Water $($h$1=2500$W$/$m$^2*$K$)$ at T$1=90\backslash$deg C standing in glass beaker$($k$=0\mathrm{.}8$ W$/$m$*$K$)$ whose inner and outer diameters are D$1=7$cm and D$2=7\mathrm{.}5$cm respectively.

All things surrounded by glass wool insulation with k$=0\mathrm{.}032$ W$/$m$*$K$.$

Heat is lost to the sorroundings at T$2=20\backslash$deg C by natural convection. Taking heat transfer coefficient of h$2=25$W$/$m$^2*$K

Something different we have air access for thermometer with diameter $8$mm above from glass beaker.$($If you cant solve it$,$ please just neglect it$.)$

Assume that glass beaker is center of insulation cube just like figure uploaded.

Heat transfer is steady, heat transfer is two$-$dimensional$($I hope you can manage it$)$ Thermal properties are constant.

If there are not any useful given properties$($my bad$),$ please just assume it$.$

I want final temperute of water after $20$ min with heat transfer and thermodynmaics equations. I experimentally find that Tfnlexp$=75\backslash$deg after $20$min Access for

thermometer

air d$(8$mm$)$

d$17$cm with beaker

d$27\mathrm{.}5$cm

nearly $300$ml water

Glass BeakerAccess for

thermometer

air $d(8mm)$

d$17cm$ with beaker

d$27\mathrm{.}5cm$

nearly $300ml$ water

Glass Beaker