Entropy analysis of nanofluid convection in a heated porous microchannel under MHD field considering solid heat generation

Highlights

• Entropy generation of nanofluid in a porous microchannel is studied.

• Two-energy-equation model has been used for porous media.

• MHD field noticeably affects the distribution of temperature and velocity

• Increments in φ reduced the deviation between the two models

Abstract

Present study analyzes the issue of entropy generation of water with Al₂O₃ nanoparticles in a horizontal porous microchannel heated symmetrically. 2D distribution of temperature in both phases are derived using two-energy-equation model. An analytic investigation is carried out and the parameters of magnetohydrodynamic (MHD) field, solid heat generation and symmetric thermal condition are explored thoroughly. The results revealed that the MHD field noticeably affects the distribution of temperature and velocity and as an output the heat transfer irreversibilities during the process. The solid and fluid heat transfer irreversibilities for the case under MHD field are lower than those of the case without it, which proves the advantages to MHD field in declining the heat transfer irreversibility. Then, it was obtained that when Ha number is constant and Reynolds number has the optimum value of 6.5, total entropy generation is minimum and it decreases when MHD is intensified at Re_op. Also MHD was effective merely when the value of Reynolds number was lower than the critical value. By applying heat generation to the solid, for the MHD cases, no significant changes were observed in MHD irreversibility, however, entropy generation of the solid was achieved to be the most effective parameter and the value of total irreversibility increased noticeably. The analysis of thermal equilibrium and non-equilibrium models and the differences in irreversibilites showed that the increments in suspension of nanoparticles reduced the deviation between the two models, and intensification of Ha number at low biot numbers further reduces it.

Introduction

In order to miniaturize new electronic systems, thermal management of high heat fluxes as a result of different uses of such systems is becoming vital. On the other side, the generated heat in electronic components has a crucial effect on the operation of the whole system to hold the temperature of the chips in a safe zone. Microchannels are considered to be as one of the most efficient systems to meet these characteristics due to being small in size and dimensions and excess-heat removal capability. Also, they have various applications in automotive, computer and aerospace [1]. In this manner, a large number of articles have been examined about thermal characteristics of different types of microchannels over the recent decades. Generally, microporous heat exchangers perform much better than the normal ones thermally [2], and porous medium is broadly employed to improve the heat transfer efficiency of different heating systems [[3], [4], [5]]. The heat generation in porous-medium can be emanated from different processes including electromagnetic heat generation [6], joule heating [7] and radiation [8].

There are growing interests to achieve optimal heating systems by analyzing entropy generation in different ways. Entropy generation is strongly related thermodynamic irreversibilities in a process, both of which are essential parts of the real processes. Due to the second low thermodynamic, the generation of entropy is inevitable. Entropy generation reduction of nanofluid when flowing through a porous MHD channel can usefully influence the required input power to obtain appropriate heat transfer and mass flow rate. Hence, in most heat removal systems, it is worth specifying the parameters contributed to entropy generation for the purpose of reducing the influences and increasing their useful work [9].

In addition, a large amount of research has been carried out to analyze the entropy generation, which is proposed by Bejan [10]. Many studies on entropy generation of the permeable media employ the entropy generation, assuming that both phases are thermally equal. However, some researchers considered the thermal inequality between phases inside the porous medium. The thermal non-equilibrium irreversibility function was suggested by Ting et al. [11] by using differential model. They investigated the viscous dissipation effect on the heat transfer process and fluid flow irreversibility in a porous space surrounded by a microchannel. Employing the similar technique, Torabi et al. [12] analytically scrutinized entropy generation of a water based flow with copper particles through a porous duct considering partial filling.

On the other hand, applying an electric or electromagnetic field (known as MHD pumps) to microfluidic devices such as micropumps would be a non-intrusive method for fluid control [13,14]. Hashim et al. [15] studied the thermophysical properties of the flow of Williamson fluid with nanoparticles, by employing a numerical approach to perform the simulations. Their results revealed that when magnetic field becomes stronger, the velocity of the nanofluid and boundary layer decrease. Also, nanofluid flows under MHD fields in microchannels were investigated in various articles [[16], [17], [18]]. Zhang et al. [19] analytically studied MHD effect on a nanofluid flow within a porous duct. They displayed that MHD field can significantly affect the velocity and temperature fields. Solar radiation effects of nanofluid flow due to MHD impact were investigated by Mushtaq et al. [20] by applying a numerical method to solve the resulting differential equations. They revealed that the temperature gradient of the wall was intensified by the radiation factor. Jian [21] provided an unsteady investigation of MHD flow and generation of entropy through a microchannel under pressure and electronic effects. Habibi et al. [22] examined a theoretical examination to minimize the entropy generation through a duct under MHD field. They showed that an optimum value for the overall generated entropy is obtained which increases by increasing the electrical efficiency of power generator. Investigation of MHD nanofluid free convective hydrothermal analysis was performed by Shermet et al. [23]. They reported that the change in waviness of enclosure can enhance the heat transfer. Sheikholeslami et al. [[24], [25], [26], [27], [28], [29]] implemented many studies in recent years about the influence of variable magnetic force on forced convection. Also, Sheikholeslami and Abelman [30] employed new model to analyze a nanofluid migration. They also investigated the annulus heat exchange under an axial MHD field.

Considering the importance of solid heat generation in engineering applications and the fact that its effect on forced convection is neglected in many researches [11,31,32], it is investigated here. In an exact solution research, Tiew et al. [33] scrutinized the frictional entropy generation in a heated permeable channel. The results revealed that intensifying the solid-phase heat generation notably decreases the differences between the two models to be under 1%.

In this work, convection of water-based nanofluid containing water and Al₂O₃ nanoparticles in a porous horizontal microchannel under a magnetohydrodynamic (MHD) field was investigated. 2D temperature distributions are taken out for two phases of fluid and solid. In the end, an analytical solution of the non-equilibrium entropy generation is carried out.