# Methodological Considerations of Using Thermoelectrics with Fin Heat Sinks for Cooling Applications
## 1 Introduction  
A thermoelectric (TE) module consists of a number of thermocouples connected electrically in series and thermally in parallel. TEs are used with fin heat sinks (FHS) to dissipate the heat to the atmosphere. During operation, heat is generated within the thermoelectric cooler (TEC) device due to the Joule heating effect. As a consequence more heat is transferred to the heat sink than absorbed from the heat source. Typical thermal cooling with an air-cooled FHS is shown in Figure 1a and a water-cooled plate heat sink in Figure 1b. Natural convection (NC) or forced convection (FC) by air could be employed. A typical FHS consists of a flat metal base with an array of cooling fins on top with aluminum or copper as the most common metals used. Thermal contact resistances occur at the interfacing metal contacts. In addition, thermal heat spreading resistance exists whenever there is a difference between the heat sink and heat source surface areas. As semiconductor chips become more powerful and compact, they require greater heat dissipation. Hence, more effective thermal cooling systems have to be devised. A thermal cooling device consisting of an air-cooled FHS coupled to a TE module is shown in Figure 2.  
Thermal heat spreading has been investigated by various researchers. [PERSON] et al. [1] investigated the spreading resistances of various flat rectangular plates with various surface heat transfer coefficients. They compared their simulations with other known existing theories and found that for relatively thick plates, the constriction thermal resistance is insensitive to plate thickness and Biot number. It was solely dependent upon the relative contact size between the heat sink and heat source. [PERSON] [2] simulated thermal heat spreading resistance using exact partial differential heat transfer equations and compared them with those obtained by [PERSON] et al. [1] using aluminum and copper flat plate heat spreaders and under forced convection air cooling. [PERSON] et al. [3], on the other hand, applied the conductive thermalinterface material to reduce the resistance. [PERSON] [4] derived an exact three-dimensional solution to determine the maximum heat spreading resistance for rectangular heat sources centered on larger sized plane heat sinks. [PERSON] et al. [5] presented a general solution based on the separation of variables method for the thermal spreading resistances of eccentric heat sources on a rectangular flux channel. General expressions of an isoflux rectangular source on the surface of finite isotropic and compound rectangular flux channels were presented, as well as the solution for the temperature at the surface of a rectangular flux channel. An overview of applications of TE devices for thermal cooling could be found in [PERSON] [6], [PERSON] and [PERSON] [7], and [PERSON] [8]. [PERSON] et al. [9] obtained hot side temperatures between 40 \({}^{\circ}\)C and 62 \({}^{\circ}\)C and cold side temperatures between 8.4 \({}^{\circ}\)C and 14.8 \({}^{\circ}\)C at a power input of less than 80 W with cascaded or stacked TEs. [PERSON] [10] presented a brief description of commercial TE modules and showed how graphs provided by manufacturers could be utilized to select a module for a specific application. [PERSON] et al. [11] developed equations that connect heat loads with material properties of the TE module and the cold and hot side operating temperatures. They went on to determine the optimum heat sink resistances for a fixed set of operating conditions and considered various existing heat sink heat exchangers to meet the resistance requirement of the heat sink. [PERSON] and [PERSON] [12] developed a computer model to show the relationship between the cooling and heating requirements and the optimum TE properties. [PERSON] and [PERSON] [13] presented a theoretical model to determine the performance of a TE device for electronic cooling by assuming values of the hot and cold junctions and then determined the resistance of micro-channel heat sinks. [PERSON] et al.