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Abstract. The main aim of this paper was to analyze possible utilization of the low concentration nanofluids and the magnetic field to enhance heat transfer. The studied fluids were based on water with an addition of copper particles (40-60 nm diameter). They belonged to the diamagnetic group of materials. As a first attempt to stated target the analysis of enclosure placed in the maximal value of square magnetic induction gradient was carried out. The maximum was in the centre of investigated cavity and it caused the most complex system of gravitational and magnetic buoyancy forces. In the lower part of cavity both forces acted in the same direction, while in the upper part they counteracted. Therefore an enhancement and attenuation of heat transfer could be observed. Due to the particle concentration and magnetic field action the character of flow was changed. In the case of 50 ppm nanofluid the flow was steady end the strong magnetic field didn't change much in its structure except for the suppression of some vortices. In the case of 500 ppm nanofluid the flow was not steady even without magnetic field, but increasing magnetic induction caused change of its structure towards the inertial-convective regime of turbulent flow.

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Classical boundary and initial-boundary value problems in heat and mass transfer are generally formulated in a mathematically unique way. Boundary and initial conditions together with physical properties of the thermodynamic system are treated as exactly known. The influence of different kinds of mathematical model simplifications on the accuracy of solution and reliability of the model are not usually analyzed. The problems become more complicated when inverse ill-posed initialboundary problems are considered. The widely used procedure of model validation is based on direct comparison of analytical or numerical solution, unique in a mathematical sense, with measurement results. The main feature of the method presented in this article is that all experimental results are included into the mathematical model. Thus, because of the inevitable errors of measurements, the system of model equations becomes internally contradicted as the number of unknown variables is less than the number of equations. In consequence, basic laws of energy and mass conservation are not satisfied. To adjust the experimental data to the mathematical model, an orthogonal least-squares method is proposed. Special attention has been paid to the coupling of experimental data with the nucleation and grain growth models formulated by Rappaz and co-workers. Theoretical considerations are illustrated with experimental data for an Al-Si alloy.

Purpose Nanofluids’ properties made them interesting for various areas like engineering, medicine or cosmetology. Discussed here, research pertains to specific problem of heat transfer enhancement with application of the magnetic field. The main idea was to transfer high heat rates with utilization of nanofluids including metallic non-ferrous particles. The expectation was based on changed nanofluid properties. However, the results of experimental analysis did not meet it. The heat transfer effect was smaller than in the case of base fluid. The only way to understand the process was to involve the computational fluid dynamics, which could help to clarify this issue. The purpose of this research is deep understanding of the external magnetic field effect on the nanofluids heat transfer. Design/methodology/approach In presented experimental and numerical studies, the water and silver nanofluids were considered. From the numerical point of view, three approaches to model the nanofluid in the strong magnetic field were used: single-phase Euler, Euler–Euler and Euler–Lagrange. In two-phase approach, the momentum transfer equations for individual phases were coupled through the interphase momentum transfer term expressing the volume force exerted by one phase on the second one. Findings Therefore, the results of numerical simulation predicted decrease of convection heat transfer for nanofluid with respect to pure water, which agreed with the experimental results. The experimental and numerical results are in good agreement with each other, which confirms the right choice of two-phase approach in analysis of nanofluid thermo-magnetic convection. Originality/value The Euler–Lagrange exhibit the best matching with the experimental results.