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

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

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

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

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

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