Jacob A. Gbadeyan

The thermal analysis in a cylindrical pipe with surface cooling and possible heat loss

ABSTRACT This present study investigates the steady state of exothermic chemical reaction in a cylindrical pipe, taking into consideration the possible heat loss to the ambient due to Newtons law of cooling. The energy equation with generalized Arrhenius chemical kinetics is solved via Modified Adomian Decomposition Method combined with Padé approximants to extract numerical approximations of the critical explosion of Frank–Kamenetskii parameter () and the dimensionless maximum temperature (). The present parametric examination of the effects of Biot number (), heat loss parameter (), activation energy parameter () and the exponent of the generalized Arrhenius kinetic on the and provide quantitative properties for the sensitized reaction kinetics.

Natural Frequencies of an Euler-Bernoulli Beam with Special Attention to the Higher Modes via Variational Iteration Method

In this chapter, natural frequencies of an Euler-Bernoulli prismatic beam on different supports are analyzed. The variational iteration method (VIM) is employed to compute the said natural frequencies especially for the higher modes of vibration. Some numerical examples are presented with the view to demonstrating excellent agreement between the results obtained using VIM and other methods.

Influence of a Moving Mass on the Dynamic Behaviour of Viscoelastically Connected Prismatic Double-Rayleigh Beam System Having Arbitrary End Supports

This paper deals with the lateral vibration of a finite double-Rayleigh beam system having arbitrary classical end conditions and traversed by a concentrated moving mass. The system is made up of two identical parallel uniform Rayleigh beams which are continuously joined together by a viscoelastic Winkler type layer. Of particular interest, however, is the effect of the mass of the moving load on the dynamic response of the system. To this end, a solution technique based on the generalized finite integral transform, modified Struble’s method, and differential transform method (DTM) is developed. Numerical examples are given for the purpose of demonstrating the simplicity and efficiency of the technique. The dynamic responses of the system are presented graphically and found to be in good agreement with those previously obtained in the literature for the case of a moving force. The conditions under which the system reaches a state of resonance and the corresponding critical speeds were established. The effects of variations of the ratio of the mass of the moving load to the mass of the beam on the dynamic response are presented. The effects of other parameters on the dynamic response of the system are also examined.