Nonlinear Convection Flow of Micropolar Nanofluid due to a Rotating Disk with Multiple Slip Flow
Chaluma Zemedu, Wubshet Ibrahim
Abstract
In this analysis, steady, laminar, and two-dimensional boundary layer flow of nonlinear convection micropolar nanofluid due to a rotating disk is considered. The mathematical formulation for the flow problem has been made. By means of appropriate similarity transformation and dimensionless variables, the governing nonlinear boundary value problems were reduced into coupled high-order nonlinear ordinary differential equations with numerically solved. The equations were calculated using method bvp4c from matlab software for various quantities of main parameters. The influences of different parameters on skin friction coefficients <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo>″</mml:mo></mml:mrow></mml:msup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:mfenced></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msup><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:mfenced></mml:math>, wall duo stress coefficients <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:msubsup><mml:mi>H</mml:mi><mml:mn>1</mml:mn><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:mfenced></mml:math>, -<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:msubsup><mml:mi>H</mml:mi><mml:mn>2</mml:mn><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:mfenced></mml:math>, and -<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:msubsup><mml:mi>H</mml:mi><mml:mn>3</mml:mn><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:mfenced></mml:math>, the Nusselt number -<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:msup><mml:mrow><mml:mi>θ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:mfenced></mml:math>, and Sherwood number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:msup><mml:mrow><mml:mi mathvariant="normal">Ω</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:mfenced></mml:math>, as well as the velocities, temperature, and concentration are analysed and discussed through tables and plotted graphs. The findings indicate that an increase in the values of thermal and solutal nonlinear convection parameters allow to increase the value of velocities <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>η</mml:mi></mml:mrow></mml:mfenced></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mi>G</mml:mi><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>η</mml:mi></mml:mrow></mml:mfenced></mml:math> near surface of the disk and reduce at far away from the disk as well as thermal and solutal Grashof numbers tolerate to increase in the value of radial velocity <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>η</mml:mi></mml:mrow></mml:mfenced></mml:math> near surface of the disk.