AUTHOR=Hussain Majeed Afraz , Mahmood Rashid , Hamadneh Nawaf N. , Siddique Imran , Khan Ilyas , Alshammari Nawa 

TITLE=Periodic Flow of Non-Newtonian Fluid Over a Uniformly Heated Block With Thermal Plates: A Hybrid Mesh-Based Study

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.829085

DOI=10.3389/fphy.2022.829085

ISSN=2296-424X

ABSTRACT=<p>In this work, we analyze the characteristics of periodic flows in non-isothermal viscous fluid over a heated block in the presence of thermal plates at Reynolds number <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:mi>R</mml:mi><mml:mi>e</mml:mi><mml:mo>=</mml:mo><mml:mn>100</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>. The unsteady, incompressible Navier–Stokes (NS) equations with suitable initial and boundary data in 2D are executed by the finite element technique using a highly refined hybrid mesh. The temporal discretization is performed by an implicit stable backward differencing in time and a stable choice of finite elements from the finite element library for spatial discretization. The discrete nonlinear system arising from this discretization is linearized by Newton’s method and then solved through a direct linear solver PARDISO. For this forced convective study, the range of dimensionless parameters, namely, the Prandtl number <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:mi>P</mml:mi><mml:mi>r</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> and power law index <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, are varied from 1 to 10 and 0.6 to 1.4 with a low Grashof number varying as <inline-formula id="inf4"><mml:math id="m4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>1</mml:mn><mml:mo>≤</mml:mo><mml:mi>G</mml:mi><mml:mi>r</mml:mi><mml:mo>≤</mml:mo><mml:mn>10</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> to produce a forced convection regime, respectively. For the authentication, we have compared our results with the literature at a similar configuration. After simulation, the results accomplished in the velocity profile, pressure, isotherm contours, drag and lift coefficients (trajectory motion), average Nusselt number <inline-formula id="inf5"><mml:math id="m5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mi>v</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, etc. are considered. For convergence of solution at low shear rate <inline-formula id="inf6"><mml:math id="m6" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, crosswind stabilization (CWS) function has been incorporated. It is observed that <inline-formula id="inf7"><mml:math id="m7" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>N</mml:mi><mml:msub><mml:mi>u</mml:mi><mml:mrow><mml:mi>a</mml:mi><mml:mi>v</mml:mi><mml:mi>g</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> becomes oscillatory for the shear-thinning case <inline-formula id="inf8"><mml:math id="m8" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, while for the shear-thickening cases <inline-formula id="inf9"><mml:math id="m9" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula>, it converges to a single value. Furthermore, the drag <inline-formula id="inf10"><mml:math id="m10" 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:mi>D</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> and lift <inline-formula id="inf11"><mml:math id="m11" 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:mi>L</mml:mi></mml:msub></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> coefficients are more pronounced for shear-thinning cases <inline-formula id="inf12"><mml:math id="m12" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></inline-formula> as compared with shear-thickening cases <inline-formula id="inf13"><mml:math id="m13" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>&gt;</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mo>.</mml:mo></mml:mrow></mml:math></inline-formula></p>