*2.5. Data Reduction*

The MHD pump flow is generated by the application of electric and magnetic field, which interacts with the conducting fluid. The developed flow is described as Hartmann flow and the non-dimensional number, known as the Hartmann number (Ha), is defined as shown in Equation (14), where *B* is magnetic flux intensity, *L* is characteristics length, σ is electrical conductivity and µ is dynamic viscosity [21]. The Hartmann number gives an estimation of the magnetic forces compared to viscous force [9].

$$\text{Ha} = \text{BL} (\sigma / \mu)^{0.5} \tag{14}$$

**Figure 3.** Mesh details (**a**) Mesh independency test (**b**) Meshing of magnetohydrodynamic (MHD) pump microchannel cooling system for heat dissipating element. **Figure 3.** Mesh details (**a**) Mesh independency test (**b**) Meshing of magnetohydrodynamic (MHD) pump microchannel cooling system for heat dissipating element.

(**b**)

*2.5. Data Reduction*  The MHD pump flow is generated by the application of electric and magnetic field, which interacts with the conducting fluid. The developed flow is described as Hartmann flow and the non-The convective heat transfer rate is used to obtain heat transfer coefficient and calculate average Nusselt number (*Nuavg*). The heat transfer rate is evaluated as shown in Equation (15) [43].

$$Q\_{conv} = m\_{in} \mathcal{C}\_p (T\_{bulk,out} - T\_{bulk,in}) \tag{15}$$

dynamic viscosity [21]. The Hartmann number gives an estimation of the magnetic forces compared to viscous force [9]. *Ha=BL( σ*⁄*µ ) 0.5* (14) The average heat transfer coefficient is evaluated from Equation (16). The numerator is convective heat transfer from wall to fluid and the denominator is a combined term consisting of the wall convective surface area and logarithmic mean temperature difference of the wall-and-bulk fluid [25].

$$h\_{\text{avg}} = \frac{Q\_{\text{conv}}}{A\_{\text{wall}} \left(T\_{\text{wall}} - T\_{\text{bulk}}\right)\_{\text{LMTD}}} \tag{16}$$

$$(T\_{\text{wall}} - T\_{\text{bulk}})\_{\text{LMTD}} = \frac{\Delta T\_{\text{wall} - \text{bulk}, \text{in}} - \Delta T\_{\text{wall} - \text{bulk}, \text{out}}}{\log(\Delta T\_{\text{wall} - \text{bulk}, \text{in}} / \Delta T\_{\text{wall} - \text{bulk}, \text{out}})} \tag{17}$$

**Mesh Type Number of Elements**  Type 1 5.43 × 104 where ∆*Twall*−*buk*,*in* and ∆*Twall*−*buk*,*out* indicate the differences between the wall temperature and bulk fluid temperature at the inlet and outlet of the channel, respectively (Equation (17)). The average

> Type 2 1.56 × 105 Type 3 6.09 × 105

Nusselt number is calculated as shown in Equation (10) where *D<sup>h</sup>* represents the hydraulic diameter and *k<sup>f</sup>* represents the thermal conductivity of the fluid.

$$\text{Nu}\_{\text{avg}} = \frac{h\_{\text{avg}} \times D\_h}{k\_f} \tag{18}$$
