Abstract

The aim of and inspiration behind this paper was to explain the reasons, also observed by other researchers, of the discrepancy in the results of experimental free convection, which for small Rayleigh and Nusselt numbers in the initial phase of research can sometimes reach several hundred percent. These discrepancies decrease with increasing heating power and plate surface temperature, in proportion to the increase in Ra and Nu, reaching typical values for this type of research. To explain this phenomenon, a comprehensive theoretical and experimental analysis of the influence of the physical properties of a fluid (air and water) as well as primary (tw and t∞) and secondary (tav and Δt) temperatures on the Rayleigh number was carried out. The impact was found to be unequal. The plate temperature tw is of greater importance, which is much higher than the much lower and almost constant temperature t∞ of the undisturbed area, especially since it causes convective movement, generating differences in fluid density and thus driving the phenomenon. Similarly, the direct contribution of the temperature difference Δt to Ra suggests that it has a greater influence on convective heat transfer than the average temperature of the medium tav. By analysing the effect of each of these temperatures separately, it was possible to show that their mutual, compatible or opposite interaction (tw/t∞) causes a different scattering of results, or may even lead to unusual Rayleigh numbers (Ra temperature dualism). This study led not only to a better understanding of the phenomenon, but even to a prediction of its unusual behaviour, unheard of in typical experimental studies of free convection. For example, if we consider the theoretical convective heat transfer from a plate l = 0.15 m in air in the context of the interaction of tav and Δt, it turns out that for the same Δt = 40 K, the Rayleigh number may assume, depending on tav = (tw + t∞)/2, different values. So, for tw = 50 °C, t∞ = 10 °C and tav = 30 °C, Ra = 1.213.107, whereas for tw = 90 °C, t∞ = 50 °C and tav = 70 °C it is ≈ 1.7 times smaller (Ra = 0.687.107). This hypothetical phenomenon, unheard of in typical experimental studies, which could occur, and maybe even does occur in smelting, thermal energy, etc., forces us to think about the values of Nusselt numbers, heat transfer coefficients and heat fluxes for these two cases. This lies beyond the scope of the present paper, but it is a topic for possible future research.

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