**3. Design of digital boiler**

#### **3.1 Spray cooling mechanism-theory**

Why spray cooling has been selected as an alternative to extensively used immersion cooling and how to determine the parameters of spray cooling are the challenges in this design. Tracking the motion trajectory of the coolant liquid out of the sprayer, spreading out of the sprayer holes, receding due to viscous effects, splashing by droplet collision, stationary film generating by fluid viscosity on the solid surface, liquid file flowing by liquid momentum and gravity, and liquid flooding and draining will happen in sequence [19, 20]. The interfacial flow of coolant liquid film on the heat sink surface determines the flow pattern of film, through which heat transfer will happen. The flow patterns of droplets out of the sprayer depends basically on their outlet velocity, which are single droplet, droplet train, and droplet burst in the sequence of velocity increments. The impinging momentum of droplets onto the film attached to the solid surface coupled with the film flow pattern are the two main factors of the heat transfer mechanism of spray cooling. In this study, the droplet flow is designed as the droplet train flow- fresh droplets continuously impact the surface at a certain frequency. To investigate the heat transfer of spray cooling from this aspect, Soriano et al. [21] found that the decisive factor to achieve optimal cooling performance is to let the film velocity not be disturbed by the adjacent droplet streams. Zhang et al. [22, 23] further proved that both impact spacing and impingement pattern affect local and global cooling performance on the hot surface. The droplet train impingement among various impingement patterns is the best one for the highest thermal performance, which has also been recommended by Gao [24] after comparing the circular jet impingement cooling with droplet train impingement. As an advanced methodology [25], droplet trains broken by piezoelectric nozzles from more groups of jet flow can make cooling heat flux up to 170 W/cm<sup>2</sup> with a nozzle diameter of 25 μm.

In the field of Fluid Dynamics, Nusselt number (*Nu*) is the ratio of convective to conductive heat transfer at a boundary in a fluid, by which the convective heat transfer coefficient could be calculated.

$$N\_u = hL/k \tag{1}$$

where *h* is the convective heat transfer coefficient of the flow, *L* is the characteristic length, *k* is the thermal conductivity of the fluid.

In the single-phase regime, Rybicki and Mudawar [26] proposed the correlation for dielectric PF-5050 spray, which is

$$N\_u = 4.7 R\_e^{0.61} P\_r^{0.32} \tag{2}$$

in which *Re* is Reynolds number and *Pr* is Prandtl number.

As the heat transferring mechanism of immersion cooling, *Nu* of an isothermal flat plate at a specified temperature in the free stream flow can be calculated by [27, 28]:

$$\text{For laminar flow } (R\_\epsilon < 5 \text{x105}): N\_\text{u} = 0.664 R\_\epsilon^{0.5} P\_r^{0.33} \tag{3}$$

Refer to the quantitative comparison in **Figure 1** with constant *Pr* as 95 and *Re* varying from 0 to 4500, *Nu* of spray flow from Eq. (2) is far higher than that of laminar flow in Eq. (3). Refer to Eq. (1), no doubt to say that *h* in spray flow will be much higher than that in immersion cooling. In this case, to get the optimal convection heat transfer coefficient coupled with minimal pressure drop and coolant distribution, a series of testing has been conducted to get the best diameter and distribution of spraying holes. 0.6 mm spraying hole has been proved to be a good option to achieve the droplet train flow and can wet the surface of the heat sink effectively.

**Figure 1** presents the comparison of *Nu* between single-phase spray and singlephase immersion under *Re* number varying from 0 to 4500. *Nu* will be 200 for immersion cooling, and 3100 for spray cooling with *Re* number 4000. It means under the same access liquid velocity, spray cooling can create much higher heat transferring coefficient than immersion cooling.

## **3.2 Spray cooling mechanism-design**

**Figure 2** presents a schematic diagram of dielectric coolant being sprayed on the hash boards and heat sinks. The noisy fans in the air-cooled design have been removed and replaced by a liquid sprayer in the liquid cooling. The miner with the original heat sinks designed for air-cool was installed vertically in the reservoir, then the coolant was sprayed out of the sprayer from the top and access to hash boards and heat sinks. The coolant flush on the surface of the heat sink and drained automatically by gravity. The liquid film on the surface of the heat sink can be kept at its minimal thickness due to the excellent drainage and forceful flushing momentum. The surface area of the front and back heat sink indicates the different heat loads on the front and back side of the hash board, the spraying flow to them is distributed accordingly. The spraying holes on the top sprayer have been pinpointed to the heat sinks and their spatial distribution has been arranged based on the heat load distribution which can guarantee enough wetting on the surface of the heat sink for the best thermal performance with the least coolant consumption.
