The current investigation aims to explore the combined effects of heat and mass transfer on free convection of Sodium alginate-Fe_{3}O_{4} based Brinkmann type nanofluid flow over a vertical rotating frame. The Tiwari and Das nanofluid model is employed to examine the effects of dimensionless numbers, including Grashof, Eckert, and Schmidt numbers and governing parameters like solid volume fraction of nanoparticles, Hall current, magnetic field, viscous dissipation, and the chemical reaction on the physical quantities. The dimensionless nonlinear partial differential equations are solved using a finite difference method known as Runge-Kutta Fehlberg (RKF-45) method. The variation of dimensionless velocity, temperature, concentration, skin friction, heat, and mass transfer rate, as well as for entropy generation and Bejan number with governing parameters, are presented graphically and are provided in tabular form. The results reveal that the Nusselt number increases with an increase in the solid volume fraction of nanoparticles. Furthermore, the rate of entropy generation and Bejan number depends upon the magnetic field and the Eckert number.

Most of the conventional liquids such as saltwater, liquid metal, plasma, etc. are conducting fluids that have over the years captured immense attention of renowned researchers to the study of the dynamics of these fluids because of their significant engineering applications like MHD generators, flow meters, metal purification, metallurgy, geothermal energy extractions, and polymer technology. Some studies [

Hydromagnetic fluid flow problems are essential in the field of earth science, Meteorology. Interestingly, the Hall current induces both the primary and secondary flows in fluid governed of Coriolis force. Very recently, Krishna et al. [

Above mentioned literature was performed in the fluid flow models of a conventional fluid flow of an electrically conducting fluid. Still, fluids with the inclusion of nanometer-sized particles (nanofluid) behave quite differently from that of the traditional fluid in several vital aspects. A report from the current trend in research has shown that heat transfer is enhanced in the thermal system through the embedded nanoparticle into conventional liquids. The applications exist in a solar receiver, nuclear reactor, microbial fuel cell, thermal storage, biomedical applications, heat exchangers, industrial cooling medium. Authors have established several results about nanofluid flow in various geometries, for example, see Ali et al. [

In energy management, minimizing entropy production in a thermal system cannot be overemphasized because of its limited percentage of energy available as heat. It is, however, imperative to improve the amount of energy available for work through entropy generation. Some relevant articles that analyzed the flow and heat transfer using the 2nd law of thermodynamics are [

The objective of the current analysis is to examine the rate of entropy optimization on MHD Brinkman-type nanofluid flow over a vertical rotating plate with the influence of radiation and chemical reaction. It is, therefore, pertinent to examine the effect of this feature because entropy production occurs in moving fluid with high temperature. To the best of our knowledge, the present study has not remained investigated. By applying suitable transformations, the governing equations of the model are converted to non-dimensional form and then solved by employing the Runge–Kutta–Fehlberg scheme. Effects of all the pertinent parameters on velocity, temperature, nanoparticle concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation, and the Bejan number profiles are shown through graphs and extensively discussed.

A magnetohydrodynamic convective flow of Sodium alginate-Fe_{3}O_{4} based Brinkmann type nanofluid is examined in a vertical rotating frame. The flow is assumed to be incompressible and time-dependent.

Subject to the initial and boundary conditions

Defining

The dimensionless variables are given by

Thus, the governing equations are:

The boundary conditions are given by

where the parameters are defined by

The local skin friction

The wall shear stress is

The dimensionless form

The expression for the entropy generation of this model may be written as

Here, the characteristic entropy

In dimensionless form, Bejan number may be written as

The physical properties of the base fluid and nanoparticles have been reported in the

Physical properties | Sodium Alginate | Fe_{3}O_{4} |
---|---|---|

_{p} (J/KgK) |
4175 | 670.21 |

^{3}) |
989 | 5180 |

κ (W/mK) | 0.6376 | 80 |

^{–1} |
5.01 × 10^{–6} |
0.112 × 10^{6} |

^{–1}) |
0.001 × 10^{–5} |
20.6 × 10^{–5} |

Pr | 6 | – |

The system of partial differential Eqs. (

The impacts of

The effects of the solid volume fraction of nanoparticles and Eckert number on the dimensionless temperature are shown in the

Plots of physical quantities such as

0.00 | −0.16447 | −0.20114 | −0.23489 | −0.23139 | −0.26269 | −0.29191 |

0.01 | −0.16866 | −0.20626 | −0.24087 | −0.23728 | −0.26938 | −0.29934 |

0.02 | −0.17299 | −0.21156 | −0.24706 | −0.24338 | −0.27630 | −0.30703 |

0.03 | −0.17749 | −0.21705 | −0.25348 | −0.24970 | −0.28348 | −0.31500 |

0.04 | −0.18214 | −0.22275 | −0.26013 | −0.25625 | −0.29092 | −0.32327 |

0.05 | −0.18697 | −0.22866 | −0.26703 | −0.26305 | −0.29863 | −0.33185 |

0.06 | −0.19199 | −0.23479 | −0.27419 | −0.27010 | −0.30664 | −0.34074 |

0.07 | −0.19719 | −0.24115 | −0.28162 | −0.27742 | −0.31495 | −0.34998 |

0.08 | −0.20259 | −0.24776 | −0.28934 | −0.28502 | −0.32358 | −0.35956 |

0.09 | −0.20820 | −0.25462 | −0.29735 | −0.29292 | −0.33254 | −0.36952 |

0.10 | −0.21404 | −0.26175 | −0.30568 | −0.30112 | −0.34185 | −0.37987 |

The rate of heat transfer as a function of

0.00 | 2.20995 | 2.52955 | 2.81363 | 2.20832 | 2.52778 | 2.81176 |

0.01 | 2.27534 | 2.58652 | 2.86478 | 2.27364 | 2.58470 | 2.86287 |

0.02 | 2.34201 | 2.64462 | 2.91694 | 2.34027 | 2.64276 | 2.91500 |

0.03 | 2.41003 | 2.70388 | 2.97016 | 2.40824 | 2.70199 | 2.96819 |

0.04 | 2.47944 | 2.76435 | 3.02446 | 2.47759 | 2.76241 | 3.02245 |

0.05 | 2.55027 | 2.82607 | 3.07987 | 2.54837 | 2.82408 | 3.07782 |

0.06 | 2.62256 | 2.88906 | 3.13643 | 2.62061 | 2.88703 | 3.13435 |

0.07 | 2.69638 | 2.95337 | 3.19418 | 2.69437 | 2.95130 | 3.19205 |

0.08 | 2.77175 | 3.01905 | 3.25315 | 2.76969 | 3.01693 | 3.25099 |

0.09 | 2.84874 | 3.08613 | 3.31338 | 2.84662 | 3.08397 | 3.31118 |

0.10 | 2.92740 | 3.15466 | 3.37492 | 2.92522 | 3.15245 | 3.37268 |

The influence of the Schmidt number

0.00 | 0.50463 | 0.55363 | 0.59997 | 1.12832 | 1.23787 | 1.34143 |

0.01 | 0.49958 | 0.54810 | 0.59397 | 1.11703 | 1.22549 | 1.32801 |

0.02 | 0.49453 | 0.54256 | 0.58797 | 1.10575 | 1.21312 | 1.31460 |

0.03 | 0.48949 | 0.53702 | 0.58197 | 1.09447 | 1.20074 | 1.30118 |

0.04 | 0.48444 | 0.53149 | 0.57597 | 1.08318 | 1.18836 | 1.28777 |

0.05 | 0.47940 | 0.52595 | 0.56997 | 1.07190 | 1.17598 | 1.27436 |

0.06 | 0.47435 | 0.52042 | 0.56397 | 1.06061 | 1.16360 | 1.26094 |

0.07 | 0.46930 | 0.51488 | 0.55797 | 1.04933 | 1.15122 | 1.24753 |

0.08 | 0.46426 | 0.50934 | 0.55197 | 1.03805 | 1.13884 | 1.23411 |

0.09 | 0.45921 | 0.50381 | 0.54597 | 1.02677 | 1.12646 | 1.22070 |

0.10 | 0.45416 | 0.49827 | 0.53997 | 1.01548 | 1.11409 | 1.20728 |

The impacts of governing parameters, including

In this paper, the effects of viscous dissipation and chemical reaction on MHD flow with combined heat and mass transfer of incompressible sodium-alginate based Fe_{3}O_{4} in a rotating frame have been analyzed. The following are the main results of the present study:

The dimensionless velocity

The dimensionless temperature

An increase in the chemical reaction parameter and Schmidt number has shown a declining trend for the dimensionless concentration

Viscous drag decreases due to

The rate of heat transfer is decreasing due to the rise in

The mass transfer rate increases with an increase in

Rate of Entropy generation and Bejan number shows the opposite trend for