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In this paper, the Response Surface Methodology (RSM) and two phase mixture model are proposed to investigate the sensitivity analysis of heat transfer and heat exchanger effectiveness in a double pipe heat exchanger filled with Al₂O₃ nanofluid. The effective parameters of the Reynolds number (50 ≤ Re ≤ 250), nanoparticles volume fraction (0.01 ≤ ϕ ≤ 0.05) and the entrance status of nanofluid S (inner pipe, outer pipe and both of them) are considered to serve the purpose. The governing equations are solved with SIMPLE algorithm and Discretized using a finite volume method. It is found that the mean Nusselt number enhances with the Re number, and this enhancement is in the vicinity of 57.70% for the case with Re = 50 to 150 and ϕ = 0.03, when the nanofluid enters the outer pipe. Increasing the ϕ and S reduces the mean Nusselt number. The heat exchanger effectiveness enhances with ϕ and …