  Multiscale modelling methodologies build macroscale models of materials with
complicated fine microscale structure. We propose a methodology to derive
boundary conditions for the macroscale model of a prototypical non-linear heat
exchanger. The derived macroscale boundary conditions improve the accuracy of
macroscale model. We verify the new boundary conditions by numerical methods.
The techniques developed here can be adapted to a wide range of multiscale
reaction-diffusion-advection systems.
