Abstract
In this article, free convection flow of an Oldroyd-B fluid (OBF) through a vertical rectangular channel in the presence of heat generation or absorption subject to generalized boundary conditions is studied. The fractionalized mathematical model is established by Caputo time-fractional derivative through mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s law). Closed form solutions for the velocity and temperature profiles are obtained via Laplace coupled with sine-Fourier transforms and have been embedded with regards to the special functions, namely, the generalized G-functions of Lorenzo and Hartley. Solutions of the known results from recently published work (Nehad et al. Chin. J. Phy., 65, (2020) 367–376) are recovered as limiting cases. Finally, the effects of fractional and various physical parameters are graphically underlined. Furthermore, a comparison between Oldroyd-B, Maxwell and viscous fluids (fractional and ordinary) is depicted. It is found that, for short time, ordinary fluids have greater velocity as compared to the fractional fluids.
Highlights
Fluids are classified in two categories with respect to the relation of shear stress and rate of deformation called Newtonian and non-Newtonian fluids
Oldroyd-B fluid (OBF) [1] is an exceptional non-Newtonian fluids and its transport conduct cannot be appropriately depicted by the usual relation between the shear rate and shear stress in a straightforward shear flow
Shao et al [15] found the semianalytical solutions for hydromagnetic free-convection flow of viscous fluid between vertical parallel plates with damped thermal and mass fluxes
Summary
Fluids are classified in two categories with respect to the relation of shear stress and rate of deformation called Newtonian and non-Newtonian fluids. Shao et al [15] found the semianalytical solutions for hydromagnetic free-convection flow of viscous fluid between vertical parallel plates with damped thermal and mass fluxes. Seth et al [17] have studied the effect of Hall current on MHD natural convection heat and mass transfer flow of rotating fluid past a vertical plate with ramped wall temperature. Kamran et al [45] find the exact solutions for the unsteady rotational flow of an Oldroyd-B fluid with fractional derivative through an infinite circular cylinder by means of the finite Hankel and Laplace transforms. We acquire the closed form solutions of the generalized convection flows of OBF between two parallel plates under general boundary conditions by utilizing the Laplace transform coupled with the finite sine-Fourier transform. The limiting cases of the current outcomes compare to the solutions for fractional Maxwell, ordinary Maxwell, Oldroyd-B, and Newtonian fluids
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