Mixed Convection in a Double Lid-Driven Wavy Shaped Cavity Filled with Nanofluid Subject to Magnetic Field and Internal Heat Source
Kakali Chowdhury, Md. Abdul Alim
Abstract
A numerical investigation is carried out to analyze the impacts of internal heat source size, solid concentration of nanoparticles, magnetic field, and Richardson number on flow characteristics in an oppositely directed lid-driven wavy-shaped enclosure. The left and right vertical walls of the enclosure are cooled isothermally and moving with fixed velocity in upward and downward directions, respectively. The bottom wall is wavy shaped and isothermally cooled as the vertical walls while the top wall is kept adiabatic. A rectangular heater is placed horizontally in the center of the cavity. The physical problems are characterized by 2D governing partial differential equations accompanying proper boundary conditions and are discretized using Galerkin’s finite element formulation. The study is executed by analyzing different ranges of geometrical and physical parameters, namely, internal heat source length <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mfenced open="(" close=")"> <a:mrow> <a:mn>0.2</a:mn> <a:mo>≤</a:mo> <a:mtext>CH</a:mtext> <a:mo>≤</a:mo> <a:mn>0.6</a:mn> </a:mrow> </a:mfenced> </a:math> , solid concentration of nanoparticles <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M2"> <e:mfenced open="(" close=")"> <e:mrow> <e:mn>0</e:mn> <e:mo>≤</e:mo> <e:mi>φ</e:mi> <e:mo>≤</e:mo> <e:mn>0.09</e:mn> </e:mrow> </e:mfenced> </e:math> , Hartmann’s number <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" id="M3"> <i:mfenced open="(" close=")"> <i:mrow> <i:mn>0</i:mn> <i:mo>≤</i:mo> <i:mtext>Ha</i:mtext> <i:mo>≤</i:mo> <i:mn>70</i:mn> </i:mrow> </i:mfenced> </i:math> , and Richardson’s number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" id="M4"> <m:mfenced open="(" close=")"> <m:mrow> <m:mn>0.1</m:mn> <m:mo>≤</m:mo> <m:mtext>Ri</m:mtext> <m:mo>≤</m:mo> <m:mn>10</m:mn> </m:mrow> </m:mfenced> </m:math> . The results indicate that the overall heat transfer rate declines with the increasing length of internal heat source. The presence and rising values of solid concentration of nanoparticles cause the augmentation of heat transfer whereas the magnetic field has a negative influence and the Richardson number has a positive influence on heat transfer.