AUTHOR=Mahmood Rashid , Majeed Afraz Hussain , Tahir Muhammad , Saddique Imran , Hamadneh Nawaf N. , Khan Ilyas , Mehmood Asif 

TITLE=Statistical Analysis of Hydrodynamic Forces in Power-Law Fluid Flow in a Channel: Circular Versus Semi-Circular Cylinder

JOURNAL=Frontiers in Physics

VOLUME=10

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.830408

DOI=10.3389/fphy.2022.830408

ISSN=2296-424X

ABSTRACT=<p>This numerical study is about the steady incompressible non-Newtonian fluid flow in a channel with static obstacles. The flow field is governed by the Generalized Navier-Stokes equations incorporating the constitutive relation of power-law fluids. Three cases are considered: 1) circular obstacle <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, 2) semicircular obstacle <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, and 3) both circular and semicircular obstacles. A range of values of the power-law index <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0.3</mml:mn><mml:mo>≤</mml:mo><mml:mi>n</mml:mi><mml:mo>≤</mml:mo><mml:mn>1.7</mml:mn></mml:mrow></mml:math></inline-formula> are considered at <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mn>20</mml:mn></mml:mrow></mml:math></inline-formula> to check the impact of shear-thinning and shear-thickening viscosity on the drag and lift coefficients. The correlation between drag and lift coefficients is calculated against the power-law index. The simulated results of velocity and pressure are investigated at different sections of the channel. Benchmark results of drag and lift for the Newtonian fluid are reproduced as a special case. A strong positive correlation is observed between drag and lift coefficients in the case of a single obstacle, while in the case of dual obstacles and inverse correlation, drag and lift coefficients have been found.</p>