Numerical solution of heat transfer in micropolar fluid flow in a channel with porous walls

Using the basic equations of heat conducting micropolar fluid, heat transfer through a channel of porous walls has been studied. The temperature distribution is obtained for different values of suction parameter $\text{S}$, convective parameter $\text{E}$ and micropolar parameter $\text{R}$.     

The rectilinear oscillations of a spheroid in a micropolar fluid

The paper examines the oscillatory flow of incompressible micropolar fluid arising from the harmonic oscillation of a spheroid rectilinearly along its axis of symmetry under the assumption of small amplitude of oscillation. The velocity and microrotation are obtained and the drag experienced by the spheroid is determined. The drag parameters $\text{K}$ and $\text{K'}$ are numerically evaluated.     

Flow of micropolar fluid past a continuously moving plate

A similarity analysis of the flow and heat transfer past a continuously moving semi-infinite plate in a micropolar fluid is presented. The velocity, micro-rotation distribution and the temperature profiles are shown on graphs and the numerical values of the skin friction and the rate of heat transfer are entered in tables. The effects of $\text{K}$ (coupling parameter) and $\text{G}$ (micro-rotation parameter) are discussed.     

Uniqueness of compressible micropolar fluid flows

The paper examines the uniqueness of compressible micropolar fluid flows over an arbitrary region $\text{R(t)}$ with a smooth boundary $\text{?R(t)}$. It is shown that there is at most one solution of the flow equations and boundary conditions which corresponds to suitably assigned initial values of the density, velocity, microrotation and temperature fields. The analysis rests on the use of differential inequalities involving the time derivatives of certain energy integrals.     

Double diffusive flow of a hydromagnetic nanofluid in a rotating channel with Hall effect and viscous dissipation: Active and passive control of nanoparticles

The investigation of simultaneous effects of Hall current and viscous dissipation on three-dimensional magnetohydrodynamic nanofluid flow in a horizontal rotating channel with active and passive control of nanoparticles, is carried out. The lower sheet is considered stretching while the upper sheet is kept fixed. Mathematical model is developed using boundary layer and scale analysis approach. Similarity transformation technique is employed to translate the governing partial differential equations into ordinary differential equations. The bvp4c solver of MATLAB is employed to solve transformed equations. Computations for nanofluid velocity, nanofluid temperature distribution and distribution of nanoparticles along with skin friction co-efficient and Nusselt number, are carried out for a range of values of pertinent flow parameters. A comparative analysis of effect of $\text{CuO}$ and ${\text{Al}}_2{\text{O}}_3$ nanoparticles on velocity, temperature, nanoparticle distribution, skin friction coefficient and Nusselt number is carried out. Rate of heat transfer at the lower sheet is observed to be a decreasing function of magnetic field whereas this physical quantity is getting enhanced as the volume fraction of nanoparticles are increased.     

On wave propagation in a micropolar elastic cylinder

An asymptotic analysis of the free vibrations of a micropolar elastic cylinder is earned out postulating the displacements, the micro-rotations and the frequency as power series in the nondimensional $\text{? = 2π}\text{radius/(wave length)}$.     

The torsion of a microelastic half-space by a flat annular rigid stamp

The present paper seeks to solve the problem of an elastic half space under torsion by a flat annular rigid stamp in the linear micropolar elasticity. The problem is reduced to the solution of a system of four Fredholm integral equations of the second kind in four unknown functions. An iterative solution of these integral equations has been obtained for $\text{λ = a/b ? 1}$ for the case of simple rotation through a small angle $\text{ω}{}_0$ and the corresponding classical results have been obtained.     

The problem of a griffith crack in micropolar elasticity

In the linear theory of micropolar elasticity the problem of Griffith crack in a transverse field of constant uniaxial tension is studied. The problem is reduced to three Fredholm integral equations of the second kind. These equations, which have the same kernel, are solved numerically. The stress environment at the tips of the crack is found to depend on, apart from Poisson's ratio and a material length parameter τ, another parameter $\text{N}$ which characterises the coupling of the microstructure with the displacement field. $\text{N}$ does not occur in the analogous problem in couple stress theory. Classical results are recovered in the limits: (i) $\text{N}$ tends ot zero (τ fixed) and (ii) τ tends to zero ($\text{N}$ is of the same order of magnitude as τ or of lower order).     

Magneto-thermo-elastic plane waves in rotating media

A study is made of the propagation of plane harmonic waves in an infinite conducting thermo-elastic solid permeated by a primary uniform magnetic field when the entire elastic medium is rotating with a uniform angular velocity. A more general dispersion relation is obtained to determine the effects of rotation, relaxation time and the external magnetic field on the phase velocity of the waves. This result indicates that if the primary magnetic field has a transverse component, then the longitudinal and transverse components of the displacement field are linked together. For the case of low frequency (Gc ? 1 where κ is the ratio of the wave frequency to the characteristic frequency), the rotation and the thermal relaxation time are found to have no influence on the phase velocity, and the attenuation factor for both finite and infinite electrical conductivity. In the case of high frequency (κ ? 1), no effect of rotation on the phase speed is observed to the first order of ($\text{1}\text{κ}$), while the relaxation time affects both the phase velocity and the specific energy loss. However, the effects of rotation on the phase speed, the attenuation factor, and the specific energy loss are found only to the second order of ($\text{1}\text{κ}$) in the case of high frequency. Several limiting cases of interest are discussed.     

Study of non-self similar flows behind shock waves in a dusty gas

Non-self similar solutions for plane, cylindrical and spherical unsteady flows of dusty gas (mixture of gas and small solid particles) behind shock waves of arbitrary strength initiated by the instantaneous release of finite energy and propagating into a uniform medium at rest are investigated. Two methods based upon the assumptions, namely, (i) power law density and (ii) linear velocity, are employed to study the effects of the parameters characterising the initial volume fraction $\text{Z}{}_{\mathrm{o}}$, mass concentration of the solid particles $\text{K}{}_{\mathrm{p}}$ in the dusty gas and the ratio of the density of the solid particles to that of the initial density of the gas $\text{G}$ on shock trajectory and the flow field behind the shock. Comparative study of the results obtained by the two assumptions is also made. A simple formula is derived to study the effect of the solid particles on the shock strength in the strong shock regime.     

Fundamental solutions in micropolar elasticity

In this paper the general form of the fundamental solutions and fundamental matrices associated with the equations of the micropolar elastostatics as well as the integral representation by means of these matrices are determined. For the dynamic problem the time-periodic fundamental solutions and general fundamental solutions are determined. In this last case the explicit solution is given for $\text{ρ(γ + ?) = jμ}$.     

Reflection characteristics of torsional waves in a semi-infinite cylindrical rod connected to an elastic half-space—II

Using the Pochhammer-Chree equation and applying Laplace transformations with respect to time and numerical inverse Laplace transformations, reflection characteristics of torsional waves in a semi-infinite rod connected to an elastic half-space are analyzed under a condition where the incident stress pulse varies proportionally with the distance from the rod axis. Time histories of surface torsional stress and circumferential displacement, and cross-sectional torsional stress and circumferential displacement distributions of the semi-infinite rod at an arbitrary point are shown. When the shear modulus ratio $\text{G}{}_{\mathrm{R}}\text{/G}$ and the velocity ratio $\text{K}$ are small, i.e. The half-space is hard and the rod is soft, time histories of surface stress and displacement obtained from the Pochhammer-Chree equation coincide with those obtained from the elementary equation which is derived from the assumption that each cross-section of the rod undergoes a pure rotation about the rod axis. However, when $\text{G}{}_{\mathrm{r}}\text{/G}$ and $\text{K}$ are not small, the curves obtained from the Pochhamer-Chree equation differ from those obtained from the elementary equation, and the difference in stress increases as the observed point approaches the interface between the rod and the half-space.     

Existence of periodic solutions of the equations of incompressible microstretch fluid flow

The flow of incompressible microstretch fluid is governed by a system of differential equations involving the velocity vector $\text{q}$, the microprotation vector $\text{v}$ and the scalar $\text{v}$ representing the microstretch of the fluid element. Let $\text{R = R(t)}$ be a bounded domain in space and let the field ($\text{q}$, $\text{v}$, $\text{v}$) be prescribed at each point of the boundary $\text{?R(t)}$. If the domain $\text{R(t)}$ and the boundary data depend periodically on the time $\text{t}$, it is shown that under some assumptions on the initial distribution of the flow fields and the material constants of the fluid, there exists a unique, stable, periodic solution of the microstretch flow equations in $\text{R(t)}$, taking the prescribed values on the boundary $\text{?R(t)}$ (Theorem 2 of the paper). The proof rests on some relations describing the rate of decay of the energy functionals corresponding to the difference of two microstretch flows in the domain that have the same density and gyration parameters and are subject to the same boundary conditions.     

Semi-similar solution of an unsteady compressible three-dimensional stagnation point boundary layer flow with massive blowing

A semi-similar solution of an unsteady laminar compressible three-dimensional stagnation point boundary layer flow with massive blowing has been obtained when the free stream velocity varies arbitrarily with time. The resulting partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme with a quasi-linearization technique in the nodal point region and an implicit finite-difference scheme with a parametric differentiation technique in the saddle point region. The results have been obtained for two particular unsteady free stream velocity distributions: (i) an accelerating stream and (ii) a fluctuating stream. Results show that the skin-friction and heat-transfer parameters respond significantly to the time dependent arbitrary free stream velocity. Velocity and enthalpy profiles approach their free stream values faster as time increases. There is a reverse flow in the $\text{y-}\text{wise}$ velocity profile, and overshoot in the $\text{x-}\text{wise}$ velocity and enthalpy profiles in the saddle point region, which increase as injection and wall temperature increase. Location of the dividing streamline increases as injection increases, but as the wall temperature and time increase, it decreases.     

Dugdale crack closure analysis of fatigue cracks under constant amplitude loading

Fatigue fracture mechanics which means structural analysis including crack propagation and crack closure in conjunction with a local failure criterion provides detailed insight into mechanisms of cyclic loaded crack sheets. Using the Dugdale method and rigid-perfectly plastic strip material law the infinite sheet with colinear cracks was parametrically investigated in respect of: SSY limits, crack closure occurrence, formation of contact stresses and displacements, influences of material parameters, $\text{R-}\text{ratio}$ and maximum load on effective stress ratio. Rationales for the load ratio, mean load and maximum load dependence and the form of $\text{da/dN-}\text{curves}$ are given based on crack closure analysis.     

The general solutions of the doubly periodic cracks

The purpose of this paper is to use the basic theorem of Jacobi elliptic functions and residues to find the general solutions of the stress intensity factor2 of doubly periodic cracks subjected to concentrated forces $\text{P}$, $\text{T}$ and $\text{Q}$ on the surfaces of each crack. In this paper the general solutions are expressed in simply closed forms, and they can also be applied to solve practical problems of rectangular sheet with central crack.The general solutions in this paper may be used as a fundamental Green's function for finding other solutions of the doubly periodic cracks involving arbitrary surface forces. It is easily proved that all problems of the isolated crack and the singly periodic cracks loaded by arbitrary surface forces, are the special cases of the general solutions in this paper.     

Deceleration of a porous rotating disk in a viscous fluid

The flow due to a rotating disk decelerating with an angular velocity inversely proportional to time with either surface suction (or injection) which again varies with time is investigated. The unsteady Navier-Stokes equations are transformed to non-linear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using a globally convergent homotopy method. The flow depends on two non-dimensional parameters, namely an unsteadiness parameter $\text{S}$ and a suction (or injection) parameter $\text{A}$. Some interesting numerical results are presented graphically and discussed.     

Approximate Mode II velocity correction factors for 90° unidirectional fiber composites

A static Mode III isotropic/Mode II orthotropic analogy is developed for 90° highly orthotropic fiber composites. This static analogy is extended to the dynamic regime and the velocity correction factors for the dynamic energy release rate and the dynamic stress intensity factor are obtained for the Mode II case. The complete dynamic analogies are given. The approximate Mode II 90° velocity correction factors $\text{W}{}_{\mathrm{II(90°)}}$ and $\text{S}{}_{\mathrm{II((90°)}}$ are of the same general form as the approximate Mode I velocity correction factors, $\text{W}{}_{\mathrm{I(0°)}}$, $\text{W}{}_{\mathrm{I(90°)}}$, $\text{S}{}_{\mathrm{I(0°)}}$ and $\text{S}{}_{\mathrm{I(90°)}}$ Whereas the four Mode I velocity correction factors approach zero as the crack-tip velocity approaches the composite shear wave speed, $\text{w}{}_{\mathrm{II(90°)}}$ and $\text{s}{}_{\mathrm{II(90°)}}$ approach zero as the crack-tip velocity approaches the larger extensional wave speed.     

Investigation of the electroluminescence and electroabsorption of GaS single crystals

Electroluminescence and electroabsorption in GaS single crystals have been studied at 77°K. Four maxima at energies of 1675±2, 1992±2, 2194±2 meV have been observed. Three of them were caused by recombination through local levels in the forbidden, and the high-energy maximum 2684±2 meV correspondes to the energy of the indirect transition GG₄^? ? M₃⁺ (E_q = 2591±2meV) accompanied by the radiation of two phonons with an energy of $\text{h}\text{?}\text{ω ? 46.5±2}\text{meV}$. The frequency dependence of brightness waves has been studied. The appropriate exciton parameters of GaS have been caculated.