The effect of diffusion on two-dimensional problem of generalized thermoelasticity with Green–Naghdi theory

The present paper is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with generalized thermoelastic diffusion. The formulation is applied to the generalized thermoelasticity based on the Green and Naghdi (GN) theory under the effect of diffusion. The analytical expressions for displacement components, stresses, temperature field, concentration and chemical potential are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a copper-like material and depicted graphically. Effect of presence of diffusion is analyzed theoretically and numerically. Comparisons are made with the results predicted by the type II and type III in the presence and absence of diffusion.     

Hydroxyethyl Cellulose. I. Variables Affecting the Hydroxyethylation Reaction

A few studies have been made on the mechanism of hydroxyethylation of cellulose; however, contradictory results were obtained. The studies in this work reveal that the use of a low aqueous liquor ratio leads to high percentage of ethoxyl groups per glucose anhydride. There is a maximum depending on the time, sodium hydroxide concentration, ethylene oxide-to-cellulose ratio, and the use of diluent. The explanation of the effects of these variables on the hydroxyethylation reactions is summarized as follows: (a) The reaction is diffusion controlled. (b) The increase of the number of OH groups as a result of the increase of sodium hydroxide concentration and liquor ratio leads to an increase in the rate of the hydroxyethylation reaction, but only up to a limit. (c) The use of tertiary butanol as a diluent increases the ethoxyl percent. (d) The most suitable concentrations of sodium hydroxide, which lead to the highest ethoxyl percent, are 5% and 14.5%. The manner of adding ethylene oxide was also studied. The results indicate that the addition of ethylene oxide in one portion to contact with the alkali cellulose in the presence of tertiary butanol and with continuous heating leads to the highest ethoxyl percent. The activation energies of the reaction are higher when using 5% sodium hydroxide concentration than those when using 14.5%; i.e., the energy required for the collision of molecules to undergo reaction is lower in the latter than in the former. Therefore, the use of 14.5% sodium hydroxide concentration is preferable.     

Two-temperature problem of a fiber-reinforced thermoelastic medium with a Mode-I crack under Green–Naghdi theory

A general model of equations of Green–Naghdi theory of type (II and III) with two-temperature are applied to study the influence of reinforcement on total deformation for an isotropic infinite space weakened by a finite linear opening Mode-I crack. The crack is subjected to prescribed temperature and stress. Normal mode analysis in used to obtain the exact expressions for the field variables. The variations of the considered variables with horizontal distance are illustrated graphically. Comparisons are made with the results in two types with and without two -temperatures. A comparison also is made between the two types for different depths.