The temperature of a stainless steel plate with a thickness of $2$ mm is measured as $150\backslash$deg C by an uninsulated copper$-$constantan thermocouple with a diameter of $1$ mm$.$ The properties of the system in a fluid environment at $250\backslash$deg C are given below. Find the actual temperature of the plate.

h$1=20$W$/$m$\backslash$deg C

h$2=10$W$/$m$\backslash$deg C

ht$=120$w$/$m$\backslash$deg C

k$=60$W$/$m$\backslash$deg C

kA$=25$W$/$m$\backslash$deg C

kB$=375$W$/$m$\backslash$deg C

Tf$=250$W$/$m$\backslash$deg C

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