This paper presents a gradient theory of grade two based on an axiomatic conception of a nonlocal continuum theory for materials of grade n. The general classical model of linear momentum equation that is depending on the secondorder strain rate tensor and its gradients up to grade n À 1 is Cauchy's first law of motion. In special case, the secondgradient theory, the total stress tensor is a function of the rate of stress tensor and its first gradient. The objective of the present work is to study the turbulent flow through a pipe based on this theory. The linear momentum equation in this case is reduced to an ordinary differential equation of order four, which is solved by analytical method. The boundary conditions are generated by using two cases, slip and no-slip conditions. Finally, analytical results are compared with the experimental pieces of work and show good agreement with experimental data.
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