Abstract
We present a comprehensive analytical model for laminar flow in a vertically heated rectangular convection loop, with applications to oil cooling in transformer systems. Starting from an integral equation, we apply a quasi-one-dimensional approach to derive equations for both loop velocities and temperature distributions. In this model, we account for temperature-dependent dynamic viscosity and introduce cooling at the loop top and in the fin. The analytical predictions are rigorously validated against finite volume method (FVM) simulations across different geometries and heat flux conditions, demonstrating strong agreement within a 2% discrepancy range for most parameters. This model provides a viable analytical alternative to computationally intensive simulations, offering insights into natural convection dynamics within closed-loop configurations.