Introduction

Preserving fresh foods and vegetables in clean and appropriate conditions is an important issue for human health. Generally, vapor compression refrigerator has been used for cooling applications in homes and supermarkets. But the large size of vapor compression refrigerator limits its application in small and temporary places.

Utilizing thermoelectric cooling system can be a good alternative for vapor compression refrigerator because of its several advantages. Thermoelectric refrigerators have low energy efficiency in comparison with traditional refrigerators. However, their rapid thermal response, long lifetime, high reliability, silent operation, having no fluid with environmental impact, lightweight and compact structure make them attractive to use as mini-refrigerator for preserving foods and drugs in small places and also as a portable refrigerator. In addition, thermoelectric refrigerators can be a good solution for people living in refugee camps. Furthermore, the thermoelectric device can be used in different applications such as generating electricity from waste heat, cooling electronic components and air-conditioning [1]. The Peltier effect is also utilized in thermal analysis, heat flow compensation, calorimetry and calibration. Cooling devices on the Peltier effect are used for the design and manufacturing of isothermal microcalorimeters and PC processors [2].

In the literature, thermoelectric systems have been investigated by many researchers with regard to energy efficiency and optimum working conditions. The optimum input electrical current was specified in a wide range of heat loads by Chang et al. [3]. In another study, thermoelectric materials, applications, modeling approaches were reviewed and TE cooling applications including electronic cooling systems, domestic refrigeration and automobile air-conditioning were discussed [4]. Compression vapor heat pump and refrigerator system were evaluated for increasing their efficiency by means of thermoelectric generation using compressor heat losses [5]. Thermal balance equations were developed to find out TE performance using analytical solutions by Zhang [6]. Yin et al. investigated the effect of adding thermoelectric generator on the performance of four different photovoltaic cells, including monocrystalline silicon, polycrystalline silicon, amorphous silicon and polymer photovoltaic cell. They indicated that increasing the thermal resistance of thermoelectric can remarkably enhance the performance of the system [7].

Efficient heat transfer, as one of the first-order problems in the field of cooling-heating systems and other industrial processes, is a title for many researches in the literature [8,9,10]. Mixed convection heat transfer as an advanced method was used to enhance heat transfer rate of water-based nanofluids in microchannel [11]. Mini-channel water-cooled thermoelectric refrigerator was studied, and COP value of the system was obtained in different flow rates and voltages over the time by Gokcek et al. [12]. A prototype domestic TE refrigerator was investigated to evaluate the system performance in terms of the coefficient of performance and cooling rate [13]. Two-stage thermoelectric coolers were used to increase the cooling capacity and COP value of TECs, and the applied electrical current was optimized by Cheng et al. [14]. In another study, a mini-thermoelectric refrigerator was manufactured using Peltier element to obtain optimum working conditions. Refrigerator box was equipped with Peltier–fans combination on both sides. The obtained results showed that optimum ambient temperature is 293 K. Also, COP reduces from 0.351 to 0.011 when the temperature of the cooled space decreases from 293 to 254.8 K [15]. Tan et al. theoretically analyzed a thermoelectric cooling system by using the thermodynamic second law to achieve the optimal working conditions. They investigated the effects of different parameters like electric current, thermal conductivity and cooling temperature on the system performance. From the results, it was indicated that cooling temperature was the most significant parameter affecting thermoelectric cooling system performance [16]. Modified pulse operation of thermoelectric for building cooling application was numerically investigated by Manikandan et al. The thermoelectric cooling system was analyzed by applying different cooling load, variable pulse current ratio, variable pulse width and dissimilar pulse shapes. The findings showed that modified pulse operation could enhance the cooling rate and COP by 23.3% and 2.12% in comparison with normal mode of operation [17]. Enescu et al. designed and simulated a thermoelectric refrigerator powered by solar photovoltaic cells and electric storage system [18]. Dimri et al. developed a thermal model for semitransparent photovoltaic thermal system equipped with thermoelectric. Their results showed that adding thermoelectric device to the semitransparent photovoltaic system increased the electrical efficiency by 7.266% [19]. Wang et al. used miniaturized thermoelectric device for microprocessors chip cooling. They experimentally and numerically investigated the effects of using this cooling system on microprocessors performance. The importance of thermal contact resistance was revealed, and it was shown that a higher thermal contact resistance needs a larger mini-contact to obtain optimum performance [20].

Moazzez et al. developed an experimental and numerical study to use thermoelectrics as a choice for air-conditioning inside the cars. It was revealed that the regulation in the layout of the heat sinks can improve the performance of the system [21]. The phase-change material has been integrated at the hot side of the thermoelectric cooler to maintain constant and relatively low temperature. This technique was used to increase thermal performance of the thermoelectric cooler. Variable geometric parameters of the heat sink, variable input currents to the TEC and variable cooling load conditions with different phase-change materials were investigated. The results showed that, with the use of phase-change material, temperatures of the thermoelectric cooler are reduced in both hot and cold sides [22].

The main objectives of this study are analyzing the effects of using different heat sink and comparing cooling performance of air-to-air and air-to-water modes. In this regard, three different size prototype thermoelectric refrigerators were manufactured and tested in different working conditions. CFD as a widespread method is a branch of fluid mechanics that uses numerical analysis to simulate engineering and industrial problems that involve fluid flows [23, 24]. In this work, the problem was also simulated with regard to extensive theoretical considerations established with the support of CFD software to analyze air flow structure and thermal behavior of the refrigerators.

Experimental setup and test procedure

Thermoelectric modules are also considered as energy converters consisting of a bunch of thermocouples electrically connected in series. They are made of two different semiconductors that produce a thermoelectric cooling effect when a voltage is applied in the appropriate electric direction. Thermoelectric modules generally operate with two exchangers attached to their cold and hot sides in order to enhance heat transfer and increase performance of the system. In this study, three different sizes of laboratory refrigerator boxes manufactured of styrofoam sheets were used to examine the Peltier cooling performance in different working conditions. A, B and C box capacities are 15 × 15 × 15, 20 × 20 × 20 and 30 × 30 × 30 cm respectively. In all three boxes, air-to-water and air-to-air modes were tested experimentally and obtained results have been compared. Schematic views and pictures of the refrigerators are shown in Fig. 1. The temperature variations were measured with T-type thermocouples, and the average temperature of the box was obtained. Electrical power consumption was also calculated by recorded current and voltage values obtained by using voltage/ampere meter device. For air-to-air mode, two different 12-V DC fans were employed to provide forced convection heat transfer.

Fig. 1
figure 1

Pictures and schematic views of air-to-water (I) and air-to-air (II) experimental setup

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In the air-to-water mode, however, a water pump and suitable water-cooled heat exchanger attached to the hot side of thermoelectric Peltier were used. The most important part of the system consists of a thermoelectric Peltier, which features are presented in Table 1. Features of used water pump and heat exchanger have been also presented, respectively.

Table 1 Peltier thermoelectric, water pump and heat sink features
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The processing flow diagram of experimental and numerical methods is shown in Fig. 2.

Fig. 2
figure 2

Overall numerical and experimental processing flow diagram

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Analysis

Experimental analysis

Generally, in scientific studies on thermoelectric refrigerators, performance calculations can be made by two different methods.

In the first method, analysis starts with the prediction of the thermoelectric cooling and heating power. By assuming constant thermal and electrical properties of thermoelectric, cooling power at the TEC cold side and heat transfer amount at hot side (Qc and Qh) can be expressed as (Chang et al. 2009),

$$ Q_{{\text{c}}} = \alpha T_{{\text{c}}} I - \frac{1}{2}\left( {I^{2} R} \right) - K\left( {T_{{\text{h}}} - T_{{\text{c}}} } \right) $$
(1)
$$ Q_{{\text{h}}} = \alpha T_{{\text{h}}} I - \frac{1}{2}\left( {I^{2} R} \right) - K\left( {T_{{\text{h}}} - T_{{\text{c}}} } \right) $$
(2)

COP value of the thermoelectric material can be expressed as,

$$ ({\text{COP}})_{{\text{c,max}}} = \frac{{T_{{\text{c}}} }}{{T_{{\text{h}}} - T_{{\text{c}}} }}\frac{{\sqrt {1 + ZT_{{\text{m}}} } - \frac{{T_{{\text{h}}} }}{{T_{{\text{c}}} }}}}{{\sqrt {1 + ZT_{{\text{m}}} } + 1}} $$
(3)

where ZTm is the thermoelectric material figure of merit at average hot and cold side temperature Tm.

In the second method used in the present study, power consumption of the Peltier, water pump and fan should be taken into consideration and so the total COP value of the system can be written as follows,

$$ {\text{COP}}_{{{\text{Tot}}}} = \frac{{Q_{{\text{c}}} }}{{W_{{{\text{pe}}}} + W_{{{\text{fa}}}} + W_{{{\text{Pu}}}} }} $$
(4)

On the other side, the amount of absorbed heat from the enclosed environment can be calculated by the following equation,

$$ Q_{{\text{c}}} = mC_{{\uprho ,{\text{air}}}} \left( {T_{2} - T_{1} } \right) $$
(5)

where T2 and T1 are the first and last temperatures of the refrigerator box and m is the air mass inside box. The mass of air contained in the refrigerator box can be obtained from the volume of the refrigerator box and the density of the air.

$$ m = \rho v $$
(6)

Consumed electrical power can be calculated from recorded current and voltage values as,

$$ W = IV \times \left( t \right) $$
(7)

Heat transfer by water in the air-to-water mode can be can be expressed as,

$$ Q = \dot{Q} \times t = \left( {\dot{m}C_{{\uprho ,{\text{wat}}}} \left( {T_{2} - T_{1} } \right)} \right) \times t $$
(8)

CFD analysis

Simulation of engineering problems is a widespread method, frequently utilized to provide a holistic comprehension opportunity, accurate prediction and comparing to real situation. Simulation is also a scenario that closely mimics mechanical situations as well as other physical situations, which generally merges theory with actual perspectives and often provides insight into expected behaviors. In this study, ANSYS Fluent 16 as a CFD software is used to solve the problem and to meaningfully describe the flow structure and thermal behavior in the thermoelectric refrigerator box.

The model has been solved in transient state by using the mesh motion method to operate rotational movement of fan blades. SIMPLE second-order pressure, second-order upwind discretization scheme for energy, momentum, dissipation rate and turbulent kinetic energy were applied to solve the model. In this study, time step size of 0.03 s and max iterations/time step of 40 were defined to obtain heat transfer and temperature distribution over the solution time. The boundary condition of the present study is demonstrated in Fig. 3a.

Fig. 3
figure 3

Boundary conditions and domain extends (a) and schematic view of the mesh quality of refrigerator box, fan and exchanger (b)

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Here, basic conservation equations in differential form have been presented as follows [33].

Mass conservation;

$$ \frac{\partial \rho }{{\partial t}} + \nabla .\left( {\rho {\varvec{u}}} \right) = 0 $$
(9)

Momentum equation;

$$ \frac{{\partial \rho {\varvec{u}}}}{\partial t} + \nabla .\left( {\rho {\varvec{uu}}} \right) = - \nabla {\text{p}} + \nabla .\left( {\overline{\overline{\tau }}} \right) + \rho {\varvec{g}} + {\mathbf{F}} $$
(10)

where p is the static pressure, \(\overline{\overline{\tau }}\) is the stress tensor ρg and F are gravitational body force and external body forces.

Energy conservation;

$$ \frac{\partial }{\partial t}\left( {\rho E} \right) + \nabla .\left( {{\varvec{u}}\left( {\rho E + p} \right)} \right) = \nabla .\left( {k_{{{\text{eff}}}} \nabla {\text{T}} - \mathop \sum \limits_{{\text{j}}} h_{j} {\varvec{J}}_{j} + \left( {\overline{\overline{\tau }}_{{{\text{eff}}}} .{\varvec{u}}} \right)} \right) + S_{{\text{h}}} $$
(11)

where keff is the effective conductivity, J is diffusion flux of species and Sh is volumetric heat source. k−\(\varepsilon\) Realizable model is one of the most used solution models in numerical methods which is also used in the present work as follows:

$$ \frac{\partial }{\partial t}\left( {\rho k} \right) + \frac{\partial }{{\partial x_{{\text{i}}} }}\left( {\rho ku_{{\text{i}}} } \right) = \frac{\partial }{{\partial x_{{\text{j}}} }}\left[ {\left( {\mu + \frac{{\mu_{t} }}{{\sigma_{{\text{k}}} }}} \right)\frac{\partial k}{{\partial x_{{\text{j}}} }}} \right] + G_{{\text{k}}} + G_{{\text{b}}} + S_{{\text{k}}} - Y_{{\text{M}}} - \rho \varepsilon $$
(12)
$$ \frac{\partial }{\partial t}\left( {\rho \varepsilon } \right) + \frac{\partial }{{\partial x_{{\text{i}}} }}\left( {\rho \varepsilon u_{{\text{i}}} } \right) = \frac{\partial }{{\partial x_{{\text{j}}} }}\left[ {\left( {\mu + \frac{{\mu_{{\text{t}}} }}{{\sigma_{\upvarepsilon } }}} \right)\frac{\partial \smallint }{{\partial x_{{\text{j}}} }}} \right] + C_{1\varepsilon } \frac{\varepsilon }{k}C_{{3\upvarepsilon }} G_{{\text{b}}} + S_{\upvarepsilon } + \rho C_{1} S\varepsilon - \rho C_{2} \frac{{\varepsilon^{2} }}{{k + \sqrt {v\varepsilon } }} $$
(13)

where

$$ C_{1} = \max \left[ {0.43, \frac{\eta }{\eta + 5}} \right]\quad \eta = S\frac{k}{\varepsilon }\quad S = \sqrt {2S_{{{\text{ij}}}} S_{{{\text{ij}}}} } $$
(14)

\(G_{{\text{k}}}\) represents the generation of turbulence kinetic energy due to the mean velocity gradients, \(G_{{\text{b}}}\) is the generation of turbulence kinetic energy due to buoyancy, \(Y_{{\text{M}}}\) represents the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate, and \(C_{{1\upvarepsilon }}\) and \(C_{2}\) are constants. In Fig. 3a, b schematic view of the mesh configuration is displayed where the analysis domain has been defined. In order to increase the accuracy of the calculations and reduce the error rate, various revisions in mesh generation and problem solving are required. In this study, mesh analysis has been performed to select optimum mesh number, cell types and sizes. Curvature mode and triangle mesh surface were selected with growth rate of 1.2 and maximum face size of 1.295 × 10–2 m. Skewness value was also checked in the mesh generation process; average and maximum skewness values in the solution are about 0.26 and 0.80, respectively.

Results and discussion

Experimental results

In this work, planned experiments with different box sizes (A, B and C) were conducted to determine and compare the performance of thermoelectric materials in two different modes including air-to-air and air-to-water modes. The internal temperature of the boxes was recorded during experiments, and the average temperature obtained from the thermocouples was calculated.

Figure 4 represents the experimental results for temperature variation over the test time that is 480 s. The acquired results indicate that air-to-water state has the capability to decrease temperature faster, and lower temperatures can be achieved in this mode. It seems that, in larger boxes (like case C), one thermoelectric is insufficient to access lower temperature rapidly and so more Peltier devices should be used in the system.

Fig. 4
figure 4

Temperature of refrigerator boxes (A, B and C) with respect to test time at two modes (air-to-water and air-to-air)

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In order to calculate the total COP values, the total amount of power consumed in the system should be measured. The consumed electrical power was obtained from the continuously recorded voltage and current values using a digital volt-ampere meter. In all experiments, it was revealed that the power consumption in air-to-water was about 5–10% higher than air-to-air mode.

Furthermore, at the beginning of the experiments, the power consumption is at its highest point, but decreases gradually during time. In air-to-air mode, this value was decreased and fixed at the constant value toward the end of the test time. The power consumption values of all test boxes are given in Fig. 5 for both modes.

Fig. 5
figure 5

Power consumption results of test boxes (A, B and C) in two modes

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The corresponding COP results calculated from Eq. (8) for TEC system under air-to-water and air-to-air cooling conditions are shown in Fig. 6 for different test boxes. It was revealed that small box (A) has the maximum performance among test boxes due to lower heat losses and also at the beginning COP values of the air-to-water mode is noticeably higher than air-to-air mode.

Fig. 6
figure 6

COP results of A, B and C boxes versus test time for air-to-water and air-to-air modes

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However, its value decreases gradually over test time and becomes less than air-to-air mode at the end of the experiments.

The COP diagrams presented earlier in Fig. 6 showed that its value in the air-to-water mode is reduced toward the end of the test time and become less than those of air-to-air mode. This is because the air-to-water mode is able to draw faster thermal energy out of the box at the first seconds of this experiment. Furthermore, lower temperatures were obtained in the air-to-water mode during the test time, which is an indication of their higher effective operation. For better comparison, the average COP values were also compared in two modes for the A, B and C boxes presented in Fig. 7, which shows a 30–50% improvement in the air-to-water mode.

Fig.7
figure 7

Average COP results of test boxes (A, B and C) in two modes

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At the first step during the calculations and analysis of the obtained results, the low COP values of the refrigerator were thought outside of expectations and unreasonable and led to a criticism. However, after a thorough and basic screening and research on the literature results, it was observed that the COP value in the refrigerators and cooling devices is low and is not a constant value as heat pumps.

In refrigerators and cooling systems, the decline of COP over time has made it more difficult to compare different types of refrigeration devices. However, even if the COP value is low and inefficient for refrigerators, cooling purpose can be achieved with very little power consumption for quotidian cooling or freezing necessities. Generally, low COP values of refrigerators have been considered and partially discussed in the literature as shown in the form of a table (Table 2). The reason for this issue is that, in the refrigerators the thermal energy reserves are only available in a certain small volume on the evaporator side (unlike heat pumps and air-conditioning systems, which extract energy from large areas and thus benefit from a wider energy source). In particular, when the cooling process begins, the temperature of the refrigerator box begins to drop and the thermal energy levels inside volume is further fallen down and consequently the COP value decreases. Although this is more remarkable in Peltier cooling systems, these systems are becoming widespread because they are considerably lighter and easier to install.

Table 2 A comparison of the results obtained in the present study with the literature
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CFD results

In this section, the velocity and temperature contours obtained from CFD solution are presented to survey flow structure and thermal behavior of the refrigerator over the cooling time.

In Fig. 8a, velocity volume-rendering methods are utilized in the first step to illustrate an overall three-dimensional visualization of the velocity and fluid flow of the model for smallest box (A). The interior space of the refrigerator, fan rotation and the air circulation is clearly indicated in the figure.

Fig. 8
figure 8

3D velocity volume-rendering results a 2D velocity contour, b and streamlines c inside refrigerator box A

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In Fig. 8b and c, two-dimensional velocity contour and streamlines inside air-to-air refrigerator box (box A) are also presented. From the velocity contour, it can be observed that a high-velocity region in front of the fan is created and consequently vorticity formation is likely to be occurred. In the next stage, formation of vortex in the flow structure is given in the streamlines configuration. The number of streamlines and line width have been adjusted to make them easier to distinguish from each other on a central plane. Another important issue is that, streamlines configuration is slightly changed over the time and small vortex is appeared from time to time, but their general configuration is similar to that provided in Fig. 8c. In the present study, numerically obtained streamlines and velocity pattern can be surveyed experimentally using particle image velocimetry (PIV) system which is a high-cost technique and needs laboratory equipment.

In thermoelectric coolers, the Peltier effect is utilized to produce a heat flux at the junction of two different types of materials. Heat exchangers have an important role in this type of cooling systems. In order to enhance the heat transfer rate from hot and cold sides and also to increase the efficiency of the Peltier device, efficient heat exchangers are required on both sides. More importantly, a Peltier device operated without cooling applications on the hot side is exposed to an internal temperature increasing exponentially until the internal joins melt and consequently the device will quickly burn out. In Fig. 9, the temperature distribution for box A is shown at 12 steps in 5-s intervals. According to CFD results, in the cooling trend, the role of Peltier thermoelectric and heat exchanger in extracting thermal energy from refrigerator box is clearly shown. In the presence of an exchanger and fan, convective heat transfer mechanism has been activated and low-temperature air flow separates from exchanger and approaches the high-temperature zone and this process causes the thermal energy to be evacuated from the refrigerator.

Fig. 9
figure 9

Temperature distribution of refrigerator (A) in 5-s intervals

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Within the same period and at the end of stage 12 (60th second), temperature distribution of all boxes (A, B and C) is presented in Fig. 10. In other words, the final contour in Fig. 9 was also provided for boxes B and C, and the results of all boxes are compared in Fig. 10.

Fig. 10
figure 10

Temperature distribution of refrigerator boxes A, B and C at 60th second

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As shown in the figure, cooling process of the smallest box in volume (A) is considerably quick compared to other boxes, which shows a good agreement with the experimental results. It can be observed that, in larger boxes, if more rapid cooling is desired, more Peltier thermoelectric should be employed.

Conclusions

In this work, different sizes of cube boxes were made using styrofoam sheets and Peltier thermoelectric efficiency was examined for air-to-air and air-to-water experimental sets in laboratory conditions. In air-to-air mode, two heat exchangers and two fans were attached on hot and cold surfaces. In the air-to-water mode, the fan and heat exchanger of the cold surface were the same, but a water-cooled exchanger was used instead of the fan on the hot surface, and the values obtained from the two modes were compared.

In this study, it was observed that the average COP value of air-to-water mode is approximately 30–50% higher than that of air-to-air mode. In other words, air-to-water thermoelectric cooling device operates more efficiently. In addition, the COP values of the refrigerators calculated by the thermodynamic method were compared with several research in the literature. However, the obtained COP results are very low in contrast to heat pumps.

In addition, ANSYS Fluent software was used to simulate the problem and required contours were prepared to survey heat and fluid flow characteristics inside refrigerator box.