Abstract
In this work, influence of hybrid nanofluids (Cu and mathrm{Al}_{2}mathrm{O}_{3}) on MHD Maxwell fluid due to pressure gradient are discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions are converted into dimensionless form. Fractional model for Maxwell fluid is established by Caputo time fractional differential operator. The dimensionless expression for concentration, temperature and velocity are found using Laplace transform. As a result, it is found that fluid properties show dual behavior for small and large time and by increasing volumetric fraction temperature increases and velocity decreases respectively. Further, we compared the Maxwell, Casson and Newtonian fluids and found that Newtonian fluid has greater velocity due to less viscosity. Draw the graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters.
Highlights
In this work, influence of hybrid nanofluids (Cu and Al2O3 ) on MHD Maxwell fluid due to pressure gradient are discussed
In industry and engineering many physical methods exist who have incomplete viscoelastic fluid, most common of these are molten plastics, synthetic propellants, exotic lubricants, suspension solutions, polymer solutions food stuffs, and so many other examples of viscoelastic fluid. These fluids have been modeled in a number of different behaviors with their constitutive equations varying greatly in complexity, among which the viscoelastic Maxwell fluid model has been studied widely Fetecau and F etecau[1], Tan and M asuoka[2], Jamil et al.[3] and Abbasbandy et al.4. Christensen[5] give the Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected in series, which has been proposed to describe the behavior of viscoelastic fluids, and has some success in describing polymeric liquids, it being more amenable to analysis and more importantly experimental
The fractional derivative models of the viscoelastic fluids are derived from classical equations, which are modified by replacing the time derivative of an integer order by precisely non-integer order integrals or derivatives
Summary
Let the unsteady flow of sodium alginate based hybrid nanofluid (Cu and Al2O3 ) in a vertical channel. Let the distance d between two parallel plates. The x-axis is taken along one of the plate which is fixed in the vertically upward direction and y-axis is normal to the plate.
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