Numerical modelling of unsteady convective-diffusive heat transfer with a control volume hybrid method

Presented in this paper is a numerical methodology for the solution of the parabolic governing partial differential equation that describes unsteady advection-diffusion heat transfer. The formulation presented here is shown to be free from the numerical oscillation commonly associated with advection-diffusion heat transfer regardless of the value of the Peclet number. The formulation involves the absorption of the advection term in the unsteady heat equation into the capacitance term. This process is achieved with the use of a control volume methodology applied to each nodal element on a finite-volume mesh. This is shown to ensure that spurious energy losses and gains are avoided and provides for consistency between temperature and energy change. This approach provides unconditional stability and it is shown that good accuracy is achievable with relatively large time-steps. In order to highlight the features of the approach it is compared against those of benchmark numerical schemes. Detailed analysis is performed for the 1D semi-infinite moving solid problem for which an exact solution is available and for a realistic engineering heat transfer problem. Oscillation free results are achieved at good accuracy for a wide range of Peclet numbers and problems considered.