Dual harvesting from exhaust gas of diesel generators using thermoelectric generators and cold water tank

The present work concerns a dual harvesting concept applied to exhaust gas of Diesel generators using thermoelectric generators and cold water tank. To proceed, a simplified thermal modelling is developed and appropriate parametric analysis of power generation with the TEGs and heat recovered is conducted in function of the Diesel generator power and the TEG thermal conductivity and thickness. It was shown that powers up to 534 W can be generated with the TEGs and heat recovery rates up to 4463 W can be obtained for a Diesel generator power of 125 kW. Also, it was shown that the temperature difference across the TEGs and the power generated increase exponentially when the Diesel generator power and ratio of thickness to thermal conductivity of TEGs increase.

As one reads through the literature on TEG applications that currently exists, it becomes clear that creating notable temperature changes is a hurdle that arises in physical applications [42][43].
At this point, this manuscript suggests a hybrid idea of power generation and heat recovery employing the hot exhaust gas of generators, a cold water tank, and TEGs.TEGs are installed in a plane wall that divides the passage of exhaust gases from a water tank that is generally chilly.Consequently, the hot exhaust gas flow will heat TEG higher surface while the cold water will cool the lower surface.Furthermore, because it allows for simultaneous direct heat exchange exhaust gas-water across TEG plate, the system is hybrid in nature.In order to continue, a basic thermal model is created, and a suitable parametric analysis of the power generation and heat recovered using TEGs is carried out based on the power of the diesel generator as well as the thickness and thermal conductivity of the TEGs.The temperature difference is determined by using the heat diffusion equation HDE to first compute the temperature field.TEGs plate is regarded as a flat wall, as was previously mentioned.Under steady-state with no heat generating circumstances, HDE simplifies to [44]:

Thermal Modeling and Calculations
Next, the boundary criteria listed below are applied [44]: TMREES-2023 Journal of Physics: Conference Series 2754 (2024) 012021 The following can be used to obtain the temperature gradient and distribution throughout the TEGs: The value of c T f in equation 5 will be determined, and c h will be derived from [44].Input values will be t , k .h T f and h h , however, are reliant on the generator's operating settings.The ratio of power is the definition of a generator's efficiency [45]: A little portion of the heat of combustion (30 to 40% [45]) is lost as power in the exhaust gases: Grouping ( 6) and ( 7) yields to: Concurrently, the exhaust gases' energy rate is: Where g m is the exhaust gas flow rate and amb T is the ambient temperature.
One can compute the fuel (Diesel) flow rate using: Where c q is the fuel heat of combustion.
The effects of the design parameters such as generator power and the TEG thickness-thermal conductivity ratio k t / on the TEGs power generation and water heating are investigated below.To .25 computations related to similar number of configurations of generator power and k t / were executed.5 generator powers equal to 25, 50, 75, 100, and 125 kW and 5 ratios of 0.002, 0.004, 0.006, 0.008, and 0.01 were adopted.According to earlier research [47][48], the ratio fluctuates between 0.002 and 0.005.In the event that ratio's future production is conceivable, the higher ratios of k t / are interpreted as a parametric test for possible suggestions of new ratios for temperature gradient enhancement and, subsequently, power production enhancement.Consideration is given to the conversion temperature difference -power of the TEG provided in [47].As Figure 2 makes evident, when the Diesel generator power and ratio k t / grow at the same time, T ' and TEGs P rise exponentially.T ' rises from 26 to 51 °C and TEGs P increases from 13 to 52 W, as an example for a ratio k t / of 0.002, when the generator power increases from 25 to 125 kW.An additional example for a ratio k t / of 0.01 shows that when the power generator is increased from 25 to 125 kW, T ' fluctuates from 116 to 210 0 C, and TEGs P is generated between 218 and 534 W. In conclusion, the increase in TEGs P and T ' is more significant as the ratio k t / rises in addition to the generator power.As a last example, using a 125 kW generator, TEGs P rises from 52 to 534 W and T '

Results and discussion
rises from 51 to 210 0 C as the ratio k t / grows from 0.002 to 0.01.
Beside power generation using TEGs due to exhaust gas-water temperature differences, there is a direct heat transfer between exhaust gas and water and then water is being heated with the time.Therefore, it is also important to look at the heat recovered from the exhaust gas and gained by water.This heat is equal to the heat transfer by conduction through the TEGs thickness minus the power generated with the TEGs and then the heat recovered can be calculated using the following relation: The energy gained by water when its temperature is raised from a temperature wi T equal to the ambient temperature of 20 0 C to a final temperature wf T of 60 0 C (temperature of water that permits its use as hot water) is given by the following relation: Where U is the water density and w p C , is the specific heat of water and considering the height of the water tank equal to its length and width L .
Finally, the time taken to heat water up to wf T is: Figure 3 shows the variation of the recovered heat (Figure 3-a

Concluding remarks
In this manuscript, a dual harvesting concept applied to exhaust gas of Diesel generators using thermoelectric generators and cold water tank is investigated.To proceed, a simplified thermal modelling is developed and appropriate parametric analysis of power generation with the TEGs and heat recovered is conducted in function of the Diesel generator power and the TEG thermal conductivity and thickness.
The following conclusions can be drawn: 1-The temperature difference and the power generated increase exponentially when the Diesel generator power and k t / increase.

Figure 2
Figure 2 depicts a simplified thermal modeling of the TEGs in the convection conditions.

Figure 1 .
Figure 1.Thermal representation of the TEGs plate situation.
proceed, computations are performed for an exhaust gas duct height H of 0.05 m, TEGs plate length and width of 0.4 m, c T f of 40 0 C (average between starting temperature of 20 0 C and heated water temperature of 60 0 C), and an ambient temperature amb T of 20 0 C. c h was considered equal to 650 W.m -2 .K -1 [46]

Figure 2
Figure 2 depicts the evolution of T ' (Figure 2-a) and the power generated by all TEGs TEGs P (Figure

Figure 2 .
Figure 2. Variation of (a) T ' and (b) TEGs P with the Diesel Generator Power and ratios k t / .(a) (b)

6 Figure 3 .
Figure 3 shows the variation of the recovered heat (Figure 3-a) and the time needed to heat water up to 60 0 C (Figure 3-b) in function of the Diesel Generator Power for different ratios k t / .
The recovered heat increases exponentially as the Diesel Generator Power increases and decreases almost linearly as k t / increases.3-The water heating time decreases exponentially as the Diesel Generator Power increases and increases almost linearly as k t / increases.