The influence of varied nanoparticle shapes on thermal–hydraulic efficacy of a boehmite nanofluid (BNF) in a mini shell and tube heat exchanger (MSTHX) in the cases of with and without fin is investigated. The five nanoparticle shapes with 90 °C inlet temperature at Reynolds number of 500 for the warm fluid side, and four Reynolds numbers of 500, 1000, 1500, and 2000 with 20 °C inlet temperature for the cold fluid side are considered. The warm fluid is the nanofluid that moves in the tube side, whilst the cool fluid is common water inside the shell side. With elevating Reynolds number, the heat transfer rate (q), overall heat transfer coefficient (U), pressure drop, effectiveness, and number of transfer unit (NTU) increase, while the performance index reduces. By increasing the Reynolds number from 500 to 2000 in the nanofluid having the oblate spheroid nanoparticles, the effectiveness rises 20%, and the performance index reduces 21.7%. The BNF with the platelet additives results in the largest q, whilst the smallest pressure loss is achieved for the Os-shaped additives. Also, the heat transfer rate, U, effectiveness, NTU, performance index, and pressure loss for the MSTHX with fin are larger than those for the MSTHX without fin.