**1. Introduction**

Magnetohydrodynamic (MHD) pumps have been focus of research owing to various advantages over traditional pumps in many specific areas of application including biological fields, solar applications and heat transfer systems [1]. The major advantage of such pumps is that they are free of any moving parts. Additionally, the miniaturization of such pumps due to their simple structure, can be utilized in microfluidic systems, microcooling systems and microelectromechanical system (MEMS) applications [2,3]. In a few applications, where it is difficult to use conventional pumps such as molten metal pumping, these pumps are more useful and efficient. Moreover, the applications requiring no moving sections, for example, in spaceships and biological applications like blood pumping, these pumps can be used [4]. Out of various applications, one of the promising usages of MHD pumps is cooling of heat dissipating element. The coolant flow is generated by MHD pumps and can be made to

flow in the microchannel where the dissipated heat from the heat dissipating element is taken away. Use of microchannels in a cooling system is one of the efficient ways of dissipating heat [5,6]. In such instances, heat transfer effectiveness and the thermal behavior of a cooling system with its influencing factors need to be investigated.

Lemoff et al. [7] developed and presented one of the first MHD micropumps with AC current using Lorentz force to pump electrolytic solution in microchannel. The authors showed that the continuous flow without any pulse can be produced. Rivero and Cuevas [8] studied MHD micropumps in one and two-dimensional flow models for laminar flows in parallel plates and rectangular ducts by considering the influence of slip condition which can be used to design MHD micropumps and characterize the flow behavior in these microfluidic devices. The 2D model presented by the authors showed more accuracy with results of experimentation as compared to 1D model [8]. Zhao et al. [9] conducted an analytical study by using the separation of variables method for generalized Maxwell fluids in a MHD rectangular micropump operated under the AC electric field and found that for given oscillating Reynolds number, large Hartmann number leads to large amplitudes of velocity. Yousofvand et al. [10] investigated heat transfer and pumping performance of electromagnetic pump considering Cu-water nanofluid as working fluid and found that for low Hartmann numbers, body force increases whereas for Ha > 200, the opposite trend is observed. Moghaddam analytically investigated the MHD micropump performance considering circular channel. The author found that average dimensionless velocity initially increases with increase in Hartmann number and dimensionless radius. However, after attaining peak, the average dimensionless velocity decreases with increase in Hartmann number and dimensionless radius [11]. Miroshnichenko et al. [12] studied MHD natural convection in a partially open trapezoidal cavity under the influence of various magnetic field orientations and found that an increase in uniform magnetic field value decreases the rate of heat transfer. A comprehensive study of power-law fluids in MHD natural convection has been conducted by Kefayati [13,14]. Shirvan et al. [15] conducted numerical investigations on MHD flow in a square cavity with different inlet and outlet ports. The authors presented optimization of mean Nusselt number using orthogonal array optimization. Kiyasatfar et al. [16] investigated thermal behavior and fluid motion in direct current (DC) MHD pump by varying magnetic flux density, applied current and channel size. The authors found that the maximum velocity increases with increase in applied current and as Hartmann number increases the velocity profile becomes flatter. Larimi et al. [17] studied the effect of non-uniform transverse magnetic field arrangements with a different Reynolds number for magnetic nanofluids on heat transfer and found that applying external magnetic fluid is strongly effective in fluid cooling at low Reynolds number. Kolsi et al. [18] performed a numerical study for 3D MHD natural convection inside a cubical enclosure with an inclined plate and found an optimal inclination angle of 180◦ for the plate. Kefayati considered various flow types including non-Newtonian nanofluids [19], blood flow [20] and power-law fluids in an internal flow [21] with focus of investigation on the effects of the power-law index, Reynolds number on thermal behavior by varying magnetic field to find optimized conditions. Further research has been conducted to understand the flow behavior of MHD considering different cases [22,23].

The MHD pump involves two types of heat transfer mechanism: forced convection and mixed convection. The micro-cooling of the heat dissipating element is a case of mixed convection owing to its microstructure and very low flow rate. Mixed convection heat transfer has attracted significant research attention of heat transfer engineers owing to various application fields including heat exchangers, electronic cooling [24], heat dissipating element cooling [25], micro-cooling, MEMS applications, solar energy applications and metal casting [26]. Micro-cooling application is one of the critical research areas which has gained importance due to recent trends of miniaturization of devices as well as high power applications, which results in large amount of heat generation in compact volume. The various cooling methods previously suggested, including direct fan cooling [27] and thermoelectric cooling, suffer from low efficiency and high-power consumption. In addition, the presence of moving components makes conventional cooling methods less desirable [28]. Therefore, in the present study, MHD pump-based microchannel cooling for a heat dissipating element is investigated. The MHD

pump performance is evaluated by varying the applied voltage and Hartmann number, and its effect on various parameters including normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity is reported. The heat transfer performance of the MHD pump-based microchannel cooling for a heat dissipating element is reported by considering the heat removal rate, efficiency, thermal field, flow field and Nusselt number. In addition, three different nanofluids, including Cu-water, TiO2-water and Al2O3-water, are considered, and their influence on heat transfer performance is compared. The comparative heat transfer performance and potentials of various nanofluids in MHD pump application for microchannel cooling have not been realized. This study provides a comprehensive understanding of MHD pump performance, heat transfer performance of MHD pump-based microchannel cooling systems, and the influence of various nanofluids on heat transfer performance. *Symmetry* **2020**, *12*, x FOR PEER REVIEW 3 of 24 Hartmann number, and its effect on various parameters including normal current density, magnetic flux density, volumetric Lorentz force, shear stress and pump flow velocity is reported. The heat transfer performance of the MHD pump-based microchannel cooling for a heat dissipating element is reported by considering the heat removal rate, efficiency, thermal field, flow field and Nusselt number. In addition, three different nanofluids, including Cu-water, TiO2-water and Al2O3-water, are considered, and their influence on heat transfer performance is compared. The comparative heat transfer performance and potentials of various nanofluids in MHD pump application for microchannel cooling have not been realized. This study provides a comprehensive understanding of MHD pump performance, heat transfer performance of MHD pump-based microchannel cooling

#### **2. Method** systems, and the influence of various nanofluids on heat transfer performance.

#### *2.1. Numerical Modeling* **2. Method**

A schematic view of an MHD pump for cooling a heat dissipating element is presented in Figure 1. A heat dissipating element can be any microsystem including microfluidic devices, micro-batteries, electronic chips, light emitting diodes (LED), etc. The basic principle of operation of MHD pumps is based on the Lorentz force in which magnetic and electrical fields are kept perpendicular, which forces conducting fluids in a perpendicular direction to both electric currents and magnetic fields, creating an MHD pump effect. The magnetic field strength and applied current both affect the flow velocity. The magnetic field is created by keeping two small permanent magnets. The origin of the coordinate system lies between two magnets and it is equidistance from the magnets. The origin of the coordinate system lies exactly at the center of the MHD pump without considering the microchannel dimensions (Figure 1). The origin of the coordinate system has been chosen specifically at the center of the MHD pump (without considering microchannel dimensions) for simplicity in the calculations. The width of the MHD pump is chosen as a characteristic length of the system considering width as an important dimension of the MHD pump system along which various parameters are evaluated. Due to the Lorentz force, the coolant flows in the positive *X*-axis direction (i.e., from the MHD pump and towards the microchannel) as shown in Figure 1. The microchannel consists of four slots. Details of the MHD pump dimensions are provided in Table 1. *2.1. Numerical Modeling*  A schematic view of an MHD pump for cooling a heat dissipating element is presented in Figure 1. A heat dissipating element can be any microsystem including microfluidic devices, micro-batteries, electronic chips, light emitting diodes (LED), etc. The basic principle of operation of MHD pumps is based on the Lorentz force in which magnetic and electrical fields are kept perpendicular, which forces conducting fluids in a perpendicular direction to both electric currents and magnetic fields, creating an MHD pump effect. The magnetic field strength and applied current both affect the flow velocity. The magnetic field is created by keeping two small permanent magnets. The origin of the coordinate system lies between two magnets and it is equidistance from the magnets. The origin of the coordinate system lies exactly at the center of the MHD pump without considering the microchannel dimensions (Figure 1). The origin of the coordinate system has been chosen specifically at the center of the MHD pump (without considering microchannel dimensions) for simplicity in the calculations. The width of the MHD pump is chosen as a characteristic length of the system considering width as an important dimension of the MHD pump system along which various parameters are evaluated. Due to the Lorentz force, the coolant flows in the positive *X*-axis direction (i.e., from the MHD pump and towards the microchannel) as shown in Figure 1. The microchannel

**Figure 1.** Schematic view of the magnetohydrodynamic (MHD) pump microchannel cooling system for a heat dissipating element. **Figure 1.** Schematic view of the magnetohydrodynamic (MHD) pump microchannel cooling system for a heat dissipating element.

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**Table 1.** MHD pump and microchannel dimensions.
