Spectral Stability Conditions for an Explicit Three-Level Finite-Difference Scheme for a Multidimensional Transport Equation with Perturbations

We study difference schemes associated with a simplified linearized multidimensional hyperbolic quasi-gasdynamic system of differential equations. It is shown that an explicit two-level vector difference scheme with flux relaxation for a second-order hyperbolic equation with variable coefficients that is a perturbation of the transport equation with a parameter multiplying the highest derivatives can be reduced to an explicit three-level difference scheme. In the case of constant coefficients, the spectral condition for the time-uniform stability of this explicit three-level difference scheme is analyzed, and both sufficient and necessary conditions for this condition to hold are derived, in particular, in the form of Courant type conditions on the ratio of temporal and spatial steps.

Implementation of improved Fourier's law and Fick's law for rotational flow of nanofluid over an exponentially stretching sheet

PurposeThe purpose of the current article is to explore the rotational behavior on nanofluid flow over an exponentially stretching surface. Heat and mass flux are formulated upon Cattaneo–Christov theory.Design/methodology/approachEffect of thermophoretic, Brownian motion and thermally convective conditions is further retained. Novel boundary layer approximations are applied to transform the governing equations of continuity, momentum, energy and nanoparticle volume fraction. Convergent series solutions are obtained to manage the rotating flow with the aid of homotopy analysis method (HAM).FindingsDepending on the several dimensionless parameters including the local rotation parameter the Prandtl number Pr, the thermophoresis parameter, the Brownian motion parameter, the Lewis number Le, Biot number Bi, Deborah number in terms of heat flux relaxation parameter and Deborah number in terms of mass flux relaxation parameter with the dimensionless physical quantities are deliberated through graphs. Present results are also likened with the foregoing results in significance.Originality/valueNo such assumptions have been made for the development of analytical solution so far.

An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation

This article considers an unsteady elastic diffusion model of Euler–Bernoulli beam oscillations in the presence of diffusion flux relaxation. We used the model of coupled elastic diffusion for a homogeneous orthotropic multicomponent continuum to formulate the problem. A model of unsteady bending for the elastic diffusive Euler–Bernoulli beam was obtained using Hamilton’s variational principle. The Laplace transform on time and the Fourier series expansion by the spatial coordinate were used to solve the obtained problem.