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PurposeThis study aims to investigate the flow and heat transfer of a hybrid nanofluid through an exponentially stretching/shrinking sheet along with mixed convection and Joule heating. The nanoparticles alumina (Al2O3) and copper (Cu) are suspended into a base fluid (water) to form a new kind of hybrid nanofluid (Al2O3-Cu/water). Also, the effects of constant mixed convection parameter and Joule heating are considered.Design/methodology/approachThe governing partial differential equations are transformed into ordinary differential equations (ODEs) using appropriate similarity transformations. The transformed nonlinear ODEs are solves using the bvp4c solver available in MATLAB software. A comparison of the present results shows a good agreement with the published results.FindingsDual solutions for hybrid nanofluid flow obtained for a specific range of the stretching/shrinking parameter values. The values of the skin friction coefficient increases but the local Nusselt number decreases for the first solution with the increasing of the magnetic parameter. Enhancing copper volume fraction and Eckert number reduces the surface temperature, which intimates the decrement of heat transfer rate for the first and second solutions for the stretching/shrinking sheet. In detail, the first solution results show that when the Eckert number increases as 0.1, 0.4 and 0.7 at λ = 1.5, the temperature variations reduced to 10.686840, 10.671419 and 10.655996. While in the second solution, keeping the same parameters temperature variation reduced to 9.750777, 9.557349 and 9.364489, respectively. On the other hand, the results indicate that the skin friction coefficient increases with copper volume fraction. This study shows that the thermal boundary layer thickness rises due to the rise in the solid volume fraction. It is also observed that the magnetic parameter, copper volume fraction and Eckert number widen the range of the stretching/shrinking parameter for which the solution exists.Practical implicationsIn practice, the investigation on the flow and heat transfer of a hybrid nanofluid past an exponentially stretching/shrinking sheet with mixed convection and Joule heating is crucial and useful. The problems related to hybrid nanofluid have numerous real-life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical and drug reduction.Originality/valueIn specific, this study focuses on increasing thermal conductivity using a hybrid nanofluid mathematical model. The novelty of this study is the use of natural mixed convection and Joule heating in a hybrid nanofluid. This paper can obtain dual solutions. The authors declare that this study is new, and there is no previous published work similar to the present study.

Purpose This study aims to investigate the heat transfer characteristic of the magnetohydrodynamic (MHD) hybrid nanofluid over the linear stretching and shrinking surface in the presence of suction and thermal radiation effects. Design/methodology/approach Mathematical equations are transformed into pairs of self-similarity equations using similarity transformation. Boundary value problem solver (bvp4c) in MATLAB was adopted to solve the system of reduced similarity equations. In this study, the authors particularly examine the flow and heat transfer properties for different values of suction and thermal radiation parameters using single-phase nanofluid model. A comparison of the present results shows a good agreement with the published results. Findings It is noticed that the efficiency of heat transfer of hybrid nanofluid (Cu-Al2O3/H2O) is greater than the nanofluid (Cu/H2O). Furthermore, it is also found that dual solutions exist for a specific range of the stretching/shrinking parameter with different values of suction and radiation parameters. The results indicate that the skin friction coefficient and the local Nusselt number increase with suction effect. The values of the skin friction coefficient increases, but the local Nusselt number decreases for the first solution with the increasing of thermal radiation parameter. It is also observed that suction and thermal radiation widen the range of the stretching/shrinking parameter for which the solution exists. Practical implications In practice, the investigation on the flow and heat transfer of MHD hybrid nanofluid through a stretching/shrinking sheet with suction and thermal radiation effects is very important and useful. The problems related to hybrid nanofluid has numerous real-life and industrial applications, for example microfluidics, manufacturing, transportation, military and biomedical, etc. Originality/value In specific, this study focused on increasing thermal conductivity using a hybrid nanofluid mathematical model. This paper is able to obtain the dual solutions. To the best of author’s knowledge, this study is new and there is no previous published work similar to present study.

This paper deals with a stagnation-point boundary layer flow and heat transfer of a Casson fluid towards a stretching/shrinking sheet. The main objective of the present study is to analyse the effects of the injection parameter and heat source on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. It is vital to study the heat transfer and fluid flow problems in the presence of injection and heat source effects due to a wide variety of applications in engineering and industry. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations by using similarity transformation, before being solved numerically using the boundary value problem solver bvp4c routine in MATLAB. Dual solutions are found to exist for the shrinking sheet case, whereas the solution is unique for the stretching case. The stability analysis has been performed to determine the stable solution. It is shown that the first solutions are stable and physically reliable while the second solutions are not. Further, the present results have been compared with the previous published results for a particular case and the comparisons are found to be in good agreement. The local Nusselt number is decreases with an increase in heat source parameter. Rising values of the injection parameter has decreases both the skin friction coefficient and the local Nusselt number.