Optimization of Heat Sink Geometry for Improved Thermoelectric Generator Efficiency

Thermal management is essential for electronic devices. A Thermoelectric generator device is the solid state of device that is straightaway converted into electricity. Thermoelectric generators device has non-movable parts and are ecosystem friendly compared with the conventional usable electric power generators.

A thermoelectric Generator device transforms the Thermal energy into usable Electrical energy. Electronic devices, such as Central processing unit, microprocessor-based electronic circuits, and Integrated Circuit chips, dissipate heat during operation. If the upper limit is exceeded, the machine is destroyed.

Therefore, the machine requires cooling achieved by the heatsink, which performs well without any damage. The thermoelectric generator output of the electrical voltage depends on the input of the temperature gradient; the temperature gradient needs to be optimized to obtain high-efficiency thermoelectric generator. A heat sink is a non-electrical device that absorbs heat from electric components, electronic systems, and integrated circuits (ICs).

The thermoelectric device under a heat load, temperature gradient, $\Delta \mathrm{T}$, across the thermoelectric terminal. Heatsinks geometry models designs of fin sizes, and different shapes of the Heatsink fins, comparing the heatsink parameters through different geometries of the heatsink. Here the different heat sinks design modules chosen the material is aluminium, aluminium material has high thermal conductivity, low density, and non-magnetic properties of the material.

Convection cooling of high heat flux is one of the most effective thermal energy management operation methods among the various heatsinks. Modern electronic devices have been miniaturized [1]. Thermoelectric generator harvesting waste-heat converting into usable electrical power producing a sustainable and eco-friendly energy solution depends on the optimal functioning of the TEG is the efficient management of the waste heat. Which requires to consider the heatsink. TEG operation principle is Seebeck effect, where temperature between Hot side and Cold side of device TEG induces an electric voltage and current flow, generating the electrical power. Teg finds applications in diverse fields from automotive and industrial sectors to remote power generation and space exploration offering a clean and reliable energy source. For maximize an Electricity generated output of the Thermoelectric Generator device it is essential to maintain a significant change in temperature among the Hot side-surface and Cold side-surface. This requires efficient heat-energy dissipation on the Hot side surface as excess heat accumulation can hinder performance designed to manage heat transfer and maintain temperature differentials. A heatsink is the passive thermal management device that absorbs heat and dissipates heat away from the TEG’s hot side ensuring that the temperature remains within the specified range and efficient heatsink design is paramount for achieving the following objectives. Optimal heat transfers a well-designed heatsink maximizes the amount of heat transferring from the ‘TEG’ Hot side base-surface to the outside of the environment there by maintaining a desirable temperature differential for electricity generation. Enhanced TEG efficiency by preventing overheating and minimizing thermal resistance the heat sink contributes to higher TEG efficiency and increased electrical power output. Sustainability efficient heat management through heatsinks reduces the reliance on external cooling systems or energy intensive mechanisms making TEG’s a sustainable and environmentally friendly energy source. Need for geometrical design and analysis is the geometrical design heat sink models that can improve heat dissipation within the TEG systems and selecting thermally conductive materials suitable for heat sink construction.

The heatsink dissipates heat from a heated surface by utilizing colder ambient air. Expanding heat transfer area is one method for improving heat dissipation [1]. The existence of a finned object surface and the shape and layout of the fins affect thermal performance. Fin optimization is a critical step in improving Heat transferring and lowering the pressure, dropping across Heat sinks. The fin geometry design and array optimization are also available. This necessitates the presence of outside airflow. Ambient airflow is used to create a heat sink that helps cool the gadget efficiently.

Here Figure 1 shows the temperature of the air within the heatsink fins increases during natural convection cooling as a function of heat energy from heat source. The hot-air pressure was less dense than that of the surrounding air. The thermal energy of the flow between physical systems is known as heat transfer. This is strongly influenced by the environment in which the system resides [2]. The device of the heat sink device deals with three operations heat energy transfer convection, conduction, and radiation.

Conduction $\quad \mathrm{Q}^{00}=-K \cdot \nabla t$

Convection $\quad \mathrm{Q}^{01}=-h \cdot\left(T_S-T_{\infty}\right)$

Radiation $\quad J=E+\rho G$

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Figure 1. Workflow overview of heat sink geometry and fin design analysis for enhanced thermoelectric generator efficiency

A thermoelectric generator (‘TEG’) is the devices such this transforms the heat energy into the electrical energy using of the principle of See beck effect. Figure 2 gives the details of methodology. It makes use of the change of temperature in between two sides of surfaces of the thermoelectric material to generate a voltage and subsequently produce electric power. The effects of Temperature gradient ∆T, and the geometrical parameters through which heat energy transported determine the rate at which conduction q_k transfers heat [10].

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Figure 2. Block diagram of thermoelectric generator with heat sink setup

3.1 Thermoelectric modules design

These modules consist of multiple pairs are ‘P-type’ of thermoelectric material, ‘N-type’ of Thermoelectric materials are electrically joined with in the series and the thermally connected with in allined. Thermoelectric materials are often made from semiconductors with different properties, allowing them to generate voltage when exposed to temperature gradients. Absorbing side: This one side of a thermoelectric Module is with direct connection accompanied by the heat source. It absorbs heat and allows it to transfer to the other side, creating a temperature difference across the thermoelectric material. On the heatsink side, this side surface of the thermoelectric modules make contact with the heatsink. It is designed to have a lower-Temperature than the heat absorbing side. Temperature differences are essential for electricity production. Module geometry of the heatsink.

The heatsink is the part responsible for dissipating heat from the thermoelectric modules. It typically consists of a thermally conductive material, such as aluminium or copper, with fins or other structures to increase surface area and improve heat dissipation through conduction, convection, and radiation. Electrical load: Electrical load is a device or system that consumes electrical energy generated by thermoelectric modules. It can be a battery charger, an electronic circuit or any other electrical device. Electricity output: It is connected to the electrical load, thus providing the necessary power for its operation. The basic operating principle is: When there is a temperature difference between thermoelectric modules, the temperature difference causes free electrons within Material for a be diffused from the hot side surface (P-type) to cold side (N-type). This movement of electrons creates a voltage difference known as the Seebeck voltage. By connecting multiple pairs of p-n modules in series, voltage will be accumulated and can be extracted into electrical energy. The heatsink plays an important role in maintaining low temperatures on cold side of surface of thermoelectric generator device module. It absorbs, dissipates the Heat to ambient environment, creating the necessary temperature gradient for continuous power generation. Overall, the thermoelectric generator system utilizes the Seebeck effect, temperature gradient, and heat sink is to transform the unwanted the heat energy into the functional electrical energy, providing efficient and sustainable way to harness heat as a power source.

$q K=-K A \frac{d T}{d x}$       (1)

Thermal resistance is a term used to describe heat sinks [2].

Wind tunnel tests measure thermal resistance and system impedance [3]:

$Q s a=\frac{T_s-T_a}{Q}=f(C F M)$      (2)

$\mathrm{T}_{\mathrm{s}}$ : Heat sink base temperature. ${ }^{\circ} \mathrm{C}$

$\mathrm{T}_{\mathrm{a}}$ : Approaching air temperature ${ }^{\circ} \mathrm{C}$

$\mathrm{Q}$ : Power provided to the heat sink

Airflow is volume flow rate; and flow velocity is the passage through the channel.

CFM: Cubic $\mathrm{ft} /$ minute

Volume flow rate $(\mathrm{V})$ units: $\left[\mathrm{m}^3 /\right.$ Second $]$

$\mathrm{V}=$ Velocity of air $\mathrm{V} \times$ Area of cross-section $\mathrm{A}_{\mathrm{c}}$

$Mass\, flow \,rate=\rho A c \vartheta=\rho \vartheta$     (3)

If must be higher than the flow rate of air, then the flow resistance faces. (Pressure loss) in the pressure drop across the flow length(pipe).

Pi: cross-section pressure.

$\Delta P=P i-P o$        (4)

$\Delta \mathrm{P}$ increases as $\mathrm{V}$ increases.

It depends on frictional resistance, shier stress, and sheer force.

$\Delta \mathrm{P}$ is the frictional pressure drop or/frictional loss.

System impedance increased the flowrate $=\mathrm{f}(\mathrm{v})$.

$\Delta \mathrm{P}$ depends on the functions $\mathrm{V}, \mathrm{S}, \mathrm{H}$, and the fluid properties.

$\mu=$ viscosity, $\rho=$ density.

$\frac{\Delta P}{L}=f v, s, H$      (5)

Pressure drop is also depending on length 'L’.

The fin spacing should be determined based on flow impedance [3], with few fins having a low object, a low-pressure drop, and many fins having a high object high-pressure drop. There is an optimal number of fins for a particular flow condition and fin spacing estimation.

$S_{\min }=1.3(H / V)^{0.5}$    (6)

H is the heatsink length in the flow direction.

'V' is the velocity (ft/min).

3.2 Fin efficiency

The efficiency of fin is one of the parameters that force the material to be used for high thermal conductivity. The heat sink fin can be flat and cylindrical, with one end of the heat flowing and dissipating to the surrounding air as it moves toward the other [4]. When fins must be isothermal, and they have infinite thermal conductivity.

Heat sink fin efficiency:

$\eta=\frac{\tanh (m L)}{m L}$     (7)

$m L=\sqrt{\frac{2 h f}{k t f} L f}$          (8)

3.3 Heat transfer theoretical model

The forced air over a tube appropriately firms up the heatsink in the ducted flow [4]. This makes sure the certain air passes across the channels created at the heatsink Fins [2]. When airflow was not ducted, some airflow passed through the heatsink [11] The flow bypass increased as the fin density and clearance increased but was unaffected by the inlet duct [3].

In Figure 3, the thermal resistance of a heatsink consists of two resistances. Those are 1). Resistance in base R_b, and 2). Resistance in the fins, R_f.

Base-resistance:

$R b=\frac{t b}{k A b}$    (9)

The thermal resistance of base fins to air:

$R f=\frac{1}{\eta n f w f(t f+2 \eta f L f)}$     (10)

$\eta f=\frac{\tanh m L c}{m L c}$    (11)

$m L c=\sqrt{\frac{2 h f}{k t f}} L f$       (12)

$D h=\frac{L c 4 A c h}{\rho c h}$    (13)

$\operatorname{Re}=\frac{4 G p}{\eta \pi D h u}$    (14)

$f=(0.79 \ln R e-1.64)^2$

$N u=\frac{\frac{f}{8}(R e-1000) P r}{1+12.7\left(\frac{f}{8}\right)^{20.5}\left(p r^{\frac{2}{3}}-1\right)}$     (15)

$h f=\frac{N u k_{a i r}}{D h}$       (16)

$\rho=\frac{\rho a t m}{\text { RaTin }}$    (17)

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Figure 3. Heatsink (Source: Wikipedia)

Many heatsink fin shape designs have been created, varying parameters such as fin height, fin thickness, fin spacing. Each design has been carefully simulated and tested. Increasing the blade height results in a 10 mm cylindrical blade shape at a temperature of 6.7℃ and a pressure loss of up to1.8 mm, a higher heat transfer coefficient and improved energy production efficiency. However, there is an optimal fin length beyond which further increases do not provide significant benefit.

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Figure 7. Heat sink fins height vs pressure loss

Here above Figure 7 is the analysis of pressure loss for different fin heights for different shapes of heat sink fins. After analyzing the results of the heat sink pressure loss is the heat exchange varies with different shapes of the heat sink fins and different heights of the heat sink fins. Hexagonal shape fin of the heat sink at fin height is 10mm more heat exchange through ambient air.

Table 2. Heat sink variable fin height with different shapes of heat sink air flowing pressure loss

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This study of the paper aims to get increased the performance of a Heat sinks in favor to a thermoelectric generator at low temperatures. The heat distribution through the heatsink, using simulation tool seeks to investigate and study the influence of the fin height and shape of cylindrical fins, 10 mm height of Fins change into the heat sink to improve the cooling performance and results. The carry-out efficiency of the Thermoelectric generator device improved at on temperatures. The geometrical fin cylindrical shape of a relative height fin and the fin must reach a high cooling level for the energy generation surface of potential through temperature gradient ∆T. As the temperature difference of the temperature gradient increases, then this efficiency of the thermoelectric generator increases. And future work for developments of the heat sink high performance for thermoelectric generator phase change material, environmental sustainability and flexibility of the fins design.