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As in the case of enhancing the performance of high-temperature superconductors, the dynamics of colloidal mixes of water and copper-based nanoparticles exposed to an inclined magnetic field owing to free convection is a recognized issue. However, nothing is known about the dynamics mentioned above when the radius and inter-particle spacing of copper nanoparticles grow in the presence of Joule dissipation, mass flux owing to a temperature gradient, internal heating, and heat flux due to concentration gradient. When the ratio of momentum to thermal diffusivities is incorporated into the momentum equation using appropriate models, the governing equation (i.e. Partial Differential Equations) that models the transport mentioned above was scaled, solved numerically, and simulated with a focus on the nanoparticle radius and the spacing between copper nanoparticles. The resultant non-linear coupled Ordinary Differential Equation was solved using the MATLAB integrated (i.e. bvp4c software package) and the shooting approach (i.e. fourth-order Runge–Kutta integration strategy shrk4). Just because of the resulting improvement in the temperature distribution, increasing the ratio of momentum to thermal diffusivities leads to a more pronounced local skin friction within the layers adjacent to the wall and heat transfer. Because buoyancy forces are exclusively associated with the growth of concentration difference, they cause the distance covered by the transport phenomenon in terms of the spatial domain to decrease. Higher ratios of momentum to thermal diffusivities cause the full-fledged sheer stress profile, which is proportional to friction across fluid layers, to rise.

Sequel to the industrial usage of ethylene-glycol conveying copper nanoparticles, nothing is known on how the dynamics differ from ethylene-glycol conveying copper and iron oxide nanoparticles when there is Coriolis force, slip and thermal jump. This report presents the outcome of a study on the motion and heat transfer across both non-Newtonian electro-conducting Carreau hybridized nanofluids via the porous medium on a three-dimensional rotating stretchable plate. The model for hybridization of the mixture of copper (Cu) and Iron oxide (Fe3O4) nanoparticles in the ethylene-glycol base fluid under thermal radiation, uneven heat source and wall slip attributes were developed and presented. The reduction of the model equations from partial into ordinary differential equations was carried out using similarity transformation variables. Pseudo-Spectral Method (PSM) was employed to solve the emerged boundary value problem. Exponential space-based heat source/sink, stretching rates, and temperature jump levels, heat transfer rates are maximal during ethylene-glycol conveying copper nanoparticles but minimal during ethylene-glycol motion conveying copper and iron oxide nanoparticles. The hybridization of the nanoparticles induces a higher heat propagation than the unitary nanofluid for all the physical parameters considered, whereas the strength of the surface drag force depreciates with a higher magnitude of the Weissenberg number.

During the homogeneous-heterogeneous autocatalytic chemical reaction in the dynamics of micropolar fluid, relaxation of heat transfer is inevitable; hence Cattaneo-Christov heat flux model is investigated in this report. In this study, radiative heat flux through an optically thick medium is treated as nonlinear due to the fact that thermal radiation at low heat energy is distinctly different from that of high heat energy, hence classical approach of using Taylor series for simplification is ignored and implicit differentiation is used leading to temperature parameter. Uniqueness of the present analysis is the consideration of cubic autocatalytic chemical reaction between the homogeneous bulk fluid and two species of catalyst at the wall. Application of similarity analysis enabled us to recast the flow equations into a set of coupled nonlinear ODEs. The resulting equations along with the appropriate conditions are solved computationally. Graphical illustrations of the effect of pertinent parameters on momentum, heat and mass boundary layers are presented and discussed. The concentration of the homogeneous bulk fluid with microstructures and catalyst at the surface decreases and increases with diffusion ratio, respectively. Buoyancy has a decreasing effect on temperature distribution.

Homogenous and heterogeneous reactions play an essential role in combustion, polymer production, ceramic production, distillation, catalysis, and biochemical procedures. Haemoglobin molecules are magnetic from a biochemical perspective. The existence of magnetic resonance imaging (MRI) and electrical gadgets with an electromagnetic field allows explaining the essential functions of living species. Inspired by these ideas, the current research project aims to investigate the influence of homogeneous and heterogeneous responses on the peristaltic flow of MHD Jeffrey fluid. The geometry consists of a non-uniform vertical channel when subjected to velocity slip and temperature slip conditions. The solution treatment involves the perturbation series analysis strategy for solving the governing partial differential equations. Entropy generation analyses have been carried out. The consequences of velocity, temperature, skin friction, Nusselt number, pressure rise versus mean circulation, trapping phenomena, homogenous, and heterogeneous reaction are assessed for major restraints getting in the problem with the help of graphs. Furthermore, the entropy generation which plays a vital role in understanding numerous biological processes. Therefore, the present study has a potential application in industry and medicine.

Sequel to all the published facts on the dynamics of water and ethylene glycol on a convectively heated surface conveying alumina and copper nanoparticles as applicable in engineering and industry, noting is known on the significance of haphazard motion and thermo-migration. For the case of Al2O3/Cu nanoparticles, the governing equations that model the transport phenomena along a vertical surface were non-dimensionalized. The obtained dimensionless equation (ODE BVP) was numerically solved in MATLAB using the text bvp4c in-built solver. The temperature distribution is minimal when convectively heating at the horizontal wall beneath the transport phenomenon is small in magnitude. When Biot number and thermo-migration are high, and the base fluid is less thick, there is minimal friction between the wall and the last layer of hybrid nanofluid due to increasing haphazard motion of alumina/copper nanoparticles (i.e., water). Heating of the base fluid is a factor for reducing friction as water is heated faster due to lower density than ethylene glycol.

In this numerical examination, the thermal stability of an electrically conducting nanofluid is deliberated comprehensively by considering the presence of an externally applied magnetic field along with an imposed vertical throughflow. Additionally, this thin nanofluidic layer is supposed to have a Newtonian rheological behavior, heated from below, and confined horizontally between two permeable rigid plates of infinite extension. Herein, the governing conservation equations are strengthened realistically by the revised version of the Buongiorno's mathematical model, in which the vertical component of the mass flux of solid nanoparticles is presumed to vanish entirely at the horizontal permeable boundaries. After specifying the basic state of the present nanofluid problem, the linear stability theory and normal mode analysis technique are applied properly to obtain the principal stability equations. Finally, the eigenvalue problem derived analytically is tackled thereafter numerically via the Chebyshev-Gauss-Lobatto Spectral Method (CGLSM), in which the thermal Rayleigh number is chosen as an eigenvalue. As a main result, it was demonstrated that the throughflow effect exhibits a dual behavior on the complex dynamics of the system. However, the excreted magnetic field has always a stabilizing impact on the nanofluidic medium.

The current work intends to investigate the magneto-hydrodynamic peristaltic flow of a non-Newtonian fluid through a tapered asymmetric channel. The transport of fluid with variable transport properties (viscosity and thermal conductivity) takes place through a porous medium. The problem is formulated under the basic assumptions of long wavelength and low Reynolds number. The perturbation technique has been implemented to yield the solution for momentum and energy equations. The pumping characteristics such as pressure rise and frictional force have been evaluated by Weddles rule using MATLAB software. The solutions which are graphed indicate that the variable viscosity plays a major role in regulating the fluid velocity in the central part of the channel. Also, as the channel becomes more divergent, the size of the bolus trapped in the peristaltic motion is found to increase.

Bonnet of a car, the upper surface of a pointed bullet and upper surface of the pointed part of an aircraft are typical examples of an upper horizontal surface of a paraboloid of revolution (uhspr). However, the flow of some fluids past these kinds of objects fit the description of Eyring-Powell fluid flow. Theoretical investigation of two-dimensional Eyring-Powell fluid flow over such object which is neither cone/wedge nor horizontal/vertical is investigated. It is assumed that the flow of Eyring-Powell fluid is induced by catalytic surface reaction and stretching fluid layers at the free stream. The numerical solutions of the governing equation are obtained using classical fourth order Runge-Kutta scheme together with shooting techniques. The impacts of the most important parameters on the flow are presented. It is concluded that the maximum velocity of the flow is ascertained when the flow is characterized as Newtonian fluid flow. On the surface of uhspr, rapid increase and suppress in the temperature distribution and concentration with an increase in the magnitude of one of the Eyring-Powell fluid parameters are guaranteed. A significant fall in the local skin friction coefficients is ascertained due to rise in the magnitude of thickness parameter. Keywords: Boundary layer analysis, Eyring-Powell fluid, Catalytic surface, Blasius flow, Heat transfer, Mass transfer

Flow and heat transfer behavior of magnetohydrodynamic Carreau and Casson fluids past an upper part of the paraboloid of revolution with space dependent internal heat source/sink is investigated theoretically. The buoyancy induced on the flow is considered in such way that the surface is neither vertical/horizontal nor wedge/cone. The equations that govern the flow are transformed using suitable similarity variables and solved numerically by employing R-K-F integration scheme. Graphical results are obtained to discuss the behavior of flow and temperature fields for various parameters of interest. Also the wall friction is computed and heat transfer coefficient is reduced. It is found that the boundary layers of temperature and velocity distributions are non-uniform for Carreau and Casson flows. Impact of drag force is high on Casson flow when equated with Carreau fluid. Keywords: Magnetohydrodynamic (MHD), Carreau fluid, Casson fluid, Paraboloid of revolution

Geometrically, the upper pointed surface of an aircraft and bonnet of a car are examples of upper horizontal surfaces of a paraboloid of revolution (uhspr). The motion of these objects strongly depends on the boundary layer that is formed within the immediate space on it. However, each of these surfaces is neither a horizontal/vertical nor cone/wedge and neither a cone nor a wedge. This article presents the motion of 2-dimensional Blasius flow of Carreau fluid on the surface of such object. The case in which the reaction between the Carreau fluid and catalyst at the surface produces significant temperature differences which consequently set up buoyancy-driven flows within the boundary layer is investigated. Single first-order Arrhenius kinetics is adopted to model the reaction on the surface of the catalyst situated on uhspr which initiates the free convection. Suitable similarity variables are applied to non-dimensionalized, parameterized and reduce the governing partial differential equations to a coupled ordinary differential equations (BVP). The BVP is solved numerically using the shooting technique. Temperature distribution in the flow of viscoelastic Carreau fluid is greater than that of a Newtonian fluid. Local heat transfer rate decreases faster when the Carreau fluid is characterized as shear-thinning. Maximum concentration is guaranteed at a small value of power-law index n and large value of thickness parameter. Keywords: Viscoelastic-Carreau fluid, Catalitic surface, Paraboloid of revolution, Numerical method, Uhspr, Boundary layer analysis

This study reports the enhanced heat transfer of electrically conducting magnetic-nanofluids with thermal radiation and inclined magnetic field effects. We consider water as a base fluid embedded with the two different types of aluminum alloy nanoparticles namely AA 7072 and AA 7075. AA 7072 is a special type of heat treatable aluminum alloy with 98% Al and 1% of Zn with the additives such as Si, Fe and Cu. Similarly, AA 7075 contains 90% Al, 5–6% Zn, 2–3% Mg, 1–2% Cu with the additives such as Si, Fe and Mn. Numerical results are explored with the aid of R-K and Newton’s techniques. Results are depicted diagrammatically and discussed on the common profiles of interest (velocity and temperature). The heat transfer rate of water-AA 7075 nanofluid is significantly high when compared with the rate of heat transfer of water-AA 7072 nanofluid.

Boundary layer flow of two non-Newtonian fluids past an upper horizontal surface of a paraboloid of revolution (uhspr) in the presence of nonlinear thermal radiation is investigated. A new concept of parameterization is introduced to achieve comparison between the flows of both fluids (i.e. switch momentum governing equation from Williamson fluid to Casson fluid). In this study, it is assumed that buoyancy and stretching at the wall induce Casson and Williamson fluid flow over this kind of surface which is neither a perfect horizontal/vertical nor inclined/cone. Influence of space dependent internal heat source is accommodated in the energy equation. The case of unequal diffusion coefficients of reactants A and B (high concentration of catalyst on uhspr) is considered. Since chemical reactant B is of higher concentration at the surface more than the concept described as cubic autocatalytic, the suitable schemes are herein described as isothermal quartic autocatalytic reaction and first order reaction. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically by using Runge-Kutta technique along with shooting method. Comparisons of the effects of some parameters on the flow profiles are illustrated graphically and discussed.

This article presents the effects of nonlinear thermal radiation and induced magnetic field on viscoelastic fluid flow toward a stagnation point. It is assumed that there exists a kind of chemical reaction between chemical species A and B. The diffusion coefficients of the two chemical species in the viscoelastic fluid flow are unequal. Since chemical species B is a catalyst at the horizontal surface, hence homogeneous and heterogeneous schemes are of the isothermal cubic autocatalytic reaction and first order reaction respectively. The transformed governing equations are solved numerically using Runge–Kutta integration scheme along with Newton’s method. Good agreement is obtained between present and published numerical results for a limiting case. The influence of some pertinent parameters on skin friction coefficient, local heat transfer rate, together with velocity, induced magnetic field, temperature, and concentration profiles is illustrated graphically and discussed. Based on all of these assumptions, results indicate that the effects of induced magnetic and viscoelastic parameters on velocity, transverse velocity and velocity of induced magnetic field are almost the same but opposite in nature. The strength of heterogeneous reaction parameter is very helpful to reduce the concentration of bulk fluid and increase the concentration of catalyst at the surface.