Example: Accumulation of Heat

$\{\begin{array}{ccc}\text{:}[& \text{H}\text{e}\text{a}\text{t}& ]\\ & \text{E}\text{q}\text{u}\text{a}\text{t}\text{i}\text{o}\text{n}& \end{array}{d}_a\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}-$grad$*kgradT=f,$ Calculate $T$ for time from $0$ to $100.$

In addition, calculate

accumulated heat.

$U={}_{V}TdV$

$w={\displaystyle \underset{t}{\overset{\phantom{}}{}}}$Udt$>\frac{dw}{dt}=$UExample: Accumulation of Heat

$\{\begin{array}{ccc}\text{:}[& \text{H}\text{e}\text{a}\text{t}& ]\\ & \text{E}\text{q}\text{u}\text{a}\text{t}\text{i}\text{o}\text{n}& \end{array}{d}_a\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}-$grad$*kgradT=f,$ Calculate $T$ for time from $0$ to $100.$

In addition, calculate

accumulated heat.

$U={}_{V}TdV$

$w={\displaystyle \underset{t}{\overset{\phantom{}}{}}}$Udt$>\frac{dw}{dt}=U$