A circular tube of diameter D = 0.2 mm and length L = 100 mm imposes a constant heat flux of q" = 20 X 10³ W/m² on a fluid with a mass flow rate of m = 0.1 g/s. For an inlet temperature of T_m,i = 29°C, determine the tube wall temperature at x = L for pure water. Evaluate fluid properties at T = 300 K. For the same conditions, determine the tube wall temperature at x = L 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 +2kbf - (kpkbf). 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 Mr (1+2.5p) 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/m. K. pp = 3970 kg/m³, and Cpp = 0.765 kJ/kg-K.