Tariq Darabseh

Analytical Solution for Transient Laminar Fully Developed Free Convection in Open-Ended Vertical Concentric Porous Annuli

Free and mixed convection problems in a vertical porous annulus have been extensively studied. These studies use numerical or experimental techniques to investigate the thermal behavior of the mental porous annulus. Parang and Keyhani have obtained closed-form solutions for the special case where the inner and outer walls are heated by uniform but unequal heat fluxes. The lack of analytical solutions for transient fully developed laminar natural convection in vertical concentric porous annuli, with different fundamental combinations of isothermal and isoflux thermal boundary conditions, motivated the present work. The purpose of this paper is to present, in closed forms, transient fully developed free convection solutions, corresponding to four fundamental thermal boundary conditions in vertical concentric annuli. The solutions obtained, which take both Darcian and Brinkman effects into consideration, may be used as a preliminary check for numerical solutions of more practical situations. 4 refs.

Transient Thermal Stresses in an Orthotropic Cylinder under the Hyperbolic Heat Conduction Model

An important consideration in design involving high temperature variation is the determination of the thermal stresses developed. The numerical solution for thermoelastic transient response of orthotropic cylinder subjected to a constant temperature at the surface is presented. The thermoelastic equations with one relaxation time developed by Lord and Shulman with uncoupled thermoelasticity assumption are used in the present work. The hyperbolic heat conduction model is used for the prediction of the temperature history. Thermally induced displacement and stresses are determined. A numerical method based on implicit finite difference scheme is used to calculate the temperature, displacement, and stress distributions within the cylinder. Numerical examples for orthotropic, transverse isotropic, and isotropic cylinders were carried out for the stresses. Furthermore, the results of the numerical solution and the exact solution at the steady state condition are compared.

Dynamic stability of viscoelastic columns loaded by a follower force

Abstract This paper analyses the motion of a linear viscoelastic column using the dynamic approach. The viscoelastic material is mathematically represented by the four-element model. Using this model as a recursion equation, the elastic, one-, two-, three- and four-element models are solved and their results compared. The stability analyses of these systems are investigated by studying the eigenvalues of the characteristic equations for the solution to the boundary value problems. The stability analyses determined the smallest value of the follower load beyond which the system, under a suitable disturbance, will perform oscillations with increasing amplitudes. The dynamic instability is found to occur in the form of flutter. The effect of damping on the critical follower load is also examined. Three damping parameters are considered that affect the results. They are the damping coefficients related to a Maxwell unit, to a Kelvin unit and one appropriate to a combination of the two. The destabilization effects of viscosity are discussed.

Thermoelastic analysis of 2D-FGM hollow circular cylinder with finite length by finite element method

This paper studies the thermoelastic analysis of thick hollow cylinder made of two-dimensional functionally graded material FGM by finite element method. The FGM cylinder with finite length is simply supported and subjected to thermal and mechanical loading. The mechanical and thermal properties are graded in the radial and axial directions. The rule of mixtures and a power law distribution in terms of the volume fractions of the constituents are used to model the material properties. Temperature dependency of the material properties is taken into consideration. The temperature, displacement and stress distributions within the cylinder are found by finite element method. Variation of two-dimensional temperature and components of stresses through the cylinder are analysed. The effect of power index parameters on thermal stresses, displacement and temperature distributions are investigated.