Thermal transport characteristics of fluid-particle suspension in a vertical uniform tube: A computational study on Rabinowitsch fluid with uniform heat source

Abstract

Problem statement

The thermal transport of fluid-particle suspension in Rabinowitsch fluid is discussed theoretically in a vertical uniform tube under the consideration of a uniform heat source.

Methodology

The fluid and particle phase models are used to develop the mathematical model in the form of partial differential equations which are solved through the symbolic software MATHEMATICA version 12.0 and present the exact solution of temperature distribution, velocity of fluid and particle phases, wall shear stress, pressure gradient, pressure rise, and stream function, etc.

Computational results and findings

The volume fraction density of the particles slows down the motion of the fluid particles. The velocity of Newtonian fluid is maximum as compared to pseudo-plastic and Dilatant fluids. The fluid phase velocity is superior to particle phase velocity distribution for all pertinent parameters of the analysis. The pressure rise increases in the case of Newtonian and pseudo plastic fluid and decreases in Dilatant fluid. The trapping phenomena are strongly associated with the volume fraction density of the particle. The shear stress shows a decreasing trend against the volume fraction density of the particles, Grashoff number, and heat source parameter.

Special case

The current fluid model (Rabinowitsch fluid) can be reduced in Newtonian, pseudo plastic, and Dilatant fluid for taking $\kappa \to 0,\kappa <0,$ and $\kappa >0,$ respectively.

Applications

The current analysis can be useful in biomedical engineering to observe the blood supply through the arteries, the removal of kidney stones, and also the passage of urine to the bladder from the ureter.

Originality

The present research is original and has not been published before.

Keywords:

• Exact solution
• fluid-particle suspension
• Rabinowitsch fluid
• uniform heat source
• uniform tube

Disclosure statement

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