A 3-dimensional incompressible laminar flow and heat-transfer in a plate-fin heat exchanger (PFHE) where investigated numerically in this article. The influence of mounting a longitudinal vortex generator (LVG) on the offset rectangular-triangular fin (ORT) in the PFHE, on thermal and hydro-dynamic fields are presented. The novelty of this study is by attaching a LVG to an offset strip fin (OSF) surface. The cases of study for the PFHE are established, by using a built-in rectangular winglet pair type RWP longitudinal vortex generator carried out and fitted on this fin to improve the convective heat transfer of the (ORT) fin while minimizing pressure loss. The upper and lower plates are exposed to constant heat flux and the working fluid is air where chosen under a laminar range of RE (600 to 1400). The laminar flow and heat-transfer are governed by continuity, momentum and energy equations. ANSYS FLUENT (2021 R1) is used to get the numerical results, based on the finite volume method. The performance of the VG is assessed for an optimum winglet attack angle (45°), as well as by modifying the geometrical size parameters, namely the height and placement (L) of the RWP LVG. The result shows that the Nusselt number reaches its optimum enhancement values by using a common flow up CFU built-in rectangular winglet pair type RWP VG with a height and entrance length of (h=1.25mm, L=0.5mm), by 22.23% as compared with base case configuration (ORT). Finally, a two more LVG are tested with the optimum conditions of the RWP, which they are a delta winglet pair (DWP) and trapezoidal winglet pair (TWP). In addition, the temperature fields for the primary and secondary flows were shown in contour and streamline diagrams