## Abstract

Epilepsy is a common chronic neurological disorder characterized by abnormally excessive and synchronized brain cell activities causing seizures. For proper functioning of the brain, epilepsy should be diagnosed with existing treatments such as medication therapy, lorazepam, benzodiazepine drug intake, and surgery. However, 30–40% of people continue to have a seizure because of the available treatments. So, the focal brain cooling device (FBC) is a new alternative cooling method in which affected brain tissue is cooled to suppress unprovoked seizures. The present numerical study investigates the cooling effectiveness by adding three different structured titanium micro pin fins in the existing base model. A finite volume-based software fluent-15.0 is used to perform transient heat transfer analysis and flow hydrodynamics. The numerical results obtained show that the temperature distribution is found and more uniform and diamond-structured micro pin fin takes less than 7 min to reach below 15 °C, which is desirable to diminish the high-frequency and high-amplitude epileptic discharges.

## Introduction

Epilepsy is a neurological disorder that refers to a small part of the brain getting affected because of excessive and abnormal brain cell activities characterized by high-frequency and high-amplitude disturbances in a synchronized manner, resulting in an electrical storm [1]. Epilepsy is used to describe seizures, which are sudden events that cause temporary changes in physical movement, sensation, awareness, and behavior. During a seizure, a group of neurons starts firing at the same time from the epileptic focus site where the volume of brain tissue becomes hotter by 0.3 °C–0.5 °C depending on the type of seizure. This causes involuntary movements and loss of awareness for a short period. A group of neurons starts firing electrical signals simultaneously, which lasts from short time seconds to minutes depending on their various types and results in hyperexcitability [2]. Simple focal seizures and complex focal seizures are mainly two types of seizures occurring on both sides of the brain. However, the larger part of the brain is affected in complex focal seizures, and the person becomes unaware of what is happening around [3].

The causes of epilepsy can change by age of the individual. Autism spectrum disorder causes seizures in children, while in young adults, head injuries and brain infection are the main reason for seizure onset. Tumors, strokes, and injuries are more frequent in middle-aged individuals; however, stroke can be the most common cause of seizure onset for people older than 65 years. Also, the cause of most epilepsy cases is unknown [4]. Seizures often happen without giving any information and can happen anywhere. Generally, situations like flashing lights or moving patterns or shapes can bring on or trigger a seizure. Some people have seizures triggered by flashing lights or moving patterns or shapes [5]. Few cases occur because of genetic factors and congenital conditions, and in some people, epilepsy is triggered by brain stroke, brain tumor, brain injury, Alzheimer's disease, and trauma [6].

Medical statistics indicate that epilepsy influences 50 million people around the world and almost 80% of people do not receive adequate treatment because they are from nonindustrialized countries [7]. However, antiseizure medications such as different drugs, namely, lorazepam, phenytoin, benzodiazepines, and phenobarbital, are used as initial treatment to terminate seizures but fail in 30–40% of people, and longer duration cases are more difficult to treat [8]. Therefore, alternative approaches are needed to abolish seizure activity and reduce brain injury. Surgery is one of the main medication treatments wherein the part of the brain causing the seizures is removed to make seizure-free patients. But it rarely results in seizure freedom because it mainly focuses to reduce the seizure frequency and amplitude.

Epilepsy is often monitored by electroencephalography, which records and tracks the electrical activity of the brain over some time [9]. It is noninvasive, with the small metal discs made up of thin wires (electrodes) placed on the scalp, and signals to a computer are sent to record the results [10]. However, epilepsy cannot be ruled out by a normal noninvasive method. To suppress the onset of seizures quickly, the exact location of unprovoked seizures is required. Throughout the late years, medical and biological research has made inconceivable types of progress in understanding the pathogenesis of epilepsy and in making a reasonable prescription for various types of epilepsy [11]. The main aim of the treatment is to control the unprovoked seizures and stop them from firing synchronized electrical pulses as well as to decrease the amplitude and frequency of these electrical pulses from the seizure onset location called epileptic focus [12]. Advanced surgical treatments are used to suppress focal seizure onset from the epileptic focus site but only with a success rate of 50–60% of the cases. So, the inefficiency of these existing treatments for epilepsy requires headway in the advancement in the existing treatments. Recently, several biomedical devices have been investigated to develop an alternative devices and implants for several conventional treatments including but not limited to artificial urinary sphincters [13,14], retinal implant [1517], blood oxygenators [18,19], tissue scaffold [20,21], and tissue regeneration [22]. One such technique is focal brain cooling (FBC), and a bio-implantable device is used as an attractive alternative treatment to suppress seizures [23].

A new alternative focal brain cooling bio-implantable device was first proposed by Masami et al. [24] in which they kept a cooling device inside the brain to make seizure-free patients. With the help of this cooling device epileptic discharges (EDs) were suppressed when the brain surface temperature was maintained below 25 °C. The results obtained showed good agreement with the experimental work of Yang et al. [25,26] in which they concluded that the brain surface temperature should lie between 15 °C and 20 °C. The normal body temperature also known as euthermia ranges from 36.5 °C to 37.5 °C [27]. A 1–2 °C rise in body or brain temperature, especially when it develops early after injury, is widely regarded as harmful [28]. To cause brain damage, a child's temperature would need to reach 42 °C. When the temperature starts increasing from 37 °C, human being physiology becomes detrimental, proteins begin to denature, and the cells ultimately die. Barone et al. [29] concluded that a significant decrement of 2 °C–3 °C was observed just by keeping the cooling device on the skull, which was initially at 37 °C. During experiments, isotonic saline is used as a coolant fluid to cool the skull surface, which was at a constant temperature of 37 °C. Oku et al. [30] investigated the influence of a focal brain cooling device on the brain tissues and detected the range of threshold temperature to make seizure-free patients. They also concluded that the cooling device did not show any aftereffect, while placed for more than an hour above 0 °C. In addition, Soriano et al. [31] used a computational approach to find the exact location of the epileptic focus site by a neural mass model. Proctor et al. [32] demonstrated that due to advancement and miniaturization in electronic devices, soft, flexible implantable devices can be made that interfaces well with the human brain tissue. These thin organic electronic fibers do not show aftereffect in the brain tissue.

Dinis et al. [33] proposed a novel bio-implantable FBC device attached to the Peltier module. The main purpose was to eliminate the robust water circulation system from the existing design. Battery management, wireless power transfer, and power modules were needed, which increased the cooling device's working space and made the existing cooling system bulky [34]. The results showed that the Peltier device cooled up to 28 °C when inside the circulating water is at 37 °C. Kei et al. [35] also proposed a focal brain cooling device based on the Peltier effect. They used cold saline as a coolant fluid, and the outflow was cooled by a Peltier device for recirculation. They used computational fluid dynamics (CFD)-based model of the device to find out the total time required to cool the brain. They also observed that the cooling device did not attain a temperature of 25 °C even after 20 min of cooling. So, these devices did not provide effective cooling to suppress epileptic discharges. Although the Peltier device is cooled below 25 °C, it is not used to keep inside the brain because of the large electric current required to operate this module. Later, keeping this in mind, Hata et al. [36] developed bio-implantable and wearable focal brain cooling devices to cool epileptic focus sites using cold saline as the circulating fluid. Results showed that with the low flowrate of saline and complex channel structure, uniform temperature can be obtained. Their results also showed that it takes less than 10 min for the average temperature to reach 25 °C below 2 mm from the brain surface.

Since focal brain cooling has been a well-established method for suppressing EDs. This cooling device is directly placed on the brain surface at the epileptic focus site. Generally, FBC is actively working in a part of the brain called as somatosensory and motor cortex. Epileptic activity is suppressed during cooling of the brain surface from the epileptic focus site through bath application in saline at 4 deg. FBC is implanted and performed for 30 min twice every week [37]. Because of recirculation of cooling fluid outside the body, FBC provides adequate cooling and making this device a promising therapy for the treatment of epilepsy as discussed by King et al. [38] in which they performed the analysis by taking a monkey model and giving Penincilin G to induce a focal seizure, and also Inoue et al. [39] developed cat and monkey model using the recirculation method in a titanium bio-implantable cooling device to suppress seizures. The experimental results showed that the titanium bio-implantable cooling device terminates seizures, while bringing down the temperature of the cooling device to 15 °C in less than 10 min. However, cooling effectiveness was not achieved properly, and temperature distribution was highly nonuniform, which is nondesirable. Along with the cooling device, only half of the portion was cooled even after a steady state was achieved.

As stated earlier, the focal brain cooling device provides a promising method to cool the epileptic focus site because of the advantage of fluid recirculating outside and sending cold fluid inside using the pump, battery, and Peltier device keeping outside the body as a whole. This system is a promising method for the patients because the cooling is easy at an epileptic location, whereas surgery is very difficult in those areas because of its aftereffect. However, FBC does not provide uniform cooling, and cooling effectiveness is not up to the mark in the base model of Inoue et al. The cooling effect was not seen to a larger extent inside the FBC because of parallel inlet and outlet plenums. Complex structured micropins can be provided inside the cooling device to obtain the desired cooling, which results in uniform temperature distribution and lower pressure drop at the outlet plenum to maintain the required pressure difference for the flow to happen [40,41]. However, the flow distribution pattern in the parallel channels develops suitable hydrodynamic condition for maximum heat flux extraction [42]. From thermodynamics point of view, the energy lost by the implant cooling device is an irreversible process termed as exergy, and it is proportional to the entropy gained by the system combined with the surrounding [43].

Based on the already developed base model shown in Fig. 1(a), a computational model is constructed with the same dimensions and gives a 0.5 mm base thickness for effective heat transfer as shown in Fig. 1(b). Our main motive behind the computational study is to provide complex structured micro pin fins attached to the base of the focal brain cooling device to obtain the cooling effectiveness as well as uniform temperature distribution on the base surface. The already existing base model is evaluated using commercial software fluent-15.0 simulations by adding three different structured micro pin fins. So, the present numerical study provides an optimum design of the present focal brain cooling device out of ellipse micro pin fin, diamond micro pin fins, and mixed ellipse and diamond micro pin fins. Also, the current numerical study examines the transient heat transfer analysis and flow hydrodynamics of rectangular-shaped microchannel constructed to three different micro pin fins with parallel inlet and outlet plenum using saline water. This numerical study will result in the development of a better-optimized design of a focal brain cooling device for the treatment of epileptic seizures.

Fig. 1
Fig. 1
Close modal

## Methodology

The titanium bio-implantable focal brain cooling base model of Inoue et al. has a bottom dimension of 20 mm in length and 10 mm in width with a thickness of 4 mm. A base plate with thickness of 0.5 mm is used to enhance the heat transfer, as shown in Fig. 1(a). Inlet and outlet plenum of 2 mm diameter is attached to the heat sink to ease the fixation of the device on the epileptic focus site inside the brain. The base model of Inoue et al. [39] describes that the fluid has to go inside and circulate throughout the chamber to pick heat from the bottom titanium plate, which is at a constant surface temperature of 37 °C and exits from the outlet portion.

The computational base model suggests that the top portion and near inlet portions get the maximum cooling because fluid gets circulated only through the sidewalls of the base model through its continuous motion. Since inlet and outlet plenums are parallel to each other, it also creates large pressure difference-making fluid to come out as quick as possible. Also, fluid shows impinging motion as it is coming from some height because of the space constraint since it is designed to keep inside the brain on the epidural surface implanted chronically. Since it is seen throughout the flow duration of the computational domain, the majority of the fluid interacts only through the top surface wall of FBC, and hence, maximum cooling is achieved on the ceiling part as shown in Fig. 2 because of fluid getting jumping action after falling on the bottom surface. Due to this, the fluid cooling is not seen in the neighboring zone because fluid does not reach the end of the FBC due to very less velocity. Hence, less velocity gradient and the high thermal gradient are seen in the device, which leads to irreversible losses and makes the device ineffective.

Fig. 2
Fig. 2
Close modal

So, the motivation behind the present work is to achieve uniform cooling and to make the existing model, which is shown in Fig. 3(a), more effective by adding three different types of structured micro pin fins, i.e., ellipse-structured micro pin fin, as shown in Fig. 3(b); diamond-structured micro pin, as shown in Fig. 3(c); and mixed structured micro pin fin, as shown in Fig. 3(d). By adding structured micro pin fins, micro gaps are obtained, which increases the velocity gradient and in turn decreases the irreversible losses and increases the cooling effectiveness. Figure 4 presents the schematics of the models with dimensions. In all the models, the pin fins are with staggered configuration with even fin height and fin spacing.

Fig. 3
Fig. 3
Close modal
Fig. 4
Fig. 4
Close modal

## Numerical Methodology

The fluid inlet temperature is taken at 12 °C for the FBC device with mass flow ranging from 0.02 to 0.05 m/s. The saline water is considered an incompressible laminar single-phase fluid, without viscous dissipation of energy. Laminar fully developed flow is considered throughout the flow domain, and uniform zero pressure is assumed at the outlet. All the walls satisfy the no-slip condition, and both heat transfer and flow hydrodynamics are steady and three dimensional. The bottom wall of the FBC device is kept at a uniform temperature of 37 °C.

Laminar forced convection is considered for the present numerical study by using CFD software fluent-15.0. The computational model is consisting of two domains, namely, fluid and solid, which correspond to the titanium plate. The closed recirculating coolant system taken by the author has many advantages compared to the open system, including better temperature control in the cooling equipment.

A single-phase model has been adopted for the conjugate studies of laminar forced convection heat transfer in a focal brain cooling device. This model involves solving conduction and convection heat transfer simultaneously. Thus, steady-state mass, momentum equation, and energy equations are solved for saline water. The steady-state heat conduction equation is solved for the bottom wall made up of a titanium plate. The corresponding governing equations are listed from Eqs. (1)(6).

Continuity equation:
$∂u∂x+∂v∂y+∂w∂z=0$
(1)
X-momentum equation:
$u∂u∂x+v∂u∂y+w∂u∂z=−1ρ∂p∂x+v(∂2u∂x2+v∂2u∂y2+w∂2u∂z2)$
(2)
Y-momentum equation:
$u∂v∂x+v∂v∂y+w∂v∂z=−1ρ∂p∂y+v(∂2v∂x2+v∂2v∂y2+w∂2v∂z2)$
(3)
Z-momentum equation:
$u∂w∂x+v∂w∂y+w∂w∂z=−1ρ∂p∂z+v(∂2w∂x2+v∂2w∂y2+w∂2w∂z2)$
(4)
Energy equation of the fluid:
$∂T∂t+u∂T∂x+u∂T∂y+u∂T∂z=α(∂2T∂x2+∂2T∂y2+∂2T∂z2)$
(5)
Energy equation of the solid:
$∂2T∂x2+∂2T∂y2+∂2T∂z2=ρCp∂T∂t$
(6)

## Numerical Scheme

A computational unstructured mesh is generated using commercial CFD software fluent-15.0 in ANSYS. The grid is unstructured due to the complex computational domain taken for analysis. SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm of Patanker and Spalding is used to solve the velocity and pressure fields. Pressure discretization is performed with a standard scheme. Least-square cell-based gradient and second-order upwind schemes taken from the fluent user's guide are used for spatial discretization. The momentum and energy equations are solved with the second-order upwind scheme. The computations are considered to have converged when residuals are less than 10−6.

### Grid Independence Study.

The grid system employed in the numerical analysis of the focal brain cooling device case has 1,845,694 elements in the x, y, and z directions, respectively. The sensitivity of the numerical results is checked with five different grids 532,568, 83,568, 1,250,261, 1,845,694, and 2,308,296 elements, respectively, as presented in Fig. 5. The results of the last two grids do not have considerable change, and further deviations are very close to each other. Taking into account less computational time, the grid size of 1,845,694 elements is used in the current work. For the grid independence study, temperature of the cooling fluid is taken at the outlet plenum for an inlet velocity of 0.02 m/s. The models solid and fluid regions are discretized separately using the finite volume method. The unstructured grid is generated with prismatic elements. Mesh density is refined for the solid titanium plate with pin fins. The increment in mesh density is made from 2 cells per 0.2 mm2 to 8 cells. The orthogonal and skewness ratio are in the order of 0.8 and 0.15. The diamond fin microgap implant with mesh details is shown in Fig. 6.

Fig. 5
Fig. 5
Close modal
Fig. 6
Fig. 6
Close modal

## Results and Discussion

### Validation Study.

The present numerical study is validated with the experimental base model of Inoue et al. [39] and Hata et al. [36] taking laminar forced convection under a very low flowrate of 0.02 m/s using saline water with a constant base surface temperature condition of 37 °C. The obtained numerical result provides considerable agreement with Inoue et al.’s work. A maximum of 1.65% deviation in outlet temperature was obtained in the numerical model. A titanium focal brain cooling device was implanted chronically on the epidural surface to enable the cooling of animal brains in the focal epileptic region. Coolant circulation with a very low flowrate at constant pressure is used. After the start of the cooling device, temperature of the cortical surface decreased to 15 °C within 7 min after which seizures can be suppressed by mitigating hotspots, as shown in Fig. 7. Cold saline water is perfused in the cooling device at a temperature of 12 °C, which is having a good thermal conductivity of 0.56 W/m K. Saline water is taken as a cooling fluid because of its similar properties to that of cerebrospinal fluid to act as a protecting agent.

Fig. 7
Fig. 7
Close modal

### Flow Hydrodynamics Study.

Figure 8 shows the velocity contours of ellipse-structured micro pin fins, diamond-structured micro pin fins, and mixed structured micro pin fins for a mass flowrate of 0.02 m/s. In the base case model, the coolant coming out from the inlet top portion is impinging and moving upward, and fluid circulation is observed only near the zone of inlet and outlet. Since the inlet and outlet are parallel to each other, most of the cooling fluid flows near the outlet, which in turn decreases the cooling effectiveness in the base model. Also, fluid is not getting enough velocity to reach the extreme ends of the wall, and hence, cooling effectiveness is very less in the case of the base model. However, increased velocity contours are observed in the case of all three different structured pin fins. In the case of diamond-structured micro pin fins, a maximum velocity of 0.038 m/s is observed because of diverging and converging shaped nozzle occurring between any two diamond-shaped fins. Also, the maximum velocity is achieved near the inlet, which in turn forces the fluid to go inside, and cooling is achieved at a larger distance along with the flow. Fluid is forced to go to extreme ends, and better cooling distribution is achieved throughout the FBC device. A large velocity gradient is observed, which also provides a uniform cooling and in turn provides uniform temperature distribution.

Fig. 8
Fig. 8
Close modal

Figure 9 depicts the velocity contours taken at section 1 mm from the bottom plate. It is observed that the fluid is penetrating more in the diamond-structured pin fins due to the converging shape created between the two structured micro pin fins. So, maximum cooling can be seen in diamond-structured pin fins.

Fig. 9
Fig. 9
Close modal

### Temperature Study for the Base Model.

The temperature distribution of the base model, FBC device, is shown in Fig. 10 for different time-steps ranging from 25 s to 200 s. It is observed that the maximum cooling happens in the ceiling part of the cooling device because the inlet and outlet are parallel to each other, and the fluid coming from the top impinges and moves upward. As time progresses, cooling can be seen only in the front portion of the cooling device, but the remaining zones are kept unaffected. Also, it is seen that the fluids are going at a lower temperature from the outlet portion as time progresses, which indicates the ineffectiveness of the cooling device. The maximum portion of the FBC remains unaffected because fluid does not reach the extreme ends.

Fig. 10
Fig. 10
Close modal

Temperature contour and velocity vector are shown in Fig. 11 for the base model case at time t = 150 s. It is observed that the maximum cooling happens in the ceiling part of the FBC device because the inlet and outlet are parallel to each other, and the fluid is about to leave the outlet as soon as possible at every instant time as shown in Fig. 11(a). Also, some of the fluid is coming out at lower temperatures without going up to extreme ends, so this shows the ineffectiveness of the cooling device. Figure 11(b) shows how the outlet velocity vector is going parallel to the inlet velocity vector, and maximum fluid moves from the outlet after impinging and does not reach up to the extreme ends. Most of the time fluid picks heat from ceiling portions only because the fluid will spend more time because of its reduced velocity. The bottom part of FBC remains unaffected because the fluid is impinging faster and spends very less time.

Fig. 11
Fig. 11
Close modal

### Temperature Study for Three Different Structured Micro Pin Fins.

The temperature distribution of the base model, FBC device, and structured micro pin fins are shown in Fig. 12 for the increased time variation of 25 s–125 s by taking into account of conjugate heat transfer analysis. Figures 12(a)12(c) show the temperature distribution for the base cases, and it was observed that mixing of the working fluid is very low and delivered lower temperature at the top wall of the fluid region, as shown in Fig. 12(c). Figures 12(d)12(f) show the temperature distribution for the case of ellipse pin fin structures. The use of the ellipse pin fin structure alters the temperature distribution of the device and allowing the fresh fluid to reach the entire section of the device. In addition, the smooth structure of the ellipse fin acts as an obstruction near the inlet of the device and generates the fluid recirculation, as shown in Fig. 12(f). It is observed that the maximum mixing happens in the diamond-structured micro pin fins because fluid is forced to move inside due to converging passage between two micro pin fins, creating micro gaps that result in increased velocity as shown in Figs. 12(g)12(i). Also, this effect is not seen in the case of base model, FBC, as shown in Figs. 12(a)12(c). At t = 25 s, base model cooling is seen only on the top wall, as shown in Fig. 12(a). However, in the case of diamond-structured micro pin fin, fluid picks heat from the top wall as well as from the sides of the FBC because of the converging passage.

Fig. 12
Fig. 12
Close modal

Also, from outlet, the plenum fluid is left at a low temperature, which shows the ineffectiveness of the cooling device in the case of the base model, but this effect is not seen in diamond-structured micro pin fins. Figures 12(j)12(l) show the temperature distribution of mixed pin type, and the temperature characteristics of both ellipse and diamond pin fins are noticed. Further, the effect of ecliptic fins is more than that of diamond fin, and this can be noticed critically with the temperature distribution on the implant. In Figs. 12(j) and 12(k), the temperature distribution in the device is almost same as that of the diamond pin fin model. This is due to the fact that the fluid has entered in the first case of t = 25 s, and in the case of t = 75 s, the fluid has crossed the two stages of the pin fin structures. The first diamond fin diverts the fluid with higher velocity, and ellipse pin fin act as the obstruction at the next stage and reduces the fluid velocity. This consequent obstruction of the velocity of the fluid by the ellipse pin fin in the device develops a temperature distribution almost similar to that of the ellipse pin fin model, as shown in Fig. 12(l). Compared with diamond pin fin, the ellipse pin fin performance is evident to large flow separation and reduction in fluid momentum, and see Figs. 6 and 7. By curving the diamond sides, the fluid momentum effectively diverted and reticulation of the fresh fluid is increased, and this similar phenomenon is observed by Reddy et al. [44]. With the addition of the pin fins, the velocity near the pin fin wall increases and delivers a better temperature distribution [45].

Figure 13 depicts the temperature distribution on the bottom plate of the cooling devices. Figures 13(a) and 13(b) depict the effect of coolant in the bottom plate in the case of the base model and ellipse-structured micro pin fin. For the base model, fluid falls on the bottom plate and impinges back to the top wall and thereby spending very less time cooling bottom faces. However, in the case of an ellipse-structured micro pin fin, fluid gets time to go along the flow and picks heat from the bottom plate. This shows that the temperature distribution is more uniform in the case of the different structured micro pin fins cooling devices, and this, in turn, enhances the performance of the cooling device. Figures 13(c) and 13(d) depict the bottom surface temperature of diamond and mixed fins implant. In both cases, the bottom surface temperatures reached below the base case.

Fig. 13
Fig. 13
Close modal

### Overall Temperature Distribution of the Cooling Device.

Figure 14 depicts the total temperature distribution of the base model and micro pin fin cooling device along the whole length of the cooling device. The maximum temperature of the cooling device is maintained at 37 °C, but at 5 °C, temperature drop is noticed near the inlet and outlet regions of the base models. It is observed that the temperature distribution in the base model is not uniform, and only a 5 °C difference is observed in the interior of the base model, as shown in Fig. 14(a). The interior of the titanium is observed to be at high temperature. Also, a maximum outlet temperature of 35 °C is observed in the case of the base model. However, the interior fluid is at a uniform temperature, and the fluid coming out is also at a high temperature, which signifies the ineffectiveness in the cooling device of the base model.

Fig. 14
Fig. 14
Close modal

But in the case of elliptic-structured micro pin fins, uniform temperature distribution is obtained in the inner portion of the cooling device along the length, and an 18 °C temperature difference was observed, as shown in Fig. 14(b). The green-shaded area conveys that the maximum cooling is observed in that area since interior titanium and interior fluid are at a uniform temperature, and hence, mixing is proper. Also, a maximum outlet temperature of 23 °C is observed in the outlet, which ensures further improvement in the cooling device to increase its effectiveness. Also, the temperature distribution is observed more uniform in the case of diamond-structured micro pin fins, which show the increased cooling performance of the cooling device, as shown in Fig. 14(c). Similar results were observed in the mixed fin case as shown in Fig. 14(d).

Figure 15 depicts the average temperature and maximum temperature of the cooling device. It is observed that the maximum temperature of the cooling device takes less than 7 min to reach below 15 °C for the base case as shown in Fig. 13(a). The difference between maximum temperature and average temperature is significantly higher. However, the average temperature of the cooling device takes almost 6 min to reach below 15 °C in elliptic-structured micro pin fins as shown in Fig. 15(b). The range of 15–20 °C temperature is enough for suppression of high-amplitude and high-frequency seizures observed in the case of diamond fin as shown in Fig. 15(c). Also, the uniform temperature distribution is obtained in the different structured micro pin fin cooling devices, which shows the effectiveness and cooling performance. Hence, a diamond-structured micro pin fins cooling device shows more optimum conditions because of its temperature uniformity. In the mixed case, the average temperature is slightly higher than the diamond fin case as shown in Fig. 15(d).

Fig. 15
Fig. 15
Close modal

## Conclusions

To improve the cooling effectiveness of the FBC device, three different types of structured micro pin fins are constructed. The transient heat transfer analysis and flow hydrodynamics are numerically investigated to provide optimum cooling performance. From the numerical studies mentioned earlier, the following main fundamental conclusions are drawn:

• For the same flowrate, the bottom surface temperature of the micro pin fin models developed lower temperature than the base model due to more even fluid mixing and constant redevelopment of the fluid.

• However, increased velocity contours are observed in the case of all three different structured pin fins. In the case of diamond-structured micro pin fins, a maximum velocity of 0.038 m/s is observed because of diverging and converging shaped nozzle occurring between any two diamond-shaped fins.

• The maximum velocity is achieved near the inlet, which in turn forces the fluid to go inside, and cooling is achieved at a larger distance along with the flow. The fluid is forced to go to extreme ends, and better cooling distribution is achieved throughout the FBC device.

• A micro fin pin design model forces fluid to go to extreme ends, and better cooling distribution is achieved throughout the FBC device. A large velocity gradient is observed, which also provides a uniform cooling and in turn gives uniform temperature distribution.

• It takes less than 7 min for the maximum temperature to reach below 15 °C, which can suppress seizures and also takes less than 6 min for the average temperature to reach below 15 °C.

Diamond-shaped micro pin fins provide better thermal uniformity because of their increased velocity gradient, and a maximum of 0.38 m/s velocity is observed in between micro gaps, which help the fluid to reach the extreme ends.

## Conflict of Interest

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent not applicable. This article does not include any research in which animal participants were involved.

## Data Availability Statement

The authors attest that all data for this study are included in the paper.

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