# Private Notes The form of the local energy conservation equation which governs the microwave water heating process during stady state conditions can be written as : where and are the microwave power and the temperature of water at a distance away from the inlet, , , and are the volumetric mass, flow rate and specific heat of water respectively. However the microwave power at a distance away from the inlet is given by, ,  : where and are the input microwave power and the heat transfert absorption coefficient respectively. For a WR 340 water heat transfer for which is the thickness of the liquid slab, in the temperature range 25 < < 75° C where is the following physical constant : = 7.35 230 dB.° C/m = 1.690 dB.° C/mm = 0.194 °C/mm where is in mm.

Integrating eqn.(1) gives : where is totally absorbed along the heat transfer, and are the input and output temperatures of water respectively.

Differentiating eqn.(2) gives : Substracting eqn.(4) from eqn.(1) yields : eqn.(3) gives : Substituing , eq.(5) yields : Integrating eqn.(7) along the heat transfer gives : where and:  is related to the process parameters by the formula : Ignoring the absorption coefficient variation with gives the simplified equation : where is the approximate position at ratio . Now let us consider a volume of water of thickness and height described as follows : This design is well adapted to minimize microwave reflections on the inner pipe. The corresponding heat transfer absorption coefficient can be written as: where is the height of the wave guide. By following the same procedure as for the rectangular slab, eqn.(7) becomes : Integrating eqn.(11) along the heat transfer gives : where is the necessary volume of water which leads to the required ratio . Therefore : By definition is the volume of a rectangular liquid slab of eight at a point distance away from the inlet : As the thickness is substantially smaller than the width of the heat transfer, varies linearly with , therefore as well as at a given ratio do not depend upon the shape of the inner pipe.

It will be noted that the volume is the appropriate parameter for describing the microwave heating process.