Topological Characteristics of Obstacles and Nonlinear Rheological Fluid Flow in Presence of Insulated Fins: A Fluid Force Reduction Study

In this work, a comprehensive study of fluid forces and thermal analysis of two-dimensional, laminar, and incompressible complex (power law, Bingham, and Herschel–Bulkley) fluid flow over a topological cross-sectional cylinder (square, hexagon, and circle) in channel have been computationally done by using finite element technique. The characteristics of nonlinear flow for varying ranges of power law index <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")" separators="|"> <a:mrow> <a:mn>0.4</a:mn> <a:mo>≤</a:mo> <a:mi>n</a:mi> <a:mo>≤</a:mo> <a:mn>1.6</a:mn> </a:mrow> </a:mfenced> <a:mo>,</a:mo> </a:math> Bingham number <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" id="M2"> <f:mfenced open="(" close=")" separators="|"> <f:mrow> <f:mn>0</f:mn> <f:mo>≤</f:mo> <f:mtext>Bn</f:mtext> <f:mo>≤</f:mo> <f:mn>50</f:mn> </f:mrow> </f:mfenced> </f:math> , Prandtl number <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M3"> <k:mfenced open="(" close=")" separators="|"> <k:mrow> <k:mn>0.7</k:mn> <k:mo>≤</k:mo> <k:mtext>Pr</k:mtext> <k:mo>≤</k:mo> <k:mn>10</k:mn> </k:mrow> </k:mfenced> </k:math> , Reynolds number <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" id="M4"> <p:mfenced open="(" close=")" separators="|"> <p:mrow> <p:mn>10</p:mn> <p:mo>≤</p:mo> <p:mtext>Re</p:mtext> <p:mo>≤</p:mo> <p:mn>50</p:mn> </p:mrow> </p:mfenced> </p:math> , and Grashof number <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" id="M5"> <u:mfenced open="(" close=")" separators="|"> <u:mrow> <u:mn>1</u:mn> <u:mo>≤</u:mo> <u:mtext>Gr</u:mtext> <u:mo>≤</u:mo> <u:mn>10</u:mn> </u:mrow> </u:mfenced> <u:mo> </u:mo> </u:math> have been examined. Considerable evaluation for thermal flow field in the form of dimensionless velocity profile, isotherms, drag and lift coefficients, and average Nusselt number <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" id="M6"> <z:mfenced open="(" close=")" separators="|"> <z:mrow> <z:msub> <z:mrow> <z:mtext>Nu</z:mtext> </z:mrow> <z:mrow> <z:mtext>avg</z:mtext> </z:mrow> </z:msub> </z:mrow> </z:mfenced> </z:math> is done. Also, for a range of <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" id="M7"> <eb:mtext>Bn</eb:mtext> </eb:math> , the drag forces reduction is observed for circular and hexagonal obstacles in comparison with the square cylinder. At <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" id="M8"> <gb:mtext>Bn</gb:mtext> <gb:mo>=</gb:mo> <gb:mn>0</gb:mn> <gb:mo> </gb:mo> </gb:math> corresponding to Newtonian fluid, maximum reduction in drag force is reported.