Numerical Solution Skin Supersolidity

To verify the prediction on the presence of thermal conductivity gradient due to the joint effect of heating and skin supersolidity, one needs to solve the one-dimensional nonlinear Fourier equation [41] numerically by introducing the supersolid skin [17] in a tube container. Considering a one-dimensional approach, water in a cylindrical tube can be divided into the bulk (B) and the skin (S) region along the x-axial direction and put the tube into a drain of constant temperature 0 °C. The other end is open to the drain without the skin. The heat transfer in the partitioned fluid follows this transport equation and the associated initial and boundary conditions 

The first term describes diffusion and the second convection. The known temperature dependence of the thermal conductivity k 0), mass density p i9), and specific heat under constant pressure CpB(0) see Appendix A4—6 determines the diffusion coefficient b. For simplicity, one can take the s in the skin (z — 2) as an adjustable for optimization. The following initial and boundary conditions apply  

The heat transfer coefficient h of the cooling ends remains at 30 w/(m K) and V = 10 m/s is the heat flow convection velocity in bulk water [42]. 

41 Mpemba Paradox H-Bond Memory and Skin Supersolidity 

Conveetion flow rate Thermal diffusion coefiieient as/ B Mpemba effect Skin bottom A0 

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