Investigation of non-Newtonian fluid flow over a linearly moving sheet at a transient state

Abstract

Laminar flow of a non-Newtonian fluid over a moving flat solid boundary has been investigated. The power-law model was used for describing the non-Newtonian behavior of the fluid. The fluid was stationary at free stream and the motion of the solid boundary imposed the fluid to flow. Velocity of the solid boundary varied linearly along its length which is called stretching sheet. Also, the velocity of this boundary increased in time as a hyperbolic function. A new similarity variable for this type of transient motion of the stretching sheet based on the non-Newtonian behavior of the fluid has been proposed. This similarity variable transforms three independent variable (t,x,y) into an independent variable (η). By the use of this transformation, the governing partial differential equations of mass and momentum conservations were transformed into a single non-linear ordinary differential equation. Also, a numerical algorithm based on the finite difference method was proposed to solve the obtained non-linear differential equation. The proposed similarity variable reduced the complexity of the flow simulation and it represented all the three independent variables of the physical phenomenon at the same time. To see the results of the similarity transformation and the numeric algorithm, effects of the fluid and flow characteristics on the hydrodynamic behavior of the flow have been investigated.

Keywords

• stretching sheet
• un-steady flow
• non-newtonian fluid
• similarity transformation
• numerical algorithm