Fuel cells are new power sources which produce electricity without any noise or environmental contamination. Fuel cells are used nowadays for rural, military portable and station applications [1]. Direct methanol fuel cells are one of prominent fuel cells which have high current density. Unfortunately direct methanol fuel cells have some technical problems such as methanol toxicness, expensive Pt-based catalysts, and high methanol cross over, thus, there are trends to substitute methanol with other fuels. Ethanol, acid acetic and acetaldehyde are proposed alternatives [2-5]. Recent ethanol fuel cell activities have been more experimental to date and only 1D analytical model has been proposed for DEFC so far. This model has been proposed by G. Andreadis and his colleagues by considering over potential changes inside catalyst layer [6-9]. In this paper, we try to present a 2D fully analytical model with simple consideration. With regard to Fuel cell coordinates, which have been illustrated in Figure 1, following assumptions have been made

1) Fluid flows in the steady state.

2) Fuel cell temperature is constant in the active area and chemical reaction takes place under constant temperature.

3) Reactants diffusion and transportation in catalyst layer along y direction is not considered.

4) Due to low diffusion layer thickness before its size long channel length, reactants concentration change across diffusion layer is ignored.

5) Reactants diffusion inside diffusion layer along y direction has been ignored because of low diffusion layer thickness before its length.

6) Because the thickness of membrane is so smaller than its thickness, reactants diffusion along y direction is ignored.

7) Due to smaller depth of ethanol and water transporttation channel than its length, reactants concentration change along x direction inside the channel has been neglected.

8) Pressure drop inside channel is neglected.

9) Fluid flows at constant velocity inside the channels.

Anode and cathode overall reaction is as follows

Ethanol concentration inside anodic channel, could be mentioned as below

Whereas is mass flux from anodic channel through diffusion layer. Based on Fick’s law, we can write the following equation for mass flux, whereas is diffusion coefficient of ethanol through diffusion layer

It can be noticed that for 12 M electron production, 1 M ethanol is consumed. Furthermore ethanol crossover lead to a part of ethanol permeate through membrane, so

Current density can be written as below

In which is anodic over potential and is crossover from membrane as below

The equations for cathode are similar to those for the anode, so

, current density is

That is cathodic over potential. Equations (2) and (3) can be written for cathode, thus

For oxygen concentration variation inside channel

At last, for fuel cell voltage and current density, following equations is determined

That is current density, membrane thickness, membrane conductivity, ideal electromotive force, and is electromotive difference rate. (Difference of exchanged gas moles between two sides of reaction in (1)) and (number of exchanged electrons) are constants which are –1 and 12 for (DEFC) respectively. Other symbols are listed in Table 1 or Nomenclature.

In this solution, ethanol concentration in cathode layer in neglected (zero) and ethanol is linearly distributed, thus

and are substituted with, respectively, and then will be found 

By substituting Equation (7) in Equation (9) and integrating from 0 to, oxygen concentration in catalyst layer is

By assuming and substituting Equation (8) in Equation (15)

Whereas is defined as follows

With regard to Equations (7), (8), (10) and (16) the below equation is acquired

whereas is

At last, by integrating Equation (18) and assuming, oxygen concentration inside anode channel will be found

Concentration of oxygen in the catalyst layer can be determined by substituting (20) into (16)

Substituting Equation (21) into (8) and integrating

Such trend can be implemented for anode side, thus Ethanol concentration variation inside anode channel could be written as follows

Ethanol concentration distribution in the catalyst layer is

Ethanol concentration average in the catalyst layer, by integrating (24) through to is

Average current density

, , are variants as below

Finally, by using Equations (14), (25), and (26), following equations between anode over potential and cur rent density is attained

Using Equations (14), (22), (25), following equation between cathode over potential and current density could be presented

By using Equations (11) and (12) and combining them with Equations (30) and (31) polarization curves will be obtained. It should be mentioned that these two equations are solved by numerical methods

In this paper by an analytical 2D model, (DEFC) performance was predicted. This model is capable of estimating polarization curves up to 0.5 M. This model is precise in the first and second zone (Activation and Ohmic loss region), but in the third zone (Concentration loss region) because of neglecting concentration loss and increasing inlet ethanol concentration, model error will increase and it will have more difference with experimental curves. Based on model, ethanol concentration varies almost linearly inside anodic channel. By increasing current density cathodic over potential remains zero but anodic over potential will increase up to certain value.