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The purpose of this paper is to address the impact of induced magnetic field in mixed convective stagnation flow of TiO₂-Cu-water hybrid nanofluid towards a stretchable sheet. Non-linear thermal radiation and heat source/sink are accounted. Flow of hybrid nanofluid is discussed. Non-linear partial differential expressions are converted to ordinary ones through appropriate transformations.

The obtained systems are solved for convergence solutions via homotopy analysis method. Graphical results are discussed for different physical variables on the velocity, induced magnetic field and temperature fields for both Cu water nanofluid and TiO₂-Cu-water hybrid nanofluid. Finally, the effect of different physical variables on skin friction coefficient (C_fx) and Nusselt number Nu_x in the presence of water nanofluid and TiO₂-Cu-water hybrid nanofluid are discussed.

Velocities and induced magnetic field are increasing functions of mixed convection parameter and nanoparticle volume fraction. Temperature rises for higher radiation parameter. Skin friction is greater in case of Cu-water nanoliquid, while Nusselt number is less for Cu-water nanofluid when they are compared with hybrid nanoliquid TiO₂-Cu-water.

No such work is not yet present in the literature.

This paper aims to present an analytical investigation of energy and exergy performance on a solar flat plate collector (SFPC) with Cu-CuO/water hybrid nanofluid, Cu/water and CuO/water nanofluids as collector running fluids.

Heat transfer characteristics, pressure drop and energy and exergy efficiencies of SFPC working on these nanofluids are investigated and compared. In this study, a comparison is made by varying the mass flow rates and nanoparticle volume concentration. Thermophysical properties of hybrid nanofluids are estimated using distinctive correlations available in the open literature. Then, the influence of these properties on energy and exergy efficiencies of SFPC is discussed in detail.

Energy analysis reveals that by introducing the hybrid nanoparticles in water, the thermal conductivity of the working fluid is enhanced by 17.52 per cent and that of the individual constituents is enhanced by 15.72 and 15.35 per cent for Cu/water and CuO/water nanofluids, respectively. This resulted in 2.16 per cent improvement in useful heat gain for hybrid nanofluid and 1.03 and 0.91 per cent improvement in heat gain for Cu/water and CuO/water nanofluids, respectively. In line with the above, the collector efficiency increased by 2.175 per cent for the hybrid nanofluid and 0.93 and 1.05 per cent enhancement for Cu/water and CuO/water nanofluids, respectively. Exergy analysis elucidates that by using the hybrid nanofluid, exergy efficiency is increased by 2.59 per cent, whereas it is 2.32 and 2.18 per cent enhancement for Cu/water and CuO/water nanofluids, respectively. Entropy generation is reduced by 3.31, 2.35 and 2.96 per cent for Cu-CuO/water, Cu/water and CuO/water nanofluids, respectively, as compared to water.

However, this is associated with a penalty of increment in pressure drop of 2.92, 3.09 and 2.74 per cent for Cu-CuO/water, Cu/water and CuO/water nanofluids, respectively, compared with water.

It is clear from the analysis that Cu-CuO/water hybrid nanofluids possess notable increment in both energy and exergy efficiencies to use them in SFPCs.

The purpose of this paper is to investigate the combined effects of buoyancy force and variable viscosity on unsteady flow and heat transfer of water-based nanofluid containing copper and alumina as nanoparticles through a porous pipe.

Using the Boussinesq and boundary-layer approximations with Buongiorno nanofluid model. The governing nonlinear partial differential equations for the continuity, momentum and energy balance are formulated. The equations obtained are solved numerically using a semi-discretization finite difference method (know) as method of line coupled with Runge-Kutta-Fehlberg integration scheme.

Numerical results for the skin-friction, heat transfer and for the velocity and temperature profiles are obtained. The results show that with suction, Cu-water produces higher skin friction and heat transfer rate than Al₂O₃-water. Both nanofluids velocity and temperature increase with a decrease in viscosity and an increase in buoyancy force intensity.

Buoyancy-driven flow and heat transfer in porous geometries has many significant applications in industrial and engineering such as, electrical and microelectronic equipments, solar-collectors, geothermal engineering, petroleum reservoirs, thermal buildings insulation. This work provides very important information for researchers on this subject.

This paper illustrates the effects of buoyancy force and temperature dependent on heat transfer and fluid flow problem using Cu-water and Al₂O₃-water nanofluids in a porous pipe.

The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature.

The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations.

The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m.

The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered.

The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods).

This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.

The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al₂O₃/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion and thermophoresis are considered here.

Similarity transformations are used to reduce the governing partial differential equations to a system of ordinary (similarity) differential equations. A MATLAB solver called the bvp4c is then used to compute the numerical solutions of equations (12) to (14) subject to the boundary conditions of equation (15). Then, the effects of various physical parameters on the flow and thermal fields of the hybrid nanofluid are analyzed.

Multiple (dual) solutions are found for the basic boundary layer equations. A stability analysis is performed to see which solutions are stable and, therefore, applicable in practice and which are not stable. Besides that, a comparison is made between the hybrid nanofluid and a traditional nanofluid, Cu/water. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than that of the other nanofluid. Thus, the hybrid nanofluid has a higher heat transfer rate than the other nanofluid. However, the increase in the shrinking parameter reduces the velocity of the hybrid nanofluid.

The present results are original and new for the study of the flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al₂O₃/water hybrid nanofluid.

The purpose of this paper is to investigate numerically the unsteady MHD Couette flow and heat transfer of viscous, incompressible and electrically conducting nanofluids between two parallel plates in a rotating channel.

The nanofluid is set in motion by the combined action of moving upper plate, Coriolis force and the constant pressure gradient. The channel rotates in unison about an axis normal to the plates. The nonlinear governing equations for velocity and heat transfer are obtained and solved numerically using semi-discretization, shooting and collocation (bvp4c) techniques together with Runge-Kutta Fehlberg integration scheme.

Results show that both magnetic field and rotation rate demonstrate significant effect on velocity and heat transfer profiles in the system with Cu-water nanofluid demonstrating the highest velocity and heat transfer efficiency. These numerical results are in excellent agreements with the results obtained by other methods.

This paper provides a very useful source of information for researchers on the subject of hydromagnetic nanofluid flow in rotating systems.

Couette flow of nanofluid in the presence of applied magnetic field in a rotating channel is investigated.

The purpose of this paper is to theoretically investigate the boundary layer nature of magnetohydrodynamic nanofluid flow past a vertical expanding surface in a rotating geometry with viscous dissipation, thermal radiation, Soret effect and chemical reaction.

The self-similarity variables are deliberated to transmute the elementary governing equations. The analytical perturbation technique is used to elaborate the united nonlinear ODEs.

To check the disparity on the boundary layer nature, the authors measured two nanofluids, namely, Cu-water and Cu-Kerosene based nanofluids. It is found that the Cu-water is effectively enhancing the thermal conductivity of the flow when compared with the Cu-kerosene.

Till now no analytical studies are reported on heat transfer enhancement of the rotating nanofluid flow by considering two different base fluids.

The purpose of this paper is to investigate the combined effects of viscous dissipation and Newtonian heating on boundary-layer flow over a flat plate for three types of water-based nanofluids containing metallic or nonmetallic nanoparticles such as copper (Cu), alumina (Al2O3), and titania (TiO2) for a range of nanoparticle volume fractions.

The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically by a Runge-Kutta-Fehlberg method with shooting technique.

It is found that the heat transfer rate at the plate surface increases with increasing nanoparticle volume fraction and Biot number, while it decreases with the Brinkmann number. Moreover, the heat transfer rate at the plate surface with Cu-water nanofluid is higher than that of Al2O3-water and TiO2-water nanofluids.

The heat transfer enhancement performances presented by nanofluids have led to innovative way of improving the thermal conductivities of working media in engineering and industries. This work provides a very useful source of information for researchers on this subject.

This paper illustrates the combined effects of viscous dissipation and Newtonian heating on boundary-layer flow of nanofluids past a flat plate.

Outstanding features such as thermal conductivity and superior electrical conductivity of nanofluids unfold a new window in the context of their extensive applications in engineering and industrial domains. The purpose of this study to simulate numerically the magneto-nanofluid flow and heat transfer over a curved stretching surface. Heat transport is explored in the presence of viscous dissipation. At the curved surface, the convective boundary condition is adopted. Three different nanoparticles, namely, copper, aluminium oxide and titanium dioxide are taken into consideration because of easily available in nature.

The basic flow equations are framed in terms of curvilinear coordinates. The modelled partial differential equations are transformed into a system of non-linear ordinary differential equations by means of appropriate similarity transformation. The subsequent non-linear system of equations is then solved numerically by using the Runge–Kutta–Felhberg method with the shooting scheme via bvp4c MATLAB built-in function. Impacts of various physical parameters on velocity, pressure and temperature distributions, local skin-friction coefficient, local Nusselt number and wall temperature are portrayed through graphs and tables followed by a comprehensive debate and physical interpretation.

Graphical results divulge that augmenting values of the magnetic parameter cause a decline in velocity profiles and stream function inside the boundary layer. The magnitude of the pressure function inside the boundary layer reduces for higher estimation of curvature parameter, and it is also zero when the curvature parameter goes to infinity. Furthermore, the temperature is observed in a rising trend with growing values of the magnetic parameter and Biot number.

This research study is very pertinent to the expulsion of polymer sheet and photographic films, metallurgical industry, electrically-conducting polymer dynamics, magnetic material processing, rubber and polymer sheet processing, continuous casting of metals, fibre spinning, glass blowing and fibre, wire and fibre covering and sustenance stuff preparing, etc.

Despite the huge amount of literature available, but still, very little attention is given to simulate the flow configuration due to the curved stretching surface with the convective boundary condition. Very few papers have been examined on this topic and found that its essence inside the boundary layer is not any more insignificant than on account of a stretching sheet. A numerical comparison with the published works is conducted to verify the accuracy of the present study.

The purpose of this paper is to study heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet placed in saturated porous medium with internal heat generation or absorption. The authors further introduce a new algorithm for solving heat transfer problems in fluid mechanics. The model used for the nanofluid incorporates the nanoparticle volume fraction parameter and a consideration of the chemical reaction effects among other features.

The partial differential equations for heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet were transformed into a system of nonlinear ordinary differential equations. Exact solutions for the boundary layer equations were obtained in terms of a confluent hypergeometric series. A novel spectral relaxation method (SRM) is used to obtain numerical approximations of the governing differential equations. The exact solutions are used to test the convergence and accuracy of the SRM.

Results were obtained for the fluid properties as well as the skin friction, and the heat and mass transfer rates. The results are compared with limiting cases from previous studies and they show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to numerical methods for solving nonlinear boundary value problems.

A new algorithm is used for the first time in this paper. In addition, new exact solutions for the energy and mass transport equations have been obtained in terms of a confluent hypergeometric series.