where β = β(β−1)−1, M ∈ N∪{∞}, and l0, l1, . . . is a uniquely determined (finite or infinite) sequence of non-negative integers (cf. [2]). Analogously to other types of expansions we may ask for bases β such that the set of numbers with periodic or even finite representation is as large as possible. In particular, we say that Tβ satisfies the periodicity property (P) if the orbit (T β (x))n≥1 ...

In this study, we investigated multilayer coatings fully developed with steady Newtonian and non-Newtonian fluids through parallel inclined plates. The channel was rotating about the y-axis angular velocity ?. contained three regions; Region 1 3 were filled fluid, while 2 had Jeffrey fluid a porous medium. governing equations formed by using Navier stokes energy equations. coupled non-linear du...

In this paper, some time-dependent flows of a non-Newtonian fluid between two side walls over a plane wall are investigated. The following three problems have been studied: (i) flow due to an oscillating plate, (ii) flow due to an accelerating plate, and (iii) flow due to applied constant stress. The explicit expressions for the velocity field are determined by using the integral transforms. Th...

In this article, we have considered incompressible Jeffrey fluids and studied the effects of variable viscosity in the form of a well-known Reynold’s model of viscosity in an asymmetric channel. The fluid viscosity is assumed to vary as an exponential function of temperature. The governing fundamental equations are approximated under the assumption of long wavelength and low Reynold number. The...

Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, free magnetohydrodynamic Jeffrey fluid with heat mass transfer infinite vertical plate examined. Mathematical modeling performed using Fourier’s Fick’s laws, momentu...