Non-uniform temperature effects on air natural convection from vertical radiator panels in oil natural transformers

For panel-type radiators of oil natural air natural transformers (ONAN), conventional uniform-wall-temperature correlations fail to accurately account for the prediction deviation caused by air-side surface temperature non-uniformity. This study numerically investigates the effect of non-uniform wall temperature on natural convection heat transfer in two configurations: an isolated vertical plate (end fins) and a vertical parallel plate channel (internal fin channels). Simulations are performed using the finite volume method with variable thermophysical properties of air. The results show that for both configurations, a positive wall temperature gradient enhances heat transfer compared with the uniform-temperature case, and the enhancement increases with the gradient magnitude. For the isolated vertical plate, the enhancement decreases with increasing Rayleigh number, and increasing the wall temperature gradient improves the Nusselt number by up to 25.2%. For the vertical parallel plate channel, the enhancement increases as the plate spacing decreases; in the high Rayleigh number regime, a slight rebound is observed due to the combined chimney effect and turbulence, and increasing the wall temperature gradient improves the Nusselt number by up to 38.2%. Based on the numerical results, multiple linear regression is used to develop separate predictive correlations for the two configurations. The proposed correlations are validated against experimental data from a practical transformer radiator and independent literature data, yielding prediction deviations of 14.91% and 7.17%, respectively. This work extends the parameter range of previous studies on non-uniform wall temperature effects, provides the first systematic investigation for the vertical parallel plate channel, and offers experimentally validated correlations for engineering applications.