Fluid enters a tube with a flow rate of 0.015 kg/s and an inlet temperature of 20°C. The tube, which has a length of 6 m and diameter of 15 mm, has a surface temperature of 30°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.

Example 2.2

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The bulk thermal conductivity of a nanofluid containing uniformly dispersed, noncontacting spherical nanoparticles may be approximated by [kp +2kbf +24(kp-Kot) kp + 2kpf - (kpkb) bf Kbf where is the volume fraction of the nanoparticles, and kfs Kp, and knf are the thermal con- ductivities of the base fluid, particle, and nanofluid, respectively. Likewise, the dynamic viscosity may be approximated as [20] Mat=Mb (1+2.50) Determine the values of Knis Pais Cpnis Mnts and anf for a mixture of water and Al₂O3 nanoparticles at a temperature of T = 300 K and a particle volume fraction of p = 0.05. The thermophysical properties of the particle are k, = 36.0 W/mK, pp 3970 kg/m³, and Cpp = 0.765 kJ/kg.K.