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We present a systematic study on the effects of small aspect ratios 
$\varGamma$ on heat transport in liquid metal convection with a Prandtl number of 
$Pr=0.029$. The study covers 
$1/20\le \varGamma \le 1$ experimentally and 
$1/50\le \varGamma \le 1$ numerically, and a Rayleigh number 
$Ra$ range of 
$4\times 10^3 \le Ra \le 7\times 10^{9}$. It is found experimentally that the local effective heat transport scaling exponent 
$\gamma$ changes with both 
$Ra$ and 
$\varGamma$, attaining a 
$\varGamma$-dependent maximum value before transition-to-turbulence and approaches 
$\gamma =0.25$ in the turbulence state as 
$Ra$ increases. Just above the onset of convection, Shishkina (Phys. Rev. Fluids, vol 6, 2021, 090502) derived a length scale 
$\ell =H/(1+1.49\varGamma ^{-2})^{1/3}$. Our numerical study shows 
$Ra_{\ell }$, i.e. 
$Ra$ based on 
$\ell$, serves as a proper control parameter for heat transport above the onset with 
$Nu-1=0.018(1+0.34/\varGamma ^2)(Ra/Ra_{c,\varGamma }-1)$. Here 
$Ra_{c,\varGamma }$ represents the 
$\varGamma$-dependent critical 
$Ra$ for the onset of convection and 
$Nu$ is the Nusselt number. In the turbulent state, for a general scaling law of 
$Nu-1\sim Ra^\alpha$, we propose a length scale 
$\ell = H/(1+1.49\varGamma ^{-2})^{1/[3(1-\alpha )]}$. In the case of turbulent liquid metal convection with 
$\alpha =1/4$, our measurement shows that the heat transport will become weakly dependent on 
$\varGamma$ with 
$Ra_{\ell }\equiv Ra/(1+1.49\varGamma ^{-2})^{4/3} \ge 7\times 10^5$. Finally, once the flow becomes time-dependent, the growth rate of 
$Nu$ with 
$Ra$ declines compared with the linear growth rate in the convection state. A hysteresis is observed in a 
$\varGamma =1/3$ cell when the flow becomes time-dependent. Measurements of the large-scale circulation suggest the hysteresis is caused by the system switching from a single-roll-mode to a double-roll-mode in an oscillation state.
We present an experimental study of Rayleigh–Bénard convection using liquid metal alloy gallium-indium-tin as the working fluid with a Prandtl number of 
$Pr=0.029$. The flow state and the heat transport were measured in a Rayleigh number range of 
$1.2\times 10^{4} \le Ra \le 1.3\times 10^{7}$. The temperature fluctuation at the cell centre is used as a proxy for the flow state. It is found that, as 
$Ra$ increases from the lower end of the parameter range, the flow evolves from a convection state to an oscillation state, a chaotic state and finally a turbulent state for 
$Ra>10^5$. The study suggests that the large-scale circulation in the turbulent state is a residual of the cell structure near the onset of convection, which is in contrast with the case of 
$Pr\sim 1$, where the cell structure is transiently replaced by high order flow modes before the emergence of the large-scale circulation in the turbulent state. The evolution of the flow state is also reflected by the heat transport characterised by the Nusselt number 
$Nu$ and the probability density function (p.d.f.) of the temperature fluctuation at the cell centre. It is found that the effective local heat transport scaling exponent 
$\gamma$, i.e. 
$Nu\sim Ra^{\gamma }$, changes continuously from 
$\gamma =0.49$ at 
$Ra\sim 10^4$ to 
$\gamma =0.25$ for 
$Ra>10^6$. Meanwhile, the p.d.f. at the cell centre gradually evolves from a Gaussian-like shape before the transition to turbulence to an exponential-like shape in the turbulent state. For 
$Ra>10^6$, the flow shows self-similar behaviour, which is revealed by the universal shape of the p.d.f. of the temperature fluctuation at the cell centre and a 
$Nu=0.19Ra^{0.25}$ scaling for the heat transport.
