Consider a large $0\mathrm{.}08-$cm$-$length brass plate $(k=100\frac{W}{m}*K)$ in which heat is

generated uniformly at a rate of $2{10}^5\frac{W}{m^3}.$ One side of the plate is held at $10C$

$(x=0)$ while the other side is exposed to an environment at $25C$ with a heat

transfer coefficient of $44\frac{W}{m^2}*K.$ Heat capacity and density of brass are $500$

$\frac{J}{k}gC$ and $8000k\frac{g}{m^3},$ respectively. Initial temperature of brass is $80C.$

a$.$ Develop the following partial differential equation for the unsteady state heat

conduction with heat generation.

$\frac{de{l}^{2}T}{del{x}^2}+\frac{(q^{})}{k}=\frac{C_p}{k}\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}$

b$.$ Obtain explicit equation for the distribution of temperature within brass plate.

c$.$ Take $x=0\mathrm{.}02cm$ and $t=5s,$ find the temperature distribution after $15s.$

Convective Heat Transfer $hA(T-T_{})$