Hybrid nanofluid flow through an exponentially stretching/shrinking sheet with mixed convection and Joule heating

Abstract

Purpose This 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/approach The 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. Findings Dual 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 implications In 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/value In 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.

Three Dimensional MHD Hybrid Nanofluid Flow with Rotating Stretching/Shrinking Sheet and Joule Heating

“…Besides, velocity slip between the phases can be neglected since the shape and size of the nanoparticles are uniform and significantly small, respectively (Anuar et al, [36]). The above-mentioned physical model can be represented by the basic steady conservation of mass, momentum, and thermal energy governing equations as follows (Yashkun et al, [41]; Anuar et al, [36])…”

“…Magnetohydrodynamics (MHD) is the study of the movement of electrically conducting fluids as in the existence of a magnetic field. Engineers used the MHD concept in the design of a wide range of applications in industries, notably in flow meters, space vehicle impulsion, nuclear waste disposal, MHD pumps, heat exchangers generators, nuclear reactor cooling, and geothermal energy extractors (Yashkun et al, [41]). Devi and Devi [25] investigated numerically a two-dimensional MHD steady hybrid nanofluid flow across a stretching plate with suction as well as Newtonian heating.…”

“…Joule heating is the method of producing heat by conducting an electric current through a resistor, also identified as Ohmic heating (Yashkun et al, [41]). Joule heating is used in many applications, for instance, incandescent light bulb, cartridge heaters, resistance ovens, electric heaters, food processing apparatus, soldering irons, electric fuses, and electric stoves, to name a few (Yashkun et al, [41]). A two-dimensional MHD steady hybrid nanofluid flow by a radially stretching/shrinking sheet through Joule heating was investigated by Khashi'ie et al, [50].…”

“…However, no shift in boundary layer separation was observed for different Eckert number parameters. Yashkun et al, [41] explored the heat transfer behavior of a two-dimensional steady flow within an exponentially stretching/shrinking layer, as well as Joule heating and mixed convection in hybrid nanofluid. Finding on the influence of Eckert number on the temperature of dual solutions was found similar to Yan et al, [51].…”

“…Researches on the hybrid nanofluid with the effect of MHD and Joule heating were currently limited in the case of two-dimensional steady flow (see Yashkun et al, [41], Khashi'ie et al, [50], Yan et al, [51]). From the literature review on preceding studies, it is crucial to consider such a problem as three-dimensional flow as this setting allows more comprehensive and realistic applications in the real-world.…”