Effect of inclined magnetic field on radiative heat and mass transfer in chemically reactive hybrid nanofluid flow due to dual stretching.

This research analyzes the three-dimensional magneto hydrodynamic nanofluid flow through chemical reaction and thermal radiation above the dual stretching surface in the presence of an inclined magnetic field. Different rotational nanofluid and hybrid nanofluids with constant angular velocity [Formula: see text] for this comparative study are considered. The constitutive relations are used to gain the equations of motion, energy, and concentration. This flow governing extremely non-linear equations cannot be handled by an analytical solution. So, these equations are transformed into ordinary differential equalities by using the similarity transformation and then handled in MATLAB by applying the boundary values problem practice. The outcomes for the considered problem are accessed through tables and graphs for different parameters. A maximum heat transfer amount is observed in the absence of thermal radiation and when the inclined magnetic field and axis of rotation are parallel.

Partial differential equations modeling of bio-convective sutterby nanofluid flow through paraboloid surface.

In this research article, the behavior of 2D non-Newtonian Sutterby nanofluid flow over the parabolic surface is discussed. In boundary region of surface buoyancy-driven flow occurred due to considerable temperature differences produced by the reaction happen between Sutterby nanofluid and catalyst at the surface. Free convection which is sighted easily on the parabolic surface is initiated by reaction on the catalyst surface modeled the 1st order activation energy. Applications of parabolic surfaces are upper cover of bullet, car bonnet, and air crafts. Under discussion flow is modelled mathematically by implementing law of conservation of microorganism's concentration, momentum, mass and heat. The governing equations of the system is of the form of non-linear PDE's. By the use of similarity transform, the governing PDE`s transformed as non-dimensional ODE's. The resultant system of non-dimensional ODE's are numerically solved by built-in function MATLAB package named as 'bvp4c'. Graphical representation shows the influence of different parameters in the concentration, velocity, microorganisms and temperature profiles of the system. In temperature profile, we examined the impact of thermophoresis coefficient Nt (0.1, 0.5, 1.0), Prandtl number Pr (2.0, 3.0, 4.0), and Brownian motion variable Nb (0.1, 0.3, 0.5). Velocity profile depends on the non-dimensional parameters i.e. (Deborah number De & Hartmann number Ha) and found that these numbers (De, Ha) cause downfall in profile. Furthermore, mass transfer, skin friction, and heat transfer rates are numerically computed. The purpose of the study is to enumerate the significance of parabolic surfaces for the transport of heat and mass through the flow of bio-convective Sutterby nanofluid.

Effect of thermal radiation on convective heat transfer in MHD boundary layer Carreau fluid with chemical reaction.

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 [Formula: see text] is significant with strictly increasing mass suction [Formula: see text] shear stress rate increase with minor levels and sharp increase has been observed in Nusselt number, whereas in shrinking case [Formula: see text] shear stress and heat transfer coefficient values are improved raising the value of [Formula: see text] mass suction. Further, raising the values of power law index [Formula: see text] produce reduced skin friction over stretching surface [Formula: see text] while skin friction dramatically enhance in shrinking case [Formula: see text]. It is observed that raising the non-linearity [Formula: see text] 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.

Rotating Hybrid Nanofluid Flow with Chemical Reaction and Thermal Radiation between Parallel Plates.

This research investigates the two different hybrid nanofluid flows between two parallel plates placed at two different heights, y0 and yh, respectively. Water-based hybrid nanofluids are obtained by using Al2O3, TiO2 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.

Convective Heat Transfer in Magneto-Hydrodynamic Carreau Fluid with Temperature Dependent Viscosity and Thermal Conductivity.

This study is aimed to explore the magneto-hydrodynamic Carreau fluid flow over a stretching/shrinking surface with a convectively heated boundary. Temperature-dependent variable thermophysical properties are utilized to formulate the problem. The flow governing equations are obtained with boundary layer approximation and constitutive relation of the Carreau fluid. The shooting method is utilized to obtain graphical and numeric outcomes. Additionally, initial guesses are generated with the help of Newton's method. The effect of Weissenberg number, Magnetization, stretching ratio, Prandtl number, suction/blowing parameter, and Lewis number is obtained on velocity, temperature and species continuity profile and analyzed. Shear stress rates and Nusselt number outcomes under body forces influences are present in tabulated data and discussed. It is observed that in absence of magnetization force, B = 0 and strong mass suction 5≤S≤7.5 effect high rates of Nusselt number is obtained. It is concluded that under the influence of power law index and non-linearity parameter maximum heat transfer and reduced shear stress rates are obtained.

Some Novel Results Involving Prototypical Computation of Zagreb Polynomials and Indices for SiO4 Embedded in a Chain of Silicates.

A topological index as a graph parameter was obtained mathematically from the graph's topological structure. These indices are useful for measuring the various chemical characteristics of chemical compounds in the chemical graph theory. The number of atoms that surround an atom in the molecular structure of a chemical compound determines its valency. A significant number of valency-based molecular invariants have been proposed, which connect various physicochemical aspects of chemical compounds, such as vapour pressure, stability, elastic energy, and numerous others. Molecules are linked with numerical values in a molecular network, and topological indices are a term for these values. In theoretical chemistry, topological indices are frequently used to simulate the physicochemical characteristics of chemical molecules. Zagreb indices are commonly employed by mathematicians to determine the strain energy, melting point, boiling temperature, distortion, and stability of a chemical compound. The purpose of this study is to look at valency-based molecular invariants for SiO4 embedded in a silicate chain under various conditions. To obtain the outcomes, the approach of atom-bond partitioning according to atom valences was applied by using the application of spectral graph theory, and we obtained different tables of atom-bond partitions of SiO4. We obtained exact values of valency-based molecular invariants, notably the first Zagreb, the second Zagreb, the hyper-Zagreb, the modified Zagreb, the enhanced Zagreb, and the redefined Zagreb (first, second, and third). We also provide a graphical depiction of the results that explains the reliance of topological indices on the specified polynomial structure parameters.