An electronic component schematically shown in Figure $2$ is made up of

two different components A and $B$ with thermal conductivities

$K_A=40\frac{W}{m}K$ and $K_B=10\frac{W}{m}K,$ densities ${}_A=1200k\frac{g}{m^3}$ and

${}_B=2500k\frac{g}{m^3},$ and specific heats $c_A=100\frac{J}{k}gK$ and $c_B=250\frac{J}{k}gK.$

There is a volumetric heat generation $q^{\text{'}\text{'}\text{'}}=5\mathrm{.}0M\frac{W}{m^3}$ in the component

with thermal conductivity $K_B.$ The above configuration is discretised

using the mesh shown in Figure $2$ where a uniform grid with spacing

$x=y=0\mathrm{.}04m$ is used. The side $AB$ falls on the symmetry line.

For each of the five nodes $1,2,5,6$ and $8$ evaluate the maximum allowable

time step size you are allowed to use if you were to solve an unsteady heat

conduction problem for this geometry using an explicit time advancement

method.

$(55=25$ marks $)$

Figure $2$