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PurposeTo make the finned exchanger light and compact, the design of optimized fins has become increasingly important nowadays. The purpose of this paper is to present a numerical investigation on forced convection in a horizontal parallel plate channel with inline transverse fins on channel walls.Design/methodology/approachThrough the use of a stream function vorticity transformation, solution of the transformed governing equations for the system is obtained using the control‐volume method with non‐uniform grid. The extrapolated‐Jacobi scheme was used to solve the finite‐difference equations.FindingsFor fins with fixed fin volumes, the array fins of optimum aspect ratios which dissipate maximum heat transfer in a parallel‐plate channel are obtained. For these optimum fins, it shows that the first fin is the shortest and the height of the rest of fins increases along the downstream direction of the channel. In addition, the optimum aspect ratio of a fin increases with Reynolds number and fin spacing but decreases with thermal conductivity ratio and entrance length with other parameters fixed.Originality/valueThis is the first paper devoted to the exploration of the optimized fin array in a forced convective channel, considering heat conduction in the fins and heat convection in the fluid simultaneously.