This study aimed to investigate the consequences of the Darcy–Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno’s model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier–Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others.

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Significance of Rosseland’s Radiative Process on Reactive Maxwell Nanofluid Flows over an Isothermally Heated Stretching Sheet in the Presence of Darcy–Forchheimer and Lorentz Forces: Towards a New Perspective on Buongiorno’s Model

Thermal radiation and thermophoretic particle deposition have important applications in research and engineering. These two principles are employed in practical applications such as electrical fuel, projectiles, thermal transportation, renewable energy, nuclear power plants, gas turbines, and aerospace engineering. In light of the aforementioned applications, the current study investigates the stagnation point hybrid CNTs movement around a rotating sphere in the existence of thermal radiation and thermophoretic particle deposition. Using appropriate similarity factors, nonlinear governing equations are converted into ordinary differential equations. The Runge Kutta Fehlberg 45 (RKF-45) order and a shooting approach are used to find the numerical results of the simplified equations and boundary conditions. The numerical findings are presented graphically. It is explored how different limitations impact their individual profiles. According to the research, primary velocity increases with acceleration parameter but decreases with secondary velocity. As the radiation parameter value increases, so does the thermal distribution. Concentration decreases as both the Schmidt number and the thermophoretic parameter decrease. The heat dispersion rate heightens as the percentage of volume fraction of solid and the radiation parameter increase. Mano CNTs have a higher primary velocity than hybrid CNTs. 

Flow of hybrid CNTs past a rotating sphere subjected to thermal radiation and thermophoretic particle deposition

The present contribution focuses on heat transmission in the conjugate mixed bioconvection flow of Carreau nanofluid with swimming gyrotactic microorganisms through an inclined stretchable cylinder with variable magnetic field impact and binary chemical reaction. Additionally, the investigation involves the aspects of variable decrease or increase in heat source and non-uniform thermal conductivity. A passively controlled nanofluid pattern is used to estimate this nano-bioconvection flow case, which is believed to be more physically accurate than the earlier actively controlled nanofluid typically employed. One of essential features of this investigation is the imposition of a zero-mass flux condition at the surface of the cylinder. Through the implementation of an appropriate transformation, the nonlinear PDE system is mutated into similar equations. The flow equations thus obtained are solved numerically to explore the influence of the physical constraints involved through implementation with the aid of the MATLAB bvp4c code. The solutions were captured for both zero and non-zero bioconvection Rayleigh number, i.e., for flow with and without microorganisms. The present numerical results are compared with the available data and are determined to be in excellent agreement. The significant result of the present article is that the degree of nanoparticle concentration in the nanofluid exhibits an increasing trend with higher values of activation energy constraint.

https://www.mdpi.com/2227-7390/10/3/504/pdf?version=1644392229

Influence of Bioconvection and Chemical Reaction on Magneto—Carreau Nanofluid Flow through an Inclined Cylinder

The present work investigates the thermophoresis and Brownian motion effects in nanofluid flow over a curved stretching sheet (CSS). Also, the Cattaneo–Christov heat flux and Stefan blowing (SB) conditions are considered for studying heat and mass transport characteristics. The present work's novelty is associated with considerations of convective boundary and SB conditions in nanomaterial flow over a CSS. The coupled partial differential equations are changed to ordinary differential equations by employing suitable similarity variables, and the resultant model is numerically handled using Runge–Kutta–Fehlberg's fourth fifth‐order method with the shooting scheme. The stimulation of the involved parameters/numbers on the flow, mass, and heat fields is broadly deliberated using suitable graphs. The present analysis's significant relevant outcomes are that the inclination in thermophoresis and Brownian motion parameters increases the heat transfer. The inclined values of the Brownian motion parameter decay the mass transfer. Furthermore, the increased values of both Schmidt number and SB parameter drop the mass transport. The increased values of the Brownian motion parameter and Schmidt number decays the rate of mass transference.

Cattaneo–Christov heat flux model for nanofluid flow over a curved stretching sheet: An application of Stefan blowing

Abstract The flow and heat transfer in thin film of Cu-nanofluid over a stretching sheet by considering different shape factors (platelets, blades, bricks, sphere and cylinder) along with slip and convective boundary conditions is investigated. The governing partial differential equations are converted to nonlinear ordinary differential equations by means of suitable similarity transformation and then solved by using BVP4C in MATLAB. The physical significance of various parameters on velocity and temperature profiles are investigated and provided in the form of table and also presented graphically. It is noted that the Platelet-shaped nanoparticles has the highest heat transfer rate as compare to other particle’s shapes. 

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Thin film flow and heat transfer of Cu-nanofluids with slip and convective boundary condition over a stretching sheet

The wide range of industrial applications of flow across moving or static solid surfaces has aroused the curiosity of researchers. In order to generate a more exact estimate of flow and heat transfer properties, three-dimensional modelling must be addressed. This plays a vital role in metalworking operations, producing plastic and rubber films, and the continuous cooling of fibre. In view of the above scope, an incompressible, laminar three-dimensional flow of a Casson nanoliquid in the occurrence of thermophoretic particle deposition over a non-linearly extending sheet is examined. To convert the collection of partial differential equations into ordinary differential equations, the governing equations are framed with sufficient assumptions, and appropriate similarity transformations are employed. The reduced equations are solved by implementing Runge Kutta Fehlberg 4th 5th order technique with the aid of a shooting scheme. The numerical results are obtained for linear and non-linear cases, and graphs are drawn for various dimensionless constraints. The present study shows that improvement in the Casson parameter values will diminish the axial velocities, but improvement is seen in thermal distribution. The escalation in the thermophoretic parameter will decline the concentration profiles. The rate of mass transfer, surface drag force will reduce with the improved values of the power law index. The non-linear stretching case shows greater impact in all of the profiles compared to the linear stretching case.

Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet

The current study focuses on the characteristics of flow, heat, and mass transfer in the context of their applications. There has been a lot of interest in the use of non-Newtonian fluids in biological and technical disciplines. Having such a substantial interest in non-Newtonian fluids, our goal is to explore the flow of Oldroyd-B liquid over a stretching sheet by considering Cattaneo–Christov double diffusion and heat source/sink. Furthermore, the relaxation chemical reaction and thermophoretic particle deposition are considered in the modelling. The equations that represent the indicated flow are changed to ordinary differential equations (ODEs) by choosing relevant similarity variables. The reduced equations are solved using the Runge–Kutta–Fehlberg fourth–fifth order technique (RKF-45) and a shooting scheme. Physical descriptions are strategized and argued using graphical representations to provide a clear understanding of the behaviour of dimensionless parameters on dimensionless velocity, concentration, and temperature profiles. The results reveal that the rising values of the rotation parameter lead to a decline in the fluid velocity. The rise in values of relaxation time parameters of temperature and concentration decreases the thermal and concentration profiles, respectively. The increase in values of the heat source/sink parameter advances the thermal profile. The rise in values of the thermophoretic and chemical reaction rate parameters declines the concentration profile.

The Impact of Cattaneo–Christov Double Diffusion on Oldroyd-B Fluid Flow over a Stretching Sheet with Thermophoretic Particle Deposition and Relaxation Chemical Reaction

Bheemasandra M. Shankaralingappa

Papers

Influence of Thermophoretic Particle Deposition on the 3D Flow of Sodium Alginate-Based Casson Nanofluid over a Stretching Sheet

The Impact of Cattaneo–Christov Double Diffusion on Oldroyd-B Fluid Flow over a Stretching Sheet with Thermophoretic Particle Deposition and Relaxation Chemical Reaction