Finite difference scheme for the accurate modelling of boundary layers in microchannels

Singularly perturbed heat equations are studied in the case when the heat/diffusion flux is given on the domain boundary. This paper shows that (depending on the value of perturbation parameter) the errors in the approximate solution, computed by a classical hnite difference scheme, can exceed the exact solution many times. The computed normalised heat flux fails to converge when the perturbation parameter is small. For the boundary value problem considered here, a special finite difference scheme has been constructed that allows the solution and the normalised heat flux to be found. The errors in the computed solution and normalised flux for this scheme are independent of the perturbation parameter and depend only on the number of the nodes in the grid used.