... account. φmis themaximum particle packing fraction and [η]=2.5for spherical particles. (Krieger & Dougherty, 1959)Batchelor ηr= 1 + 2.5φ + 6.2φ2Spherical particles and semi-dilute suspensions,interaction ... techniques, particle size, material, base fluids, surfactants, and also uncertainties in measurements of particle concentration and thermal conductivity [3]. It was suggested [23] that metallic nanoparticles ... heat of the fluid, Tin and Tout are the inlet and outlet fluid temperature, respectively and Ti,w (x) and Tm(x) are the inner wall temperature of the tube and the mean bulk fluid temperature...