The impetus of this numerical investigation is to explore the performance aspects of laminar forced convection flow of biologically synthesized water–silver nanofluid inside an internally spiral-ribbed heat exchanger tube from both the first and second laws of thermodynamics perspectives. The two-phase mixture model is used to perform the required simulations. The impacts of the volume concentration of nanoadditives (φ), Reynolds number (Re) as well as the width (W), height (H) and pitch (P) of the ribs on the hydrothermal aspects and irreversibility behavior of the nanofluid are assessed, and the results are compared with the findings of smooth tube. It was found that the use of nanofluid and the use of rifled tube instead of water and smooth tube, respectively, are suitable ways to improve system performance from both the first and second laws of thermodynamics perspectives. Moreover, it was reported that the best hydrothermal performance of the nanofluid through the rifled tube occurs at φ = 1%, Re = 2000, W = 3 mm, H = 1 mm, P = 4 mm, while the minimum total irreversibility in the flow of water–silver nanofluid inside a rifled tube occurs at φ = 1%, Re = 2000, W = 3 mm, H = 0.5 mm, P = 4 mm.