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Purpose The purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully. Design/methodology/approach First, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient. Findings The results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers. Originality/value A complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

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This study outlines the performances of finite-length journal bearing with textured liner, shear-thinning Rabinowitsch lubricants, and considers the elastic deformation of the bearing liner. The yielded nonlinear Rabinowitsch-Reynolds PDE system has been solved using the finite difference method combined with Elrod’s algorithm for the case of cylindrical textures. The static performance of hydrodynamic lubrication, in this case, involves different parameters such as depth of texture, eccentricity ratio, elastic deformation factor, rheological index, etc. Results showed that, at a fixed eccentricity ratio, texturing of the bearing’s converging area enhances significantly the load-carrying capacity and reduces the friction coefficient compared to the smooth bearing surface (up to [Formula: see text] in load capacity and [Formula: see text] in friction coefficient). On the other hand, using a lubricant with more pronounced shear-thinning behavior and/or elastic liner reduces the journal bearing performances (up to [Formula: see text] in load capacity and [Formula: see text] in pressure). By applying the optimization technique (particle swarm optimization), an optimal arrangement of textures that can compensate for these losses in performance even at high eccentricity has been found. This optimal texture with dimensionless dimple’s depth set to 1 [Formula: see text] improves the load capacity with [Formula: see text] for a lubricant with a rheological index [Formula: see text] and elastic bearing liner with deformation parameter [Formula: see text].

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In the present study, the static characteristics of hydrodynamic circular journal bearings of finite length are highlighted, using the combined influences of textured surface and non-Newtonian lubricants behavior, obeying to the Rabinowitsch fluid model. The associated nonlinear Rabinowitsch-Reynolds equation has been discretized using finite differences scheme and solved by the mean of Elrod’s algorithm taking into account the presence of cylindrical textures on full/optimum bearing surface. Following to the absence of textures on the bearing surface or the non-Newtonian fluid behavior, the obtained results are in good agreement with the reference ones. The hydrodynamic lubrication static performances are computed for various parameters such as textures location; eccentricity ratio and the rheological coeffcient. The results suggest that texturing the bearing’s convergent zone enhances significantly the load carrying capacity and reduces the friction coeffcient, whereas texturing the full bearing surface may leads to bad performances. It is also noticed that the pseudoplastic lubricant coeffcient decreases the bearing performances (load capacity and pressure) compared to Newtonian fluid cases. Considering the optimal arrangement of textures on the contact surface, a significant improvement in terms of load capacity and friction can be achieved, especially at low pseudoplasticity effect.