A detailed numerical investigation on laminar mixed convection has been carried out to understand the flow instability in buoyancy-aiding and buoyancy-opposing flows through a vertical pipe subjected to uniform heat flux. Two-dimensional axisymmetric steady simulations are performed with the available commercial software for aiding as well as opposing flows of water through a vertical pipe of length to diameter ratio of 500. The structured grids used for the simulation such that; it is uniform in axial and non-uniform in radial direction. The effects of Reynolds number (100 ≤ Re ≤ 2300) and Grashof number (10³ ≤ Gr 1.19 * 10⁷) on heat transfer and fluid flow are analysed by employing SIMPLE algorithm for solving pressure-velocity coupling and second order UPWIND scheme for solving momentum and various energy equations. The Boussinesq approximation has been considered for the analysis. The Richardson number (Ri) varies from 0.1 to 1.5 for the present range of Re and Gr. Results show that the heat transfer increases in case of buoyancy-assisting flow as compared to buoyancy-opposing flow for same Ri. It is inferred from the velocity profile and skin friction coefficient (C_ƒ) plots that the pressure drop is more in case of opposing flow as that of aiding flow. An increase in heat flux advances the transition from laminar to turbulent in opposing flows whereas it delays in aiding flows. The point of inflection in aiding flows and the flow separation from the wall in opposing flows have been observed with further increase of Ri which ensures the presence of flow instability.