Dalia Sabina Cimpean

On the stability of the linear differential equation of higher order with constant coefficients

Abstract We obtain a result on stability of the linear differential equation of higher order with constant coefficients in Aoki–Rassias sense. As a consequence we obtain the Hyers–Ulam stability of the above mentioned equation. A connection with dynamical sytems perturbation is established.

Hyers―Ulam stability of Euler's equation

Abstract We prove that Euler’s equation x 1 ∂ u ∂ x 1 + x 2 ∂ u ∂ x 2 + ⋯ + x n ∂ u ∂ x n = α u , characterising homogeneous functions, is stable in Hyers–Ulam sense if and only if α ∈ R ∖ { 0 } .

Natural convection in a partially heated wavy cavity filled with a nanofluid using Buongiorno’s nanofluid model

Purpose The main purpose of this numerical work is to provide a solution for natural convection in a partially heated wavy cavity filled with a nanofluid using Buongiorno’s nanofluid model. Design/methodology/approach The domain of interest is a two-dimensional cavity bounded by an isothermal left wavy wall, adiabatic horizontal flat walls and right flat wall with a partial isothermal zone. In order to study the behaviour of the nanofluid, a two-phase Buongiorno’s mathematical model with the effects of the Brownian motion and thermophoresis is used. The governing dimensionless partial differential equations with corresponding boundary conditions were numerically solved by the finite difference method of the second order accuracy using the algebraic transformation of the physical wavy cavity to computational rectangular domain. The study has been conducted at the following values of the governing parameters: Ra = 104–106, Le = 10, Pr = 6.26, Nr = 0.1, Nb = 0.1, Nt = 0.1, A = 1,  = 1–3, b = 0.2, hhs/L = 0....

The Importance of Nanoparticles Addition in a Base Fluid Flow through a Porous Medium

The present study is focused on the mixed convection fluid flow through a porous medium, when a different amount of nanoparticles is added in the base fluid. The nanofluid saturates the porous matrix and different situations of the flow between two walls are presented and discussed. Alternatively mathematical models are presented and discussed. A solution of a system which contains the momentum, Darcy and energy equations, together with the boundary conditions involved, is given. The behavior of different nanofluids, such that Au-water, Ag-water and Fe-water is graphically illustrated and compared with the previous results.The research target is to observe the substantial increase of the thermophysical fluid properties, when the porous medium issaturated by a nanofluid instead of a classical Newtonian fluid.