With regards to the specific heat of the MPCM slurries, Alisetti and Roy (1999) through numerical analysis, proposed and investigated several functions for the specific heat during phase change process.
For the mixture of MPCM and nanofluid, an energy balance equation leads to:
For MPCM slurries most researchers use Maxwell's (1954) relation as given in Equation 8.
To estimate the combined effect of nanofluid and MPCM slurry, available models for binary mixtures of liquids may be used.
Equations 11-13 can be similarly used for nanofluids and MPCM slurries as long as the assumption of Newtonian behavior holds.
Concentric-Tube Heat Exchanger Analysis Parameters Inner-Tube Inside Diameter 0.0134 (0.528) m (in) Inner-Tube Wall Thickness 0.0012 (0.047) m (in) Outer-Tube Inside Diameter 0.02 (0.787) m (in) Water-Side Temperature Raise 2 (3.6) K (R) Carbon Nanotube Volume Fraction 1 % MPCM Volume Fraction 10 % Fluid Flow Rate 0.05 (0.79) L/s (GPM) Water Flow Rate 0.12 (1.90) L/s (GPM) Fluid Inlet Temperature 31 (87.8) [degrees]C ([degrees]F) Due to the nature of the mixing process, dimensional parameters of multi-walled carbon nanotubes (MWCNT) can only be given within a range rather than a definite fixed value, so median values were considered for computational analysis.
As indicated in Table 1, the volume fractions of CNT in the nano-fluid and MPCM in the slurry are considered constant and equal to 1% and 10%, respectively.
In Figure 2, [epsilon] is the percentage of MPCM that has undergone phase change in the process.
Figure 3 shows that the effective thermal conductivity of the blend increases by increasing the amount of nanofluid in the blend regardless of the percentage of the MPCM that changes phase.
From Figure 5 it can be seen that the temperature drop in the heat exchanger can be as 4 times when there is no phase change in MPCM.
Recent experimental results for CNT-nanofluid alone reveal that higher pressures drop could be observed once it is mixed with MPCM slurry.