Compact fin-plate heat exchangers are formed by an array of periodic elements with periodicity laterally, longitudinally and vertically. One periodic element consists of two plates and the fin structure in between. Here the fins are longitudinal vortex generators. Geometrically they are rectangular plates which are attached vertically to the plate and form an angle of attack with the main flow. Eight geometrically different vortex generator configurations are considered; in-line and staggered, symmetric and parallel, attached to one and both sides. The angle of attack and relative 'fin' hight are varied. Laminar flow is considered. The full unsteady Navier-Stokes equation and energy equation are solved by a SOLA type code. From the velocity and temperature field the flow losses and the heat transfer are deduced. Heat transfer and additional pressure loss depend strongly on the specific configuration, angle of attack and relative fin hight. Heat transfer enhancement per unit area by more than a factor four can result.