Nanofluids does not show linear dependence with volume concentration. It depends on various parameters like particles size, shape, operating temperature, surfactant used for dispersion and the particle motion behavior. Particle motion behavior affects the thermal conductivity most.
Regarding density: Yes, it is a linear relationship. Regarding specific heat capacity: It depends on whether you prefer per unit mass (J/(kg.K)) or per unit volume (J/(m3.K)). Regarding viscosity and thermal conductivity: No, there is not necessarily any linear relationship.
Among the various thermophysical properties, density and specific heat shows almost linear relationship with particles concentration. However, some experimental results reveals the effect of other factors (like interfacial effect) on these properties.
If density and specific heat of nanofluids calculated from mixture models based on mass fraction basis, then, yes, they show linear relationship with particles concentration. But if density and specific heat of nanofluids were calculated by experiments, then various other factors such as particle size, shape, temperature, base fluids properties. This publication might be useful for you.
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Depending on nanofluids' condition (e.g., preparation, dispersion of nanoparticles, concentration etc) measured density and SHC data may not follow any single relationship with NP concentration.