**7. References**


[1] W.J. Bowman and D. Maynes (2001): A review of micro-heat exchanger .ow physics,

[2] G.L. Morini (2004): Single-phase convective heat transfer in microchannels: a review of

[3] T.T. Dang (2010): A study on the heat transfer and fluid flow phenomena of

[4] T.T. Dang, J.T. Teng, and J.C. Chu, Pressure drop and heat transfer characteristics of

experimental results, *Int. J. of Thermal Sciences*, Vol. 43, 631-651

York, USA, Nov 11-16, HTD-24280, pp. 385-407

Thermal and Fluid Transport Phenomena, 2011

fabrication methods and application, Proceedings of ASME IMECE 2001, New

microchannel heat exchanger, Ph.D. thesis, Chung Yuan Christian University,

microchanel heat exchangers: A review of numerical simulation and experimental data (Accepted for Publication), International Journal of Microscale and Nanoscale

h heat transfer coefficient, W/m2K k overall heat transfer coefficient, W/m2K

Kv volumetric heat transfer coefficient, W/m3K

distance from the nozzle to the breakdown point of the jet, m

Kr thermal conductivity ratio

L length of channel, m

m mass flow rate, kg/s n number of tubes

Nu Nusselt number

p pressure, Pa

NTU Number of Transfer Unit

*Nu* average Nusselt number

R thermal resistance, m2K/W

dynamic viscosity, Ns/m2

thermal conductivity, W/m K

performance index, W/kPa

T different temperature, K p pressure drop, Pa

density, kg/m3

 velocity, m/s ε effectiveness

liquid fill ratio

Chung-Li, Taiwan

P wetted perimeter, m Q heat transfer rate, W q heat flux, W/m2

Re Reynolds number T temperature, K Td mean temperature, K V volume flow rate, m3/s Z nozzle-to-wall distance, m

**Greek symbols** 

**7. References** 


**11** 

*Spain* 

**Heat Exchangers for Thermoelectric Devices** 

Heat exchangers play an important role in the performance of thermal machines, namely, electric power generators, engines and refrigerators. Regarding thermoelectrics, this influence is even higher, owing to the difficulty of transferring heat from the small surface area of a typical thermoelectric module to a bigger one. Particularly, in the hot face of an average 40 mm x 40 mm Peltier module, the heat flux readily yields 40600 W/m2. The thermoelectric effects, namely, Joule, Seebeck, Peltier and Thomson, describe the interaction between thermal and electric fields, and are well known since the XIX century (Rowe, 2006). German physicist Thomas J. Seebeck discovered in 1821 that an electric circuit composed of two dissimilar conductors *A* and *B* connected electrically in series and exposed to a thermal gradient induces an electric current -or an electromotive force (*EAB*) if the circuit is openedwhich depends on the materials and the temperature difference between junctions (*∆T*). This

> *AB AB A B E T*

Likewise, in 1834, French physicist Jean Peltier discovered that if an electrical current (*I*) is applied across the electric circuit composed of two dissimilar conductors, the inverse effect takes place, that is, heating occurs at one junction whereas cooling occurs at the other. This

> . *Q I IT <sup>P</sup>*

In 1851, William Thomson stated the *Thomson effect*, which indicates that a homogeneous material exposed to thermal and electrical gradients absorbs or generates heat. Moreover, he described the relation between Seebeck and Peltier effects, given by *Thomson coefficient τ*.

*<sup>A</sup> <sup>B</sup> TTT B A T TT*

The possibility of using thermoelectric devices to produce electric power was raised by John W. Strutt in 1885. Subsequently, between 1909 and 1911, Edmund Altenkirch proved that

 

 

thermoelectric materials must feature high Seebeck coefficient (

 ) and low thermal conductivity (

 *AB BA* 

( ) *A B*

 

(3)

 

phenomenon is called **Seebeck effect**, characterized by the *Seebeck coefficient* 

phenomenon is called **Peltier effect**, described by the *Peltier coefficient π*.

**1. Introduction** 

conductivity (

David Astrain and Álvaro Martínez

*Public University of Navarre* 

.

(2)

), in order for the material to retain heat in

), high electrical

(1)

