$(9)$ A nanofluid $($ nf $)$ contains a mixture of water as a base fluid $($ bf $)$ and $A{l}_2{O}_3$ as a nanoparticle $($p$).$

Determine the values of $k_{nf},{}_{nf},{}_{nf},c_{np,nf},$ and ${}_{nf}$ at a temperature of $300$ K and a particle

volume fraction $()$ of $0\mathrm{.}05.$

The thermophysical properties of the particles are $k_{np}=36\frac{W}{m}K,{}_{np}=3970k\frac{g}{m^3},$ and

$c_{p,np}=0\mathrm{.}765k\frac{J}{k}gK$ and water are $k_{bf}=0\mathrm{.}613\frac{W}{m}K,{}_{bf}=997k\frac{g}{m^3},c_{p,bf}=4\mathrm{.}179k\frac{J}{k}gK,$

and ${}_{bf}=855{10}^{-6}N\frac{s}{m^2}.$ Comment on your results.

$[$Ans: $k=0\mathrm{.}705\frac{W}{m}-K,=1146k\frac{g}{m^3},c_p=3\mathrm{.}587k\frac{J}{k}gK]$