$r$

Barao. F

Chapter: Four

Example $2$: Dimensions and boundary conditions of the two$-$dimensional rectangular infinite extended surface are illustrated in Figure $4-2.$ Derive an expression for the steady$-$state temperature distribution, $(x,y),$ of the extended surface for a finite heat transfer coefficient $(h).$

Solution:

$\frac{de{l}^2}{del{x}^2}+\frac{de{l}^2}{del{y}^2}=0$

The boundary conditions are needed for each of the coordinates as$,$

$(0,y)={}_0,(,y)=0,\frac{\text{d}\text{e}\text{l}(x,0)}{\text{d}\text{e}\text{l}\text{y}}=0,-k\frac{\text{d}\text{e}\text{l}(x,l)}{\text{d}\text{e}\text{l}\text{y}}=h(x,l)$

Assume the existence of a product solution of the form $($Eq$.4\mathrm{.}5)$