Numerical computation on MHD natural convective ternary nanofluid flow and heat transfer in a porous square cavity: Marker-and-cell technique

Abstract

Purpose The analysis of fluid flow and thermal transport performance inside the cavity has found numerous applications in various engineering fields, such as nuclear reactors and solar collectors. Nowadays, researchers are concentrating on improving heat transfer by using ternary nanofluids. With this motivation, the present study analyzes the natural convective flow and heat transfer efficiency of ternary nanofluids in different types of porous square cavities. Design/methodology/approach The cavity inclination angle is fixed ω = 0 in case (I) and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>ω</m:mi><m:mo>=</m:mo><m:mfrac><m:mi>π</m:mi><m:mn>4</m:mn></m:mfrac></m:mrow></m:math> in case (II). The traditional fluid is water, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>F</m:mi><m:msub><m:mi>e</m:mi><m:mn>3</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>4</m:mn></m:msub><m:mo>+</m:mo><m:mi>M</m:mi><m:mi>W</m:mi><m:mi>C</m:mi><m:mi>N</m:mi><m:mi>T</m:mi><m:mo>+</m:mo><m:mi>C</m:mi><m:mi>u</m:mi><m:mo>/</m:mo><m:msub><m:mi>H</m:mi><m:mn>2</m:mn></m:msub><m:mi>O</m:mi></m:mrow></m:math> is treated as a working fluid. Ternary nanofluid's thermophysical properties are considered, according to the Tiwari–Das model. The marker-and-cell numerical scheme is adopted to solve the transformed dimensionless mathematical model with associated initial–boundary conditions. Findings The average heat transfer rate is computed for four combinations of ternary nanofluids: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>F</m:mi><m:msub><m:mi>e</m:mi><m:mn>3</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>4</m:mn></m:msub><m:mo stretchy="true">(</m:mo><m:mn>25</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>M</m:mi><m:mi>W</m:mi><m:mi>C</m:mi><m:mi>N</m:mi><m:mi>T</m:mi><m:mo stretchy="true">(</m:mo><m:mn>25</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>C</m:mi><m:mi>u</m:mi><m:mo stretchy="true">(</m:mo><m:mn>50</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>,</m:mo><m:mi>F</m:mi><m:msub><m:mi>e</m:mi><m:mn>3</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>4</m:mn></m:msub><m:mo stretchy="true">(</m:mo><m:mn>50</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>M</m:mi><m:mi>W</m:mi><m:mi>C</m:mi><m:mi>N</m:mi><m:mi>T</m:mi><m:mo stretchy="true">(</m:mo><m:mn>25</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>C</m:mi><m:mi>u</m:mi><m:mo stretchy="true">(</m:mo><m:mn>25</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>,</m:mo><m:mi>F</m:mi><m:msub><m:mi>e</m:mi><m:mn>3</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>4</m:mn></m:msub><m:mo stretchy="true">(</m:mo><m:mn>33.3</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>M</m:mi><m:mi>W</m:mi><m:mi>C</m:mi><m:mi>N</m:mi><m:mi>T</m:mi><m:mo stretchy="true">(</m:mo><m:mn>33.3</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>C</m:mi><m:mi>u</m:mi><m:mo stretchy="true">(</m:mo><m:mn>33.3</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo></m:mrow></m:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>F</m:mi><m:msub><m:mi>e</m:mi><m:mn>3</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>4</m:mn></m:msub><m:mo stretchy="true">(</m:mo><m:mn>25</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>M</m:mi><m:mi>W</m:mi><m:mi>C</m:mi><m:mi>N</m:mi><m:mi>T</m:mi><m:mo stretchy="true">(</m:mo><m:mn>50</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo><m:mo>+</m:mo><m:mi>C</m:mi><m:mi>u</m:mi><m:mo stretchy="true">(</m:mo><m:mn>25</m:mn><m:mi>%</m:mi><m:mo stretchy="true">)</m:mo></m:mrow></m:math> under the influence of various physical factors such as volume fraction of nanoparticles, inclined magnetic field, cavity inclination angle, porous medium, internal heat generation/absorption and thermal radiation. The transport phenomena within the square cavity are graphically displayed via streamlines, isotherms, local and average Nusselt number profiles with adequate physical interpretations. Practical implications The purpose of this study is to determine whether the ternary nanofluids may be used to achieve the high thermal transmission in nuclear power systems, generators and electronic device applications. Social implications The current analysis is useful to improve the thermal features of nuclear reactors, solar collectors, energy storage and hybrid fuel cells. Originality/value To the best of the authors’ knowledge, no research has been carried out related to the magneto-hydrodynamic natural convective <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mrow><m:mi>F</m:mi><m:msub><m:mi>e</m:mi><m:mn>3</m:mn></m:msub><m:msub><m:mi>O</m:mi><m:mn>4</m:mn></m:msub><m:mo>+</m:mo><m:mi>M</m:mi><m:mi>W</m:mi><m:mi>C</m:mi><m:mi>N</m:mi><m:mi>T</m:mi><m:mo>+</m:mo><m:mi>C</m:mi><m:mi>u</m:mi><m:mo>/</m:mo><m:msub><m:mi>H</m:mi><m:mn>2</m:mn></m:msub><m:mi>O</m:mi></m:mrow></m:math> ternary nanofluid flow and heat transmission filled in porous square cavities with an inclined cavity angle. The computational outcomes revealed that the average heat transfer depends not only on the nanoparticle’s volume concentration but also on the existence of heat source and sink.