For a WR 340 heat transfer of height b with a liquid slab of thickness e, \beta or be/\beta is the physical constant which governs the microwave water heating process [4], [7] :

\beta = 7.35 e 230 dB.° C/m = 1.690 e dB.° C/mm = 0.194 e °C/mm where e is in mm.

    \[\frac{be}{\beta}= 222,5  mm^3/ ^oC \]

Using experimental data T_o  and \Delta T, the value of z^*, V^* and \Delta z/z^* can be deduced through the data given in Figs.1 and 2 in conjunction with the above formulae.  \delta is a fraction of the total temperature variation \Delta T.

Fig. 1 Approximate conjugate \delta ratio along the length of the heat tranfer.

For \delta = 0.990     z^* = 4.6 T_o/2\beta        V^* = 4.6v = 4.6 beT_o/2\beta

For \delta = 0.999     z^* = 6.9 T_o/2\beta        V^* = 6.9v = 6.9 beT_o/2\beta

Fig. 2 \delta ratio dependence on the relative error.

For \delta = 0.990    \Delta z/z^* = \Delta V/V^* = 0.78 \Delta T/T_o

For \delta = 0.999    \Delta z/z^* = \Delta V/V^* = 0.85 \Delta T/T_o

\Delta T is related to the process parameters with the formula :

\Delta T  °C = 3.79 (KW required)/GPM

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