A control volume conductance method is discussed in this paper. The method is designed for materials that exhibit heat transfer. Particular attention is put to problems where convection overpowers the mechanism of conduction. The semi-infinite solid which moves with arbitrary imposed velocities along the X-axis and has various surface conditions at x=0 is a classical problem where convection instantaneously overpowers conduction. The analytical solution for this problem becomes physically unrealistic when the strength of convection is high which is defined by the Peclet number. For small Peclet numbers, the diffusion behavior is reasonably described by linear diffusion coefficients, but at large Peclet numbers lineal behaviors become incorrect and hence bad. The true is that diffusion in the analytical solution has indeed an exponential behavior. The exponential behavior in the convection-diffusion exact solution has an exponential behavior. Here false diffusion which is related to the Peclet number corresponds to the energy being supplemented by continuous falls such as a snowfield. As standard numerical schemes do not have this exponential feature, they eventually cross the zero dividing line. The result is unrealistic solution in the form of numerical oscillations. In this paper, this problem is circumvented with a new augmented conductivity term, where false diffusion is added to the true diffusion via exponential relationships with no need of curve fitting procedures. The novelty of the approach is that convection effects are embedded into the conductivity term. This originates new equivalent governing equations for heat transfer. The control volume numerical solution of the method is similar to that of standard parabolic heat conduction. The method is shown to yield exact solutions, to be accurate and computationally competitive.
