Heat transfer using a correlation by neural network for natural convection from vertical helical coil in oil and glycerol/water solution

A physical–empirical model is designed to describe heat transfer of helical coil in oil and glycerol/water solution. It includes an artificial neural network (ANN) model working with equations of continuity, momentum and energy in each flow. The discretized equations are coupled using an implicit step by step method. The natural convection heat transfer correlation based on ANN is developed and evaluated. This ANN considers Prandtl number, Rayleigh number, helical diameter and coils turns number as input parameters; and Nusselt number as output parameter. The best ANN model was obtained with four neurons in the hidden layer with good agreement (R > 0.98). Helical coil uses hot water for the inlet flow; heat transfer by conduction in the internal tube wall is also considered. The simulated outlet temperature is carried out and compared with the experimental database in steady-state. The numerical results for the simulations of the heat flux, for these 91 tests in steady-state, have a R ≥ 0.98 with regard to experimental results. One important outcome is that this ANN correlation is proposed to predict natural convection heat transfer coefficient from helical coil for both fluids: oil and glycerol/water solution, thus saving time and improving general system performance.

Research highlights
► A physical–empirical model was developed which includes an ANN working with equations of continuity, momentum and energy in each flow.
► ANN considers Prandtl number, Rayleigh number, helical diameter and coils turns number as input; and Nusselt number as output parameter.
► Comparisons of experimental and simulated data in steady-state showed a good degree of agreement.
► This physical–empirical model can be used to design, optimize, control and on-line estimation of heat flux.