Answer:

Step-by-step explanation:
we know that biot number is given as

where Lc is characteristics length


as biot number is less than 0.1 thus apply lumper analysis to find time constant t



considerig temperature distiribution
temperature at mid length of furnase is


T(t) = 592.885 degree c
from Newton's law of cooling determine temp gradient at surface at t = 150 s
![-k (\partial T(t))/(\partial y) \at\ y = 0 is h[T(t) -T_(\infity)]](https://img.qammunity.org/2020/formulas/physics/college/j790usybhhc6rt200uu7qn0idbx76jggr3.png)
![(\partial T(t))/(\partial y) \ at\ y = 0 is (h[T(t) -T_(\infity)])/(k)](https://img.qammunity.org/2020/formulas/physics/college/io5r5vigqzanapwagk0wyy4mysf3vagnpw.png)
![(\partial T(t))/(\partial y)\ at\ y = 0 is ( 80[592.885 - 900])/(21)](https://img.qammunity.org/2020/formulas/physics/college/qi4g05vaik3e4sj7d76gxk9m9ku4ci3k8i.png)
