GENERALIZED COUPLED THERMOELASTICITY OF DISKS BASED ON THE LORD–SHULMAN MODEL

A one-dimensional generalized thermoelasticity model of a disk based on the Lord–Shulman theory is presented. The dynamic thermoelastic response of the disk under axisymmetric thermal shock loading is studied. The effects of the relaxation time and coupling coefficient are studied. The Laplace transform method is used to transform the coupled governing equations into the space domain, where the Galerkin finite element method is employed to solve the resulting equations in the transformed domain. The dimensionless temperature, displacement, and stresses in the transformed domain are inverted to obtain the actual physical quantities using the numerical inversion of the Laplace transform method.     

PROPAGATION OF GENERALIZED VISCOTHERMOELASTIC RAYLEIGH–LAMB WAVES IN HOMOGENEOUS ISOTROPIC PLATES

The present paper is aimed at studying the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The coupled dynamic thermoelasticity and generalized theories of thermoelasticity, namely, Lord and Shulman's, Green and Lindsay's, and Green and Nagdhi's are employed to understand the thermomechanical coupling and thermal and mechanical relaxation effects. Secular equations for the plate in closed from and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. In the absence of mechanical relaxations (viscous effect), the results for generalized and coupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. In the absence of thermomechanical coupling, the analysis for a viscoelastic plate can be deduced from the present one. The various forms and regions of Rayleigh–Lamb-type secular equation have been obtained and discussed in addition to Lame modes, decoupled shear horizontal (SH) modes, and thin-plate results. At short-wavelength limits, the secular equations for symmetric and skew-symmetric waves in a stress-free insulated and stress-free isothermal plate reduce to the Rayleigh surface wave frequency equation. The amplitudes of temperature and displacement components during symmetric and skew-symmetric motion of the plate have been computed and discussed. Finally, the numerical solution is carried out for copper material. The dispersion curves, and amplitudes of temperature change and displacements for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results.     

HEAT TRANSFER OF SOLID–LIQUID PHASE-CHANGE MATERIAL SUSPENSIONS IN CIRCULAR PIPES: EFFECTS OF WALL CONDUCTION

This article considers the problem of conjugate heat transfer in circular pipes with finite heated length to examine the effects of wall conduction on the heat transfer characteristics of solid–liquid phase-change material suspension flow. A mixture continuum approach is adopted in the formulation of the energy equation, with an approximate enthalpy model describing the phase-change process in the phase-change material particles. From numerical simulations via the finite-volume approach, it was found that the conduction heat transfer propagating along the pipe wall results in significant preheating of the suspension flow in the nondirectly heated region upstream of the heated section, where melting of the particles may occur and therefore the contribution of the latent heat transfer to convection heat dissipation over the heated section is markedly attenuated. Contributions of the sensible and latent heat transfer to the total heat transfer rate of the suspension flow over the heated section were delineated quantitatively for various sets of the relevant dimensionless parameters, including the particle volumetric concentration, the modified Stefan number, the Peclet number of suspending fluid, the wall thickness ratio, and the wall-to-fluid thermal conductivity ratio.     

THERMAL-STRESS PROBLEMS IN INDUSTRY. 3: TEMPERATURE DEPENDENCY OF ELASTIC MODULI FOR SEVERAL METALS AT TEMPERATURES FROM -196 TO 1000° C

The temperature dependency of the dynamic moduli of elasticity of steel and aluminum and copper alloys was investigated experimentally by an ultrasonic-wave method, in the temperature range from —196 to 1000°C. The results are compared with those obtained by the resonant-frequency method and are represented as empirical formulas. Useful data for commercial alloys are given in tables, by chemical composition.     

COMPUTATION OF TURBULENT NATURAL CONVECTION IN A RECTANGULAR CAVITY WITH THE k–ϵ– –f MODEL

A hybrid numerical method involving the Laplace transform technique and finite-difference method in conjunction with the least-squares method and actual experimental temperature data inside the test material is proposed to estimate the unknown surface conditions of inverse heat conduction problems with the temperature-dependent thermal conductivity and heat capacity. The nonlinear terms in the differential equations are linearized using the Taylor series approximation. In this study, the functional form of the surface conditions is unknown a priori and is assumed to be a function of time before performing the inverse calculation. In addition, the whole time domain is divided into several analysis subtime intervals and then the unknown estimates on each subtime interval can be predicted. In order to show the accuracy and validity of the present inverse scheme, a comparison among the present estimates, direct solution, and actual experimental temperature data is made. The effects of the measurement errors, initial guesses, and measurement location on the estimated results are also investigated. The results show that good estimation of the surface conditions can be obtained from the present inverse scheme in conjunction with knowledge of temperature recordings inside the test material.