A review of SIF evaluation and modelling of singularities in BEM

 Various boundary element method (BEM) based approaches to solve crack problems are discussed. The displacement method, J-integral method and the modified crack closure integral (MCCI) method for the evaluation of the stress intensity factors (SIFs) are reviewed. Effects of partial and total modelling of singularities on the accuracy of the results have been presented. Elements capable of partial and total modelling of the wellknown square root singularities, variable order singularities, neighbouring variable order singularities, etc., are also reviewed. Case studies are included to illustrate the effectiveness of the various methods of calculation of the SIFs and the performance of the special elements. Received 11 September 1999     

Stability of conducting viscous film flowing down an inclined plane with linear temperature variation in the presence of a uniform normal electric field

Weakly nonlinear stability analysis of a thin liquid film falling down a heated inclined plane with linear temperature variation in the presence of a uniform normal electric field has been investigated within the finite amplitude regime. A generalized kinematic equation for the development of free surface is derived by using long wave expansion method. A normal mode approach and the method of multiple scales are used to investigate the linear and weakly nonlinear stability analysis of film flow, respectively. It is found that both Marangoni and electric Weber numbers have destabilizing effect on the film flow. The study reveals that both supercritical stability and subcritical instability are possible for this type of film flow. It is interesting to note that both the Marangoni and electric Weber numbers have qualitatively same influence on the stability characteristics but the effect of Marangoni number is much stronger compare to the electric Weber number. Scrutinizing the effect of Marangoni and electric Weber numbers on the amplitude and speed of waves it is found that, in the supercritical region amplitude and speed of the nonlinear waves increases with the increase in Marangoni and electric Weber numbers, while in the subcritical region the threshold amplitude decreases with the increase in Marangoni and electric Weber numbers. Finally, we obtain that spatially uniform solution is side-band stable in the supercritical region for our considered parameter range.     

Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface

Free convective boundary layer flow and heat transfer of a fluid with variable viscosity over a porous stretching vertical surface in presence of thermal radiation is considered. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. A third-order and a second-order coupled ordinary differential equations corresponding to the momentum and the energy equations are obtained. These equations are then solved numerically. It is found that the skin-friction decreases and heat transfer rate increases due to the suction parameter. Opposite nature is noticed in case of blowing. With the increase of temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity), the fluid velocity increases but the temperature decreases at a particular point of the sheet. Due to suction (injection) fluid velocity decreases (increases) at a particular point of the surface. Effects of increasing Prandtl number as well as radiation parameter on the velocity boundary layer is to suppress the velocity field and the temperature decreases with increasing value of Prandtl number. Due to increase in thermal radiation parameter, temperature at a point of the surface is found to decrease.     

Bimetallic catalyst for synthesizing quasi-aligned,well-graphitized multiwalled carbon nanotube bundles on a large scale by the catalytic chemical vapor deposition method

An effective method of growth by catalytic chemical vapor deposition (CCVD) to get a large-scale yield of carbon nanotubes is reported. In this method, acetylene is decomposed catalytically over well-dispersed metal particles (Co-Fe and Co-Ni) embedded in commercially available zeolite at a lower temperature (600-700 degrees C). The two binary-metal catalysts (Co-Fe and Co-Ni) used are compared by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Crucial reaction parameters, such as reaction time, temperature, and the effect of purity of gas to obtain optimum production of the nanotubes, both qualitatively and quantitatively, are also reported.