The multiplicity of steady-state solutions arising from microwave heating.I. Infinite Biot number and small penetration depth

Microwave heating of porous solid materials has received considerable atten tion in recent years because of its widespread use in industry. In this stu dy, the microwave power absorption term is modelled as the product of an ex ponential temperature function with a function that decays exponentially wi th distance. The latter describes the penetration of the material by the mi crowaves. We investigate the phenomena of multiplicity in class A geometries, paying particular attention to how the penetration function affects the behaviour of the system. We explain why the phase-plane techniques which have been us ed in the case when the penetration term is constant do not extend to non-c onstant penetration.