Influence of magnetic field on double convection problem of fractional viscous fluid over an exponentially moving vertical plate: New trends of Caputo time-fractional derivative model
Open Access
- 25 July 2019
- journal article
- research article
- Published by SAGE Publications in Advances in Mechanical Engineering
- Vol. 11 (7)
- https://doi.org/10.1177/1687814019860384
Abstract
In this article, the influence of a magnetic field is studied on a generalized viscous fluid model with double convection, due to simultaneous effects of heat and mass transfer induced by temperature and concentration gradients. The fluid is considered over an exponentially accelerated vertical plate with time-dependent boundary conditions. Additional effects of heat generation and chemical reaction are also considered. A generalized viscous fluid model consists of three partial differential equations of momentum, heat, and mass transfer with corresponding initial and boundary condition. The idea of non-integer order Caputo time-fractional derivatives is used, and exact solutions for velocity, temperature, and concentration in terms of Wright function and function of Lorenzo–Hartley are developed for ordinary cases. Graphical analysis of flow and fractional parameters is made by using computational software MathCad, and discussed. The results obtained are also in good agreement with the published results from the literature. As a result, it is found that temperature and fluid velocity can be enhanced for smaller values of fractional parameters.Keywords
This publication has 25 references indexed in Scilit:
- On the unsteady rotational flow of fractional Oldroyd-B fluid in cylindrical domainsMeccanica, 2011
- New exact analytical solutions for Stokes’ first problem of Maxwell fluid with fractional derivative approachComputers & Mathematics with Applications, 2011
- RETRACTED ARTICLE: Flow of fractional Maxwell fluid between coaxial cylindersArchive of Applied Mechanics, 2011
- Exact analytic solutions for the unsteady flow of a non-Newtonian fluid between two cylinders with fractional derivative modelCommunications in Nonlinear Science and Numerical Simulation, 2009
- On accelerated flows of a viscoelastic fluid with the fractional Burgers’ modelNonlinear Analysis: Real World Applications, 2009
- Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinderComputers & Mathematics with Applications, 2008
- Unsteady flow of viscoelastic fluid with fractional Maxwell model in a channelMechanics Research Communications, 2007
- Unsteady Rotating Flows of a Viscoelastic Fluid with the Fractional Maxwell Model Between Coaxial CylindersActa Mechanica Sinica, 2006
- Algorithm 368: Numerical inversion of Laplace transforms [D5]Communications of the ACM, 1970
- Significance of Power-Law Relations in RheologyNature, 1945