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Highlights • Bulging formation can be prevented in a bilayer tube of arbitrary thickness while retaining moderate extensibility. • Several critical parameters for avoiding localized bulging are determined. • The applicability of an explicit bifurcation condition to layered tubes is validated. Abstract This paper studies the bifurcation behavior in an inflated bilayer tube of arbitrary thickness under inflation and uni-axial extension. It is assumed that both layers are composed of the Gent material with each layer having its own J m , where J m is a material parameter in the Gent model that signifies the maximum extensibility. First, we determine several critical parametrical regions where localized bulging disappears for a single-layer tube. Then we investigate localized bulging in an inflated bilayer tube, where one layer (layer I) of the tube cannot bulge whereas the other part (layer II) can. Surprisingly, we find that such a composite tube is still susceptible to localized bulging and localized bulging can be prevented only if the proportion of layer I exceeds a critical value, no matter whether layer I occupies the inner side or the outer side. Even for a very thin bilayer tube, the same feature holds. The cases of fixed axial force and fixed axial stretch are both studied, and the critical geometrical parameters marking the transition between bulging and no bulging are determined. Moreover, we carry out a numerical analysis by use of the finite element method to verify the applicability of an explicit bifurcation condition and the predicted bifurcation behavior. This paper offers a possible way to avoid bulging formation in a cylindrical tube while retaining moderate extensibility. [ABSTRACT FROM AUTHOR]

This article examined the Silver based Di‑hydrogen carbon nanotubes flow model (SDH-CNTFM) between two stretchable coaxially disks by utilizing the Method of Levenberg Marquardt with Back-propagated Neural Networks (MLM-BPNN). Here the base liquid is silver (Ag) and the nanoparticles are SWCNTs and MWCNTs (single and multiwall carbon nanotubes). The governing PDEs for SDH-CNTFM are transformed into ODEs by utilizing similarity transformation. Energy equations are developed through heat generation and viscous dissipation joule heating. Also calculated the total entropy optimization. Flow parameters velocity, entropy optimization, temperature, Nusselt number and Bejan number are discussed for both single and multi-walls carbon nanotubes (SWCNTs and MWCNTs) graphically and in Tabular form. The reference dataset is calculated through implementation of Optimal Homotopy Analysis method (OHAM) for variants of SDH-CNTFM. For the variation of different parameters this reference dataset is utilized in MATLAB to clarify the solution and error analysis plots. Moreover, the approximated solution is assessed through adopting training/testing/validation procedure and comparing it with standard solution which is endorsed by performance study based on MSE convergence, error histogram and regression studies. Heat transfer rate and surface drag force are discussed for both SWCNTs and MWCNTs numerically by using different flow parameters. From obtained outcomes, it is observed that entropy rate boosts up for higher approximation of nanoparticles of volume friction and Brickman number (Br) which is controlled due to the minimization of Brickman number. [ABSTRACT FROM AUTHOR]