Study on unsteady natural convection heat transfer of crude oil storage tank based on fractional-order Maxwell model

When considering the natural flow processes in crude oil in static storage tanks, researchers usually treat the nonlinear heat and mass transfer and flow using integer-order models. However, this ignores the nonlinear convection and heat-transfer phenomena that occur; these are dependent on time and space due to the viscoelasticity of crude oil, which is a non-Newtonian fluid. In this work, we examined the time and space dependence of the nonlinear natural convective heat-transfer processes in crude-oil storage tanks. Fractional-order Maxwell and Cattaneo–Vernotte models were applied to the traditional momentum and temperature equations considering the Boussinesq approximation. Based on the L1 discrete format, the fractional-order pressure-correction equation was derived, and an associated solver, CaputoTemporalFractionalFoam (CTfracFoam), was developed to simulate the convection processes in static crude-oil storage tanks. The results show that when α equals 0.1, the maximum velocity in monitoring area 2 is 0.1404 m/s, and the velocity gradually increases as α increases with a maximum value of 1.1468 m/s at 0.9. When the β is 0.1 and 0.2, the temperature changes in the transition region are −5.204 and −0.165 °C, respectively, while when β is greater than 0.2, the temperature changes are all positive values with a maximum value of 1.924 °C at 0.9. Compared with integer-order Fourier heat-transfer and Newtonian fluid-flow models, the developed fractional-order model can describe the natural convection phenomena of non-Newtonian fluids such as crude oil more flexible and accurately.