Several measures have been explored to improve the function of plate-fin heat exchangers (PFHEs), including improving heat transfer surface, heat transfer coefficient, finned surface thermal efficiency, and vortex generators. We employ computational approaches in this article to investigate the flow and heat transmission parameters of a plate-fin heat exchanger (PFHE) with a longitudinal vortex generator (LVG) installed on an offset rectangular-triangular fin (ORT), as proposed in a previous work. In order to improve convective heat transmission while reducing pressure loss, the research used a rectangle wing pair (RWP) LVG installed on the fin. Using the ANSYS FLUENT is used to get the numerical outcomes. The top and lower plates are subjected to constant heat flux, and the working fluid (air) is chosen to be laminar (600 Reynolds 1400). The energy conservation problem was solved using the finite volume and finite difference (FD) approaches. Wing angles of approach (25, 35, 45, and 55°) and RWP LVG height were changed to assess the LVG's effectiveness. When compared to the reference instance, the Nusselt number rises by 22.23% when a CFU integrated RWP LVG is used at an angle of approach and height of (45°, 1.25mm). Contour and streamline maps were used to illustrate the temperature distribution of both primary and secondary flows.