Purpose This paper aims to theoritically investigate the free convection flow and heat transfer of a non-Newtonian fluid with pseudoplastic behavior in a cylindrical vertical cavity partially filled with a layer of a porous medium. Design/methodology/approach The non-Newtonian behavior of the pseudoplastic liquid is described by using a power-law non-Newtonian model. There is a temperature difference between the internal and external cylinders. The porous layer is attached to the internal cylinder and has a thickness of D. Upper and lower walls of the cavity are well insulated. The governing equations are transformed into a non-dimensional form to generalize the solution. The finite element method is used to solve the governing equations numerically. The results are compared with the literature results in several cases and found in good agreement. Findings The influence of the thickness of the porous layer, Rayleigh number and non-Newtonian index on the heat transfer behavior of a non-Newtonian pseudoplastic fluid is addressed. The increase of pseudoplastic behavior and increase of the thickness of the porous layer enhances the heat transfer. By increase of the porous layer from 0.6 to 0.8, the average Nusselt number increased from 0.15 to 0.25. The increase of non-Newtonian effects (decrease of the non-Newtonian power-law index) enhances the heat transfer rate. Originality/value The free convection behavior of a pseudoplastic-non-Newtonian fluid in a cylindrical enclosure partially filled by a layer of a porous medium is addressed for the first time.

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Purpose This paper aims to investigate melting heat transfer of a non-Newtonian phase change material (PCM) in a cylindrical enclosure-space between two tubes using a deformed mesh method. Design/methodology/approach Metal foam porous layers support the inner and outer walls of the enclosure. The porous layers and clear space of the enclosure are filled with PCM. The natural convection effects during the phase change are taken into account, and the governing equations for the molten region and solid region of the enclosure are introduced. The governing equations are transformed into non-dimensional form and then solved using finite element method. The results are compared with the literary works and found in good agreement. The non-Newtonian effects on the phase change heat transfer and melting front are studied. Findings The results show that the increase of non-Newtonian effects (the decrease of the power-law index) enhances the heat melting process in the cavity at the moderate times of phase change heat transfer. The temperature gradients in porous metal foam over the hot wall are small, and hence, the porous layer notably increases the melting rate. When the melting front reaches the cold porous layer, strong non-linear behaviors of the melting front can be observed. Originality/value The phase change heat transfer of non-Newtonian fluid in a cylindrical enclosure partially filled with metal foams is addressed for the first time.