This comparative study inspects the heat transfer characteristics of magnetohydrodynamic (MHD) nanofluid flow. The model employed is a two-phase fluid flow model. Water is utilized as the base fluid, and zinc and titanium oxide ($\mathrm{Zn}$ and ${\mathrm{TiO}}_2$) are used as two different types of nanoparticles. The rotation of nanofluid is considered along the z-axis, with velocity ${\omega }^{*}$. A similarity transformation is used to transform the leading structure of partial differential equations to ordinary differential equations. By using a powerful mathematical BVP-4C technique, numerical results are obtained. This study aims to describe the possessions of different constraints on temperature and velocity for rotating nanofluid with a magnetic effect. The outcomes for the rotating nanofluid flow and heat transference properties for both types of nanoparticles are highlighted with the help of graphs and tables. The impact of physical concentrations such as heat transference rates and coefficients of skin friction are examined. It is noted that rotation increases the heat flux and decreases skin friction. In this comparative study, $\mathrm{Zn}$-water nanofluid was demonstrated to be a worthy heat transporter as compared to ${\mathrm{TiO}}_2$-water nanofluid.

The temperature dependent thermophysical fluid properties have numerous aspects in different industries and engineering processes in which heat transmission is based on fluid flow. For such heat transmission processes, heat transmission system is highly fluctuated with variation of viscosity. Thus, the aim of this study is to investigate the transfer of heat in magnetized Carreau fluid with chemical reaction and under influence of thermal radiation over nonlinear stretching/shrinking surface. Additionally, we have incorporated variable heat dependent thermophysical properties to analyze the heat transfer in magnetized Carreau fluid. Set of flow governing non linear PDE’s are obtained using Carreau fluid tensor and boundary layer approximation (BLA) theory. Dimensionless set of ODE’s are obtained using suitable similarity transforms. Shooting method in conjunction with Newton's method have been utilized to solve the problem. It is noted that when stretching $$B\ge 0$$B ≥ 0 is significant with strictly increasing mass suction $$S$$S shear stress rate increase with minor levels and sharp increase has been observed in Nusselt number, whereas in shrinking case $$B<0$$B < 0 shear stress and heat transfer coefficient values are improved raising the value of $$S$$S mass suction. Further, raising the values of power law index $$n$$n produce reduced skin friction over stretching surface $$B\ge 0$$B ≥ 0 while skin friction dramatically enhance in shrinking case $$B<0$$B < 0 . It is observed that raising the non-linearity $$m$$m values for stretching or shrinking, skin friction and Nusselt number considerably improved. Moreover, computational outcomes of the study are validated with already published previous results and the results obtained in this study are found in good agreement.

This research investigates the two different hybrid nanofluid flows between two parallel plates placed at two different heights, $y_0$and $y_h$, respectively. Water-based hybrid nanofluids are obtained by using $A{l}_2{O}_3$, $Ti{O}_2$ and $Cu$ as nanoparticles, respectively. The upper-level plate is fixed, while the lower-level plate is stretchable. The fluid rotates along the y-axis. The governing equations of momentum, energy and concentration are transformed into partial differential equations by using similarity transformations. These transformed equations are grasped numerically at MATLAB by using the boundary value problem technique. The influence of different parameters are presented through graphs. The numerical outcomes for rotation, Nusselt, Prandtl, and Schmidt numbers are obtained in the form of tables. The heat transfer rate increases by augmentation in the thermophoresis parameter, while it decays by increasing the Reynolds number. Oxide nanoparticles hybrid nanofluid proved more efficient as compared to mixed nanoparticles hybrid nanofluid. This research suggests using oxide nanoparticles for good heat transfer.

This comparative research investigates the influence of a flexible magnetic flux and a chemical change on the freely fluid motion of a (MHD) magneto hydrodynamic boundary layer incompressible nanofluid across an exponentially expanding sheet. Water and ethanol are used for this analysis. The temperature transmission improvement of fluids is described using the Buongiorno model, which includes Brownian movement and thermophoretic distribution. The nonlinear partial differential equalities governing the boundary layer were changed to a set of standard nonlinear differential equalities utilizing certain appropriate similarity transformations. The bvp4c algorithm is then used to tackle the transformed equations numerically. Fluid motion is slowed by the magnetic field, but it is sped up by thermal and mass buoyancy forces and thermophoretic distribution increases non-dimensional fluid temperature resulting in higher temperature and thicker boundary layers. Temperature and concentration, on the other hand, have the same trend in terms of the concentration exponent, Brownian motion constraint, and chemical reaction constraint. Furthermore, The occurrence of a magnetic field, which is aided by thermal and mass buoyancies, assists in the enhancement of heat transmission and wall shear stress, whereas a smaller concentration boundary layer is produced by a first-order chemical reaction and a lower Schmidt number.

This article explores the application of the reduced differential transform method (RDTM) for the computational solutions of two fractional-order cancer tumor models in the Caputo sense: the model based on cancer chemotherapeutic effects which explain the relation between chemotherapeutic drugs, tumor cells, normal cells, and immune cells using a fractional partial differential equations, and the model that describes the different cases of killing rate K of cancer cells (the killing percentage of cancer cells $K$ (I) is dependent on the number of cells, (II) is a function of time only, and (III) is a function of space only). The solutions are presented using Mathematica software as a convergent power series with elegantly computed terms using the suggested technique. The proposed method gives new series form results for various values of gamma. To clarify the complexity of the models, we plot the two- and three-dimensional and contour graphics of the obtained solutions at varied values of fractional-order gamma and the selected system parameters. The solutions are analyzed with fractional and reduced differential transform methods to obtain an idea of invariance regarding the computed solution of the designed mathematical model. The obtained results demonstrate the efficiency and preciseness of the proposed method to achieve a better understanding of chemotherapy effects. It is observed that chemotherapy drugs boost immunity against the specific cancer by decreasing the number of tumor cells, and the killing rate $K$ of cancerous cells depend on the cells concentration.