In the petroleum industry, accurately simulating wellbore heat loss through hot fluid injection remains a critical problem as heat transfer and fluid dynamics within the annulus space is complicated. In this study a 2D transient mathematical model is proposed for the conjugate natural convection and radiation within wellbore annuli. The governing equations consist of a vorticity transfer equation, a stream function equation, an energy balance equation and a radiative transfer equation. A finite volume approach with second order upwind scheme is implemented for discretization. Newton-Raphson iteration is deployed for linearization. The algorithm is validated by consistency in simulation results compared with literature. Parameters such as the aspect ratio, radius ratio, radiation and dimensionless time are examined. A case study on vacuum insulated tubing heat transfer using Marlin Well A-6 data showed the merits of the developed program by the consistency of simulation results compared with field measurements.