Numerical simulations for heat transfer in peristalsis of Bingham fluid utilizing partial slip conditions

Abstract

The buoyancy-assisted peristaltic motion of viscoplastic fluid in a vertical channel is revisited by accounting partial slip effect at the channel boundaries. Accompanying heat transfer problems due to fluid friction is addressed through the temperature jump assumption. The governing system formed under lubrication approximation is coupled owing to the existence of buoyant force. The system contains a parameter $Bn$, measuring the fluid yield stress. Moreover, in contrast to the no-slip case, the boundary conditions are Robbin-type conditions and nonlinear in the axial velocity component. An easy-to-use yet reliable package NDSolve of the software MATHEMATICA is utilized to solve the problem for broad ranges of Bingham number $Bn$ and slip coefficients. Plots of stream function, velocity, and temperature are generated, which clearly depict that the yield stress combined with partial slip assumption considerably affects the flow phenomena. To illustrate heat transfer rates, the expression of heat transfer rate is analyzed across the channel walls under different controlling parameters.

KEYWORDS:

• Viscoplastic fluid
• peristalsis
• buoyant force
• frictional heating
• yield stress
• numerical simulations

Disclosure statement

No potential conflict of interest was reported by the author(s).