Effects of relaxation time on start-up time for starting flow of Maxwell fluid in a pipe

Abstract

Although the analytical solution of the starting flow of Maxwell fluid in a pipe has been derived for a long time, the effect of relaxation time λ on start-up time t s of this flow is still not well understood. Especially, there exist a series of jumps on the t s -λ curve. In this paper we introduce a normalized mechanical energy by mode decomposition and mathematical analogy to describe the start-up process. An improved definition of start-up time is presented based on the normalized mechanical energy. It is proved that the t s -λ curve contains a series of jumps if λ is larger than a critical value. The exact positions of the jumps are determined and the physical reason of the jumps is discussed.

The accuracy analysis on control factors of hot bitumen flow

“…The solution of fractional derivation is very difficult. According to ZHEN Li's study [6], the formation temperature gradient can be predicted by means of Non-Newtonian mathematic model. The paper presents a simplified model which can solve the Non-Newtonian flowing equation.…”