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The governing equations of an electrohydrodynamic oscillatory flow were simplified, using appropriate nondimensional quantities and the conversion relationships between fixed and moving frame coordinates. The obtained system of equations is solved analytically by using the regular perturbation method with a small wave number. In this study, modified non-dimensional quantities were used that made fluid pressure in the resulting equations dependent on both axial and vertical coordinates. The current study is more realistic and general than the previous studies in which the fluid pressure is considered functional only in the axial coordinate. A new approach enabled the author to find an analytical form of fluid pressure while previous studies have not been able to find it but have found only the pressure gradient. Analytical expressions for the stream function, electrical potential function and temperature distribution are obtained. The results show that the electrical potential function decreases by the increase of the Prandtl number, secondary wave amplitude ratio and width of the channel.

A New Approach for Study the Electrohydrodynamic Oscillatory Flow Through a Porous Medium in a Heating Compliant Channel