They used the energy balance equations for moist air

Suspended plate:equation(122)I(t)sτgτwuαplApv=hc,pl−wuApv(Tpl−Twu)+hc,pl−wlApv(Tpl−Twl)I(t)sτgτwuαplApv=hc,pl−wuApv(Tpl−Twu)+hc,pl−wlApv(Tpl−Twl)
Upper water column:equation(123)I(t)sτgαwuAwu+hc,pl−wuApv(Tpl−Twu)=hc,wu−gAwu(Twu−Tg)+(Avehc,wu−wl+ApvKplLpl)(Twu−Twl)+AsuUsu(Twu−Ta)+MwuCw(dTwudt)
Lower water column:equation(124)I(t)sτgτwuαwlAve+(Avehc,wu−wl+ApvKplLpl)(Twu−Twl)+hc,pl−wlApv(Tpl−Twl)=(UbAwl+UslAsl)(Twl−Ta)+MwlCw(dTwldt)
In the above expressions, Apv=Apl−Ave.
The temperature of the suspended absorber plate is found from the following relation:equation(125)Tpl=αplτgτwuI(t)s+hc,pl−wuTwu+hc,pl−wlTwlhc,pl−wu+hc,pl−wl
The BET-BAY 002 balance equations for various parts of the still were solved analytically using the method of Gauss elimination. The theoretical model was validated with the experimental results. It was inferred that adding a suspended plate within the basin water of a conventional still decreases the preheating time required for evaporating the still water. The daily productivity of the modified still was around 18.5–20% higher than that of the conventional still. The optimum position of the baffle absorber was found to be in the middle of the basin water and with the lowest mass of the upper water with and without vents. Also histone proteins was advisable to use the suspended absorber without vents in order to obtain maximum performance. It was concluded that the developed mathematical model overestimated the daily productivity of the still only by about 8%.