Abstract <p>A numerical investigation was conducted to explore the impact of external heat transfer on combustion wave propagation in a cylindrical Ti–Si layer, employing a solid-flame combustion model. Calculations revealed the average burning velocity of the sample, presenting it as a function of layer thickness, inner radius, and outer radius. Critical conditions for the synthesis process in the combustion mode of a hollow cylindrical sample, driven by environmental heat loss, were identified. In the near-critical synthesis mode, periodic temperature fluctuations arose within the combustion wave when the layer thickness was less than 0.5 mm. Conversely, for samples with a layer thickness exceeding 1 mm, combustion consistently proceeded in a stationary manner.</p>