An optimal or near to optimal design and operation of a direct liquid fuel cell (DLFC) stack requires an understanding of the relevant physical phenomena across length scales in the stack. In particular, perturbations between cells can arise due to external manifold design as well as variations in material and design parameters between cells. In this work, we seek to derive closed-form analytical expressions that capture the global stack performance, as well as individual cell behavior such as cell potential, current density, and methanol distribution. This approach allows for the simulation of large stacks with near to negligible computational overhead. Finally, the solutions are demonstrated for a stack subjected to perturbations in the anode inlet velocity of each cell.