advection-diffusion equation and its related analytical solutions have gained wide applications in different areas. compared with numerical solutions, the analytical solutions benefit from some advantages. as such, many analytical solutions have been presented for the advection-diffusion equation. the difference between these solutions is mainly in the type of boundary conditions, e.g. time pat...

Electroosmotic flow that involves one fluid displacing another fluid is commonly encountered in various microfludic applications and experiments, for example, current monitoring technique to determine zeta potential of microchannel. There is experimentally observed anomaly in such flow, namely, the displacement time is flow direction dependent, i.e., it depends if it is a high concentration flu...

For (coupled systems of) partial differential equations for which nullcontrol is possible in arbitrarily short time, the typical blowup rate for the control cost is exponential in 1/T . It is shown how to derive this rate for a variety of systems, including the thermoelastic system with control restricted to a small patch in the domain and to a single component (thermal, displacement, or veloci...

This paper investigates the axial unsteady flow of a generalized Burgers’ fluid with fractional constitutive equation in a circular micro-tube, in presence of a time-dependent pressure gradient and an electric field parallel to flow direction and a magnetic field perpendicular on the flow direction. The mathematical model used in this work is based on a time-nonlocal constitutive equation for s...

Given the velocity field and the values of a field variable f at a large number of discrete points in a bounded 2-dimensional domain, an algorithm has been developed to compute the streamline that passes through a desired point P in the domain, and the time histories of f at the material particle starting from the instant it occupied the point P. Time histories of the effective stress, second i...

Theoretical, P, S V, and SH displacement potentials and displacements for a double couple or point shear dislocation source and for a 'mixedquadrupole' source at any arbitrary orientation in an isotropic homogeneous elastic space are expressed as multiple integral and derivative operations on the source history in the time domain and their algebraic equivalent in the frequency domain. These sou...

Though implicit constitutive relations have been in place for a long time, wherein the stress, the strain (or the symmetric part of the velocity gradient), and their time derivatives have been used to describe the response of viscoelastic and inelastic bodies, it is only recently purely algebraic relationships between the stress and the displacement gradient (or the velocity gradient) have been...

the purpose of this research is to numerically investigate the interaction of pulsatile flow of blood with an axisymmetric artery in various percentages of stenosis. the carreau non-newtonian model and the generalized maxwell rheological model were used to model the blood fluid and the viscoelastic wall of arterial, respectively. the innovation of the present research is modeling of viscoelasti...