Mathematical modeling of mixed convective MHD Falkner-Skan squeezed Sutterby multiphase flow with non-Fourier heat flux theory and porosity

In a wide variety of mechanical and industrial applications,e.g.,space cooling,nuclear reactor cooling,medicinal utilizations(magnetic drug targeting),energy generation,and heat conduction in tissues,the heat transfer phenomenon is involved.Fourier’s law of heat conduction has been used as the foundation for predicting the heat transfer behavior in a variety of real-world contexts.This model’s production of a parabolic energy expression,which means that an initial disturbance would immediately affect the system under investigation,is one of its main drawbacks.Therefore,numerous researchers worked on such problem to resolve this issue.At last,this problem was resolved by Cattaneo by adding relaxation time for heat flux in Fourier’s law,which was defined as the time required to establish steady heat conduction once a temperature gradient is imposed.Christov offered a material invariant version of Cattaneo’s model by taking into account the upper-connected derivative of the Oldroyd model.Nowadays,both models are combinedly known as the Cattaneo-Christov(CC)model.In this attempt,the mixed convective MHD Falkner-Skan Sutterby nanofluid flow is addressed towards a wedge surface in the presence of the variable external magnetic field.The CC model is incorporated instead of Fourier’s law for the examination of heat transfer features in the energy expression.A two-phase nanofluid model is utilized for the implementation of nano-concept.The nonlinear system of equations is tackled through the bvp4c technique in the MATLAB software 2016.The influence of pertinent flow parameters is discussed and displayed through different sketches.Major and important results are summarized in the conclusion section.Furthermore,in both cases of wall-through flow(i.e.,suction and injection effects),the porosity parameters increase the flow speed,and decrease the heat transport and the influence of drag forces.

Dynamics of Sutterby fluid flow due to a spinning stretching disk with non-Fourier/Fick heat and mass flux models

The magnetohydrodynamic Sutterby fluid flow instigated by a spinning stretchable disk is modeled in this study.The Stefan blowing and heat and mass flux aspects are incorporated in the thermal phenomenon.The conventional models for heat and mass flux,i.e.,Fourier and Fick models,are modified using the Cattaneo-Christov(CC)model for the more accurate modeling of the process.The boundary layer equations that govern this problem are solved using the apt similarity variables.The subsequent system of equations is tackled by the Runge-Kutta-Fehlberg(RKF)scheme.The graphical visualizations of the results are discussed with the physical significance.The rates of mass and heat transmission are evaluated for the augmentation in the pertinent parameters.The Stefan blowing leads to more species diffusion which in turn increases the concentration field of the fluid.The external magnetism is observed to decrease the velocity field.Also,more thermal relaxation leads to a lower thermal field which is due to the increased time required to transfer the heat among fluid particles.The heat transport is enhanced by the stretching of the rotating disk.

Upshot of ohmically dissipated Darcy-Forchheimer slip flow of magnetohydrodynamic Sutterby fluid over radiating linearly stretched surface in view of Cash and Carp method

The present work concerns the momentum and heat transmission of the electro-magnetohydrodynamic (E-MHD) boundary layer Darcy-Forchheimer flow of a Sutterby fluid over a linear stretching sheet with slip. The nonlinear equations for the proposed model are analyzed numerically. Suitable techniques are used to transform the coupled nonlinear partial differential equations (PDEs) conforming to the forced balance law, energy, and concentration equations into a nonlinear coupled system of ordinary differential equations (ODEs). Numerical solutions of the transformed nonlinear system are obtained using a shooting method, improved by the Cash and Carp coefficients. The influence of important physical variables on the velocity, the temperature, the heat flux coefficient, and the skin-friction coefficient is verified and analyzed through graphs and tables. From the comprehensive analysis of the present work, it is concluded that by intensifying the magnitude of the Hartmann number, the momentum distribution decays, whereas the thermal profile of fluid increases. Furthermore, it is also shown that by aug- menting the values of the momentum slip parameter, the velocity profile diminishes. It is found that the Sutterby fluid model shows shear thickening and shear thinning behaviors. The momentum profile shows that the magnitude of velocity for the shear thickening case is dominant as compared with the shear thinning case. It is also demonstrated that the Sutterby fluid model reduces to a Newtonian model by fixing the fluid parameter to zero. In view of the limiting case, it is established that the surface drag in the case of the Sutterby model shows a trifling pattern as compared with the classical case.

Artificial neural network model of non-Darcy MHD Sutterby hybrid nanofluid flow over a curved permeable surface:Solar energy applications

The conversion of solar radiation to thermal energy has recently much interest as the requirement for renewable heat and power grows.Due to their enhanced ability to promote heat transmission,nanofluids can significantly improve solar-thermal systems’efficiency.This section aims to study the heat transfer behavior of the Sutterby hybrid nanofluid flow of magnetohydrodynamics in the presence of a non-uniform heat source/sink and linear thermal radiation over a non-Darcy curved permeable surface.A novel implementation of an intelligent numerical computing solver based on multi-layer perceptron(MLP)feed-forward back-propagation artificial neural network(ANN)with the Levenberg-Marquard algorithm is provided in the current study.Data were gathered for the ANN model’s testing,certification,and training.Established mathematical equations are nonlinear,which are resolved for velocity,the temperature in addition to the skin friction coefficient,and the rate of heat transfer by using the bvp4c with MATLAB solver.The ANN model selects data,constructs and trains a network,then evaluates its efficacy via mean square error.Graphs illustrate the impact of a wide range of physical factors on variables,including pressure,velocity,and temperature.In the entire study,the thermal energy improved by the SiO2(silicon dioxide)-Au(gold)hybrid nanofluid than the SiO2-TiO2(titanium dioxide)hybrid nanofluid.The higher internal heat generation/absorption parameter values increase the temperature.

Radiative Blood-Based Hybrid Copper-Graphene Nanoliquid Flows along a Source-Heated Leaning Cylinder

Variant graphene,graphene oxides(GO),and graphene nanoplatelets(GNP)dispersed in blood-based copper(Cu)nanoliquids over a leaning permeable cylinder are the focus of this study.These forms of graphene are highly beneficial in the biological and medical fields for cancer therapy,anti-infection measures,and drug delivery.The non-Newtonian Sutterby(blood-based)hybrid nanoliquid flows are generalized within the context of the Tiwari-Das model to simulate the effects of radiation and heating sources.The governing partial differential equations are reformulated into a nonlinear set of ordinary differential equations using similar transformational expressions.These equations are then transformed into boundary value problems through a shooting technique,followed by the implementation of the bvp4c tool in MATLAB.The influences of various parameters on the model’s nondimensional velocity and temperature profiles,reduced skin friction,and reduced Nusselt number are presented for detailed discussions.The results indicated that Cu-GNP/blood and Cu-GO/blood hybrid nanofluids exhibit the lowest and highest velocity distributions,respectively,for increased nanoparticles volume fraction,curvature parameter,Sutterby fluid parameter,Hartmann number,and wall permeability parameter.Conversely,opposite trends are observed for the temperature distribution for all considered parameters,except the mixed convection parameter.Increases in the reduced skin friction magnitude and the reduced Nusselt number with higher values of graphene/GO/GNP nanoparticle volume fraction are also reported.Finally,GNP is identified as the superior heat conductor,with an average increase of approximately 5%and a peak of 7.8%in the reduced Nusselt number compared to graphene and GO nanoparticles in the Cu/blood nanofluids.