After some simplifications by hand I get the expression below which one wants to set to 0 to solve for f.
16 Ds f^3 n p W^2 -
k^3 \[Pi]^2 Q Coth[(H k \[Pi])/(4 f W)] Sec[\[CurlyPhi]]
Without numeric values for the various parameters this is unlikely to have a "useful" solution.
