In the present study, multi-walled carbon nanotubes (MWCNTs) with outside diameters of< 8 nm and 20−30 nm were covalently functionalized with β-Alanine using a novel synthesis procedure. The functionalization process was proved successful using Raman spectroscopy, FTIR, and TEM. Utilizing the two-step method with ultrasonication, the MWCNTs treated with β-Alanine (Ala-MWCNTs) with weight concentrations of 0.025%, 0.05%, 0.075%, and 0.1% were dispersed in distilled water to prepare water-based nanofluids. The aqueous colloidal dispersions of pristine MWCNTs were unstable. While for Ala-MWCNTs and after> 50 days from preparation, higher colloidal stability was obtained up to relative concentration of 0.955 and 0.939 for the 0.075-wt% samples of Ala-MWCNTs < 8 nm and Ala-MWCNTs 20−30 nm, respectively. The measured values of thermal conductivity were in very good agreement with the model of Nan, Birringer, Clarke and Gleiter and increased as temperature, specific surface area (SSA), and weight concentration increased, up to 14.74% for Ala- MWCNTs < 8 nm and 12.29% for Ala-MWCNTs 20−30 nm. The viscosity increased as weight concentration increased, up 25.69% for 0.1-wt% Ala-MWCNTs 20−30 nm, and decreased with the increase in temperature. Since the matching between the measured values of viscosity and the classical models of Batchelor, Brinkman, and Einstein was bad, a correlation was developed and revealed good agreement. The density and specific heat decreased as temperature increased. As weight concentration increased, the density slightly increased up to 0.065% for Ala-MWCNT < 8 nm while the specific heat decreased down to 0.95% for Ala-MWCNTs 20−30 nm, in comparison with water. The equations of (Pak and Cho) and (Xuan and Roetzel) were in good agreement with the measured values of density and specific heat, respectively. The aqueous colloidal dispersions of Ala-MWCNTs that were prepared in this work displayed robust candidature as successful substitutes for the conventional heat transfer fluids in different engineering applications for enhanced thermal performance.
Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if
the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are introduced and given some properties .