Effect of Couple Stress Fluid in an Irregular Couette Flow Channel: An Analytical Approach

The work embodied in this paper presents the combined effects of Soret, chemical reaction, and Dufour on Couette flow in an irregular channel for dusty viscoelastic couple stress fluid. The behavior of the boundary layer is studied with the help of Brinkman-Forchheimer's extended Darcy model as a momentum equation for the unsteady, incompressible dusty viscoelastic fluid. The heat transfers are considered due to the radiation absorption parameter and Dufour effect, the mass transfer influenced by the chemical reaction, and the Soret effect. The boundary conditions of the problem and leading equations of the physical problem are solved by a similarity transformation, and the consequent ordinary linear differential equations are solved by the perturbation method. The obtained results are shown graphically. The computational results show a good agreement between our values and a particular case of the earlier work.

Applications of Elzaki Transform to Electrical Circuit Problems

The aim of this paper is to solve the ordinary linear differential equations in electrical circuit problems with initial conditions by using a new kind of transform named as Elzaki transform.

New Symmetries of Black-Scholes Equation

Lie Point symmetries and Euler’s formula for solving second order ordinary linear differential equations are used to determine symmetries for the one-dimensional Black- Scholes equation. One symmetry is utilized to determine an invariant solutions

ELASTIC BENDING OF A THREE-LAYER CIRCULAR PLATE WITH STEP-VARIABLE THICKNESS

The bending of a three-layer elastic circular plate with step-variable thickness is considered. To describe kinematics of asymmetrical in thickness core pack, the broken line hypotheses are accepted. In thin bearing layers, Kirchhoff’s hypotheses are valid. In a relatively thick filler incompressible in thickness, Timoshenko’s hypothesis on the straightness and incompressibility of the deformed normal is fulfilled. The formulation of the corresponding boundary value problem is presented. Equilibrium equations are obtained by the variational Lagrange method. The solution of the boundary value problem is reduced to finding three required functions in each section, deflection, shear and radial displacement of the median plane of the filler. An inhomogeneous system of ordinary linear differential equations is obtained for these functions. The boundary conditions correspond to rigid pinching of the plate contour. A parametric analysis of the obtained solution is carried out.

NON-AXISYMMETRIC DEFORMATION OF A CIRCULAR THREE-LAYER PLATE IN ITS OWN PLANE

A statement is given for the boundary value problem of non-axisymmetric deformation of an elastic threelayer circular plate in its own plane. The plate contour is pinched. Physical equations of state in the plate layers are described using the linear theory of elasticity, taking into account temperature influence on the elastic characteristics of materials. Equilibrium equations are obtained by the Lagrange variational method. Boundary conditions on the plate contour are formulated. The solution of the boundary value problem is reduced to finding the radial and tangential displacements in the layers of the plate. These displacements satisfy an inhomogeneous system of ordinary linear differential equations. To solve it, the method of decomposition into trigonometric Fourier series is applied. After substituting the series into the original system of equilibrium equations and performing the corresponding transformations, a system of ordinary linear differential equations is obtained to determine the four radial functions in each term of the series. The analytical solution is written out in the final form in the case of cosine radial and sinusoidal circumferential loads that depend linearly on the radial coordinate. The load is applied in the middle plane of the filler. Numerical approbation of the solution is carried out. The dependence of radial and tangential displacements on polar coordinates and temperature is investigated. Graphs of changes in displacements along the radius of the plate for different values of the angular coordinate are given. The weak dependence of displacements on temperature is illustrated when the plate contour is fixed.

Determination of Number of Infected Cells and Concentration of Viral Particles in Plasma during HIV-1 Infections Using Shehu Transformation

In this paper, the authors determine the number of infected cells and concentration of infected (viral) particles in plasma during HIV-1 (human immunodeficiency virus type one) infections using Shehu transformation. For this, the authors first defined some useful properties of Shehu transformation with proof and then applied Shehu transformation on the mathematical representation of the HIV-1 infection model. The mathematical model of HIV-1 infections contains a system of two simultaneous ordinary linear differential equations with initial conditions. Results depict that Shehu transformation is very effective integral transformation for determining the number of infected cells and concentration of viral particles in plasma during HIV-1 infections.

MHD Heat Transfer in Two-Layered Flow of Conducting Fluids through a Channel Bounded by Two Parallel Porous Plates in a Rotating System

The paper aims to analyze the heat transfer aspects of a two-layered fluid flow in a horizontal channel under the action of an applied magnetic and electric fields, when the whole system is rotated about an axis perpendicular to the flow. The flow is driven by a common constant pressure gradient in the channel bounded by two parallel porous insulating plates, one being stationary and the other one oscillatory. The fluids in the two regions are considered electrically conducting, and are assumed to be incompressible with variable properties, namely, different densities, viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding plates are maintained at constant and equal temperature. The governing partial differential equations are then reduced to the ordinary linear differential equations by using a two-term series. The temperature distributions in both fluid regions of the channel are derived analytically. The results are presented graphically to discuss the effect on the heat transfer characteristics and their dependence on the governing parameters, i.e., the Hartmann number, Taylor number, porous parameter, and ratios of the viscosities, heights, electrical and thermal conductivities. It is observed that, as the Coriolis forces become stronger, i.e., as the Taylor number increases, the temperature decreases in the two fluid regions. It is also seen that an increase in porous parameter diminishes the temperature distribution in both the regions.