A transient free convection heat transfer study in an oil tank with vertical and horizontal arrangements of heating coils

Few studies have been conducted in the field of free convection heat transfer with the aim of improving efficiency, energy storage and proper performance of oil tank heating systems with coils. In this article, the free convection heat transfer in an oil-filled tank with a coil arrangement heating system has been numerically investigated. In the heating system where the hot coils are immersed in the fluid with high viscosity, the effects of the distances between the two coils have been studied transiently for various Rayleigh numbers. The study has been carried out for the vertical and horizontal arrangement of two coils with four distances of 0.2, 0.3, 0.4 and 0.5 times the distance between the upper and lower walls of the tank at three Rayleigh numbers of \(7.5 \times {10}^{7}\) $7.5\times {10}^7$ , \(1.5 \times {10}^{8}\) $1.5\times {10}^8$ and \(3.0 \times {10}^{8}\) $3.0\times {10}^8$ . The two-dimensional equations of continuity, momentum and energy are discretized and solved using the finite volume method.

The type of arrangement of the coils, the distance between the two coils, the oil heating time and the Rayleigh number are parameters that have a major influence on the flow pattern formed inside the oil tank and consequently the oil temperature distribution. The Nusselt number for all distances between two coils and various \({\text{Ra}}\) $\text{Ra}$ decreased with over time for both coils arrangements. At different times, the Nusselt number increased with the increment in the Rayleigh number. The Nusselt number at different conditions for the horizontal arrangement of the coils was lower than the vertical arrangement. The maximum averaged Nusselt number for both coils arrangements was obtained at Rayleigh number of \(3.0 \times {10}^{8}\) $3.0\times {10}^8$ . The correlation equations show that the average Nusselt number corresponds to \(\left( {W/L} \right)^{ - 0.24}\) ${\left(W/L\right)}^{-0.24}$ and \(\left( {H/L} \right)^{ - 0.48}\) ${\left(H/L\right)}^{-0.48}$ for horizontal and vertical coil arrangement, respectively.