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Background Hydrogels based on organic/inorganic composites have been at the center of attention for the fabrication of engineered bone constructs. The establishment of a straightforward 3D microenvironment is critical to maintaining cell-to-cell interaction and cellular function, leading to appropriate regeneration. Ionic cross-linkers, Ca2+, Ba2+, and Sr2+, were used for the fabrication of Alginate-Nanohydroxyapatite-Collagen (Alg-nHA-Col) microspheres, and osteogenic properties of human osteoblasts were examined in in vitro and in vivo conditions after 21 days. Results Physicochemical properties of hydrogels illustrated that microspheres cross-linked with Sr2+ had reduced swelling, enhanced stability, and mechanical strength, as compared to the other groups. Human MG-63 osteoblasts inside Sr2+ cross-linked microspheres exhibited enhanced viability and osteogenic capacity indicated by mineralization and the increase of relevant proteins related to bone formation. PCR (Polymerase Chain Reaction) array analysis of the Wnt (Wingless-related integration site) signaling pathway revealed that Sr2+ cross-linked microspheres appropriately induced various signaling transduction pathways in human osteoblasts leading to osteogenic activity and dynamic growth. Transplantation of Sr2+ cross-linked microspheres with rat osteoblasts into cranium with critical size defect in the rat model accelerated bone formation analyzed with micro-CT and histological examination. Conclusion Sr2+ cross-linked Alg-nHA-Col hydrogel can promote functionality and dynamic growth of osteoblasts. Graphical Abstract

Free convection heat transfer in rectangular enclosures fi lled with Al 2 O 3-water nanofl uid is investigated numerically, and the eff ects of suspended nanoparticles of diff erent diameters are considered. The governing equations in terms of primitive variables are discretized numerically using the fi nite volume method and SIMPLER algorithm. The results were obtained for width range of the Rayleigh number, nanoparticles volume fraction and aspect ratio of cavity. Also nanoparticles with two different diameters, namely 36 nm and 47 nm have been chosen. The obtained results showed that for the square enclosure utilizing the suspended nanoparticles with both considered diameters the rate of heat transfer increased only at Ra = 10 3 that conduction dominated the heat transfer process, while at other Rayleigh numbers, a deterioration on average Nusselt number was observed.

In the present paper, natural convection fluid flow and heat transfer in a square cavity heated from below and cooled from sides and the ceiling with a thin fin attached to its hot bottom wall is investigated numerically. The right and the left walls of the cavity, as well as its horizontal top wall are maintained at a constant temperature T c , while the bottom wall is kept at a constant temperature T h ,with T h > T c . The governing equations are solved numerically using the finite volume method and the couple between the velocity and pressure fields is done using the SIMPLER algorithm. A parametric study is performed and the effects of the Rayleigh number and the length of the fin on the flow pattern and heat transfer inside the cavity are investigated. Two competing mechanisms that are responsible for the flow and thermal modifications are observed. One is the resistance effect of the fin due to the friction losses which directly depends on the length of the fin, whereas the other is due to the extra heating of the fluid that is offered by the fin. It is shown that for high Rayleigh numbers, placing a hot fin at the middle of the bottom wall has more remarkable effect on the flow field and heat transfer inside the cavity.

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