double integration technique. Two versions of mixed time-space derivative, integer-order and fractional in time (Riemann-Liouville), have been considered. The solution uses the concept of finite penetration depth of diffusing momentum from the interface into the fluid bulk. The solutions provide straightforwardly the functional relationship of the penetration depth controlled by two similarity variables: related to the Newtonian flow behaviour and the Deborah number relevant to the elastic fluid performance.


Mixed Space-time Derivatives Transient Flow Second-grade Fluid Deborah Number Finite Penetration Depth 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Chemical EngineeringUniversity of Chemical Technology and MetallurgySofiaBulgaria

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