: In the present thesis, the flow through three - dimensional micro channel under an axial electric field and Transverse magnetic and electric fields with axial pressure gradient has studied numerically. Governing equations were solved steadily with respect to the non-slip and Constant Heat flux condition on channel wall and fixed physical properties by using discrete finite volume method and a numerical code. Also, the Poisson- Boltzmann equation was used with regard to the Debye-Huckel approximation for modeling the distribution of electrical potential in the vicinity of the wall. The results show that, if there is an axial electric field, the application of the lateral magnetic field will reduce the flow rate . However, if there is transverse and axial electric field, the gradual increase of the lateral magnetic field to a certain value, will increase the flow velocity through the duct, but afterwards, the increase in the magnetic field will reduce the flow rate. The Hartmann number, such as this magnetic field, is called the critical Hartmann number. Therefore, in the presence of axial and transverse electric field and lateral magnetic fields, the maximum flow through the duct occurs for a critical Hartman number. Also, by increasing the pressure gradient within the microchannel with a square cross section duct, the critical Hartman number decreases and By increasing the Transverse electric field, the sensitivity of the critical Hartman number to the gradient of pressure is reduced and its value ultimately leads to a specific number (about 4.5) In addition, the results of the present study showed that the aspect ratio of microchannels is effective on the critical Hartman number, so that , the decrease in the microchannel aspect ratio in a certain lateral electric field increases the critical Hartman number . Also in an lateral electric field for Ha Ha_cr with an increase in Ha ,the value of the poiseuille number and Nusselt number will reduce. Furthermore Ha Ha_cr the value of the poiseuille number and Nusselt number will increase with increasing Hartmann number. Keywords:Electro-osmoticFlow,Poisson-Boltzmann Equation ,MHD Flow , Critical Hartmann Number , Aspect Ratio
