Transient magnetohydrodynamic flow and heat transfer of fractional Oldroyd-B fluids in a microchannel with slip boundary condition
- 1 October 2020
- journal article
- research article
- Published by AIP Publishing in Physics of Fluids
- Vol. 32 (10), 103104
- https://doi.org/10.1063/5.0025195
Abstract
The unsteady magnetohydrodynamic flow of viscoelastic fluids through a parallel plate microchannel under the combined influence of magnetic, electro-osmotic, and pressure gradient forcings is investigated. The fractional Oldroyd-B fluid is used for the constitutive equation to simulate the viscoelastic behavior of fluid in the microchannel. Considering the important role of slip boundary condition in microfluidics, the Navier slip model at wall is adopted. The Laplace and Fourier cosine transforms are performed to derive the analytical expression of velocity distribution. Then, by employing the finite difference method, the numerical solution of the velocity distribution is given. In order to verify the validity of our numerical approach, numerical solutions and analytical solutions of the velocity distribution are contrasted with the exact solutions of the Newtonian fluid in previous work, and the agreements are excellent. Furthermore, based on the values of the velocity distribution for the fully developed flow, the energy equation including volumetric Joule heating, electromagnetic couple effect, and energy dissipation is solved to give the temperature distribution in the microchannel by using the finite difference method. Finally, the influence of fractional parameters and pertinent system parameters on the fluid flow and heat transfer performance and the dependence of the dimensionless Nusselt number Nu on the Hartmann number Ha and Brinkman number Br are discussed graphically.Funding Information
- Fundamental Research Funds for the Central Universities (2019ZRJC002)
- National Natural Science Foundation of China (11672163, 11771254)
This publication has 56 references indexed in Scilit:
- Micro-magnetofluidics: interactions between magnetism and fluid flow on the microscaleMicrofluidics and Nanofluidics, 2011
- MHD mixed convection for viscoelastic fluid past a porous wedgeInternational Journal of Non-Linear Mechanics, 2011
- Viscous dissipation effects on thermal transport characteristics of combined pressure and electroosmotically driven flow in microchannelsInternational Journal of Heat and Mass Transfer, 2010
- Thermal Transport Characteristics of Mixed Pressure and Electro-Osmotically Driven Flow in Micro- and Nanochannels With Joule HeatingJournal of Heat Transfer, 2008
- An analytical solution for thermally fully developed combined pressure – electroosmotically driven flow in microchannelsInternational Journal of Heat and Mass Transfer, 2007
- Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed pressure gradientsInternational Journal of Heat and Mass Transfer, 2006
- Electro-osmotic flow in two-dimensional charged micro- and nanochannelsJournal of Fluid Mechanics, 2005
- Stokes’ first problem for an Oldroyd-B fluid in a porous half spacePhysics of Fluids, 2005
- Numerical analysis of the thermal effect on electroosmotic flow and electrokinetic mass transport in microchannelsAnalytica Chimica Acta, 2004
- Theoretical and experimental study of MHD (magnetohydrodynamic) micropumpSensors and Actuators A: Physical, 2000