Fluid enters a tube with a flow rate of \(0.020 \mathrm{~kg} / \mathrm{s}\) and an inlet temperature of \(20^{\circ} \mathrm{C}\). The tube, which has a length of \(8 \mathrm{~m}\) and diameter of \(20 \mathrm{~mm}\), has a surface temperature of \(30^{\circ} \mathrm{C}\).

(a) Determine the heat transfer rate to the fluid if it is water.

(b) Determine the heat transfer rate for the nanofluid of Example 2.2.

Data From Example 2.2:-

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The bulk thermal conductivity of a nanofluid containing uniformly dispersed, noncontact- ing spherical nanoparticles may be approximated by = k+2k+2(k - kbt) bf. kp + 2kbf - (kp-kbf) Kpf where is the volume fraction of the nanoparticles, and kr, kp, and kn are the thermal con- ductivities of the base fluid, particle, and nanofluid, respectively. Likewise, the dynamic viscosity may be approximated as [20] Haf = br (1+2.50) Determine the values of knts Pais Cp.nfs Mn, and of for a mixture of water and Al2O3 nano- particles at a temperature of 7 = 300 K and a particle volume fraction of = 0.05. The thermophysical properties of the particles are kp = 36.0 W/m K, Pp = 3970 kg/m, and Cp.p=0.765 kJ/kg. K.