Self oscillations in homogeneous chemical systems have been studied extensively in diverse array of systems ranging from flow and non-flow, stirred and unstirred, for non-linear chemical reactions coupled with or without the effect of diffusion and multiple systems exhibiting synchronized oscillations. There are however not many examples in which specific geometric features of the reaction chamber turns an otherwise stable system oscillatory, importantly at very low Reynolds number regime. Here we describe such a phenomenon in regard to a microfluidic fuel cell for which the cell potential turns oscillatory when its smooth wall is replaced by one patterned with microscopic features. In essence, we have a membraneless fuel cell in which fuel and oxidant streams flow in laminar contact, side by side, forming a sharp interface. For smooth surface of the channel wall, with steady flow of fuel and oxidant, the cell generates a constant open circuit potential (OCP). However, when the surface of the channel is patterned with parallel triangular ridges, although the flow continues to remain temporally steady, time invariant oscillating OCP ensues within a small window of very low Reynolds number. We have presented a mechanism for occurrence of these oscillations.