On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer

• Main Authors: Shahid Khan, Mahmoud M. Selim, Aziz Khan, Asad Ullah, Thabet Abdeljawad, Ikramullah, Muhammad Ayaz, Wali Khan Mashwani
• Format: Article
• Language: English
• Published: MDPI AG 2021-05-01
• Series: Coatings
• Subjects: thermal radiations; magnetic field; Carreau fluid; stretching/shrinking surface; Hall effect; nonlinear radiations
• Online Access: https://www.mdpi.com/2079-6412/11/5/566

The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>f</mi><msup><mrow></mrow><mo>′</mo></msup></msup><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>) enhances with the higher values of the Hall and shrinking parameters (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>,</mo><mi>ϱ</mi></mrow></semantics></math></inline-formula>), while it reduces with magnetic parameter and Weissenberg number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mo>,</mo><mi>W</mi><mi>e</mi></mrow></semantics></math></inline-formula>). The y-component of fluid velocity (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>g</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math></inline-formula>) rises with the augmenting values of <i>m</i> and <i>M</i>, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math></inline-formula> enhances with the increasing values of radiation parameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>d</mi></mrow></semantics></math></inline-formula>) and Dufour number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mi>u</mi></mrow></semantics></math></inline-formula>), while it drops with the rising Prandtl number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>r</mi></mrow></semantics></math></inline-formula>). The concentration field (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ϕ</mi><mo>(</mo><mi>η</mi><mo>)</mo></mrow></semantics></math></inline-formula>) augments with the rising Soret number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>r</mi></mrow></semantics></math></inline-formula>) while drops with the augmenting Schmidt number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>c</mi></mrow></semantics></math></inline-formula>). The variation of the skin friction coefficients (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mrow><mi>f</mi><mi>x</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>C</mi><mrow><mi>f</mi><mi>z</mi></mrow></msub></semantics></math></inline-formula>), Nusselt number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><msub><mi>u</mi><mi>x</mi></msub></mrow></semantics></math></inline-formula>) and Sherwood number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><msub><mi>h</mi><mi>x</mi></msub></mrow></semantics></math></inline-formula>) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.