Applications: The dynamics of superior heat transport fluids are of much interest and dominant over traditional fluids. Applications of such fluids can be found in advanced medical sciences, to maintain the building temperature, environmental sciences, chemical engineering, food engineering, and other applied research areas where enhanced heat transfer is required. Aim and Research Methodology: The major aim of this research is to report the thermal performance of the Glycerin-titania nanofluid using a thermal conductivity model comprising the effects of nanoparticles aggregation, and CCTF over a permeable slanted surface. The enhanced heat transport model was then analyzed numerically via RK scheme and furnished the outcomes with graphical aid under the variations of physical parameters. Core Findings: It is examined that the addition of CCTF (A1) in the model potentially contributes to thermal performance of aggregated nanofluid. The temperature [Formula: see text] enhances for injecting fluid from the surface and reduces due to strong suction. Further, the fluid particles attained maximum velocity for [Formula: see text] at the surface and it shows asymptotic behavior far from the working domain.