The past decade has seen tremendous growth in areas of micro- and nano-fluidics, and MEMs flow control. Nowadays, there is considerable interest in micro- and nano/technologies consisting of small structures in contact with liquid media. By increasing the motivations of using miniaturized devices such as MEMS and NEMS and inventing new methods of their manufacturing, the inspirations of their study and analysis have been increased more and more. One of the most important characteristics of these devices which have undeniable impacts on their performances is miniaturized-channel flow field. By decreasing the dimensions of channels, the influence of surface effects becomes prominent and cannot be ignored. One of the most charismatic categories of these phenomena is elecrokinetic effect which can results in electroosmotic flow field (EOF) that has many advantages such as being vibration free, being much more compact, having flat-form velocity and etc. These beneficiaries lead to the increasing stimulus of using this type of flow field. One of the most important disadvantages of EOF is the Joule heating effect, the generation of heat due to the electroosmosis effect. Besides, miniaturized-channels are usually used as heat sink in miniaturized devices. By considering these facts, it can be concluded that heat characteristics of EOF must be studied carefully in order to manage the Joule heating effect and to utilize the cooling characteristics of miniaturized-channels. By reviewing the studies that have been performed in this field of study, it can be concluded that there is not any analytical approaches in dealing with heat transfer of EOF in miniaturized-channels though analytical formulas are completely essential for investigating, monitoring and controlling of any systems. In this regards, having some analytical studies on heat transfer analysis of miniaturized-channel flow field is completely essential. In the present study, by using the Schwartz-Christoffel mapping, an analytical tactic will be proposed in order to find electroosmotic velocity and consequently temperature distribution of EOF in micro- and transitional nano-channels.

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