A novel analytical solution of the non-uniform convective boundary conditions problem for heat conduction in cylinders

The problem of heat conduction in a still cylinder exposed to non‐uniform convective conditions on both inner and outer surfaces has been addressed by a method based on the series solution and a novel analytic solution is derived to predict the temperature field in the cylinder. Compared to previous available results this method allows a simpler implementation and its almost straightforward extension to multilayered cylinders represents one of the main advantages over more complex numerical solutions. As an example of application the effect of the non-uniform distribution of heat transfer coefficients on the solid temperature field and the heat transferred is analysed, as function of the fluid flow regime, the Biot number and the cylinder thickness.