Entropy generation in radiative motion of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms and activation energy

In this work, entropy generation is optimized through the application of the second law of thermodynamics. The slip mechanisms, Brownian diffusions, and thermophoresis are elaborated using the tangent hyperbolic nanomaterial model. Magnetohydrodynamic (MHD) fluid is taken into consideration. To characterize the impact of activation energy, a unique model involving the binary chemical reaction is deployed. The effects of mixed convection that is nonlinear in nature, bioconvection, and Joule effect are all taken into consideration. The key partial differential equations (PDEs) are reduced into ordinary differential equations (ODEs) by utilizing appropriate similarity transformations and then solved numerically with the help of a built-in ‘bvp4c’ technique of MATLAB software. Varied flow parameters’ impacts on the nanoparticle volume concentration, entropy number, microorganism concentration, temperature, and velocity fields are analyzed using graphs. Various flow variables are taken into consideration to calculate the total rate of entropy generation. The obtained results show that concentration irreversibility, Joule effect irreversibility, viscous dissipation, and heat irreversibility all influence the entropy. The numerical outcomes were observed by fixing the physical parameters as <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>α</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>4.0</mml:mn></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>M</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>1.2</mml:mn></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>N</mml:mi><mml:mi>r</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>2.2</mml:mn></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m4"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>L</mml:mi><mml:mi>e</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>2.2</mml:mn></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m5"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>N</mml:mi><mml:mi>b</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>0.4</mml:mn></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m6"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>N</mml:mi><mml:mi>t</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>1.0</mml:mn></mml:mrow></mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m7"><mml:mrow><mml:mn>2.0</mml:mn><mml:mo>&lt;</mml:mo><mml:mo>⁡</mml:mo><mml:mi>Pr</mml:mi><mml:mo>⁡</mml:mo><mml:mo>&lt;</mml:mo><mml:mn>5.0</mml:mn></mml:mrow></mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m8"><mml:mrow><mml:mn>0.1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>L</mml:mi><mml:mi>b</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>2.0</mml:mn></mml:mrow></mml:math> , as well as their impact on the momentum, thermal, concentration, and microorganism density profiles. From results, an increasing estimate of the variable representing chemical reaction indicates a decline in the concentration. The higher the chemical reaction variable, Hartmann number, and Weissenberg number, the higher the entropy number, while the Bejan number has a contrary behavior. Subsequently, all the outcomes are plotted in graphs and discussed in detail, when subjected to the involving physical quantities.