DIFFUSION-CONVECTION PROCESS IN A BRANCHING FIN

The diffusion-convection transport process in a branching fin with a power-law type transfer coefficient (h = a0m) was investigated theoretically. The governing equations were formulated and the solution was obtained analytically. For systems with m> - 1, the steady-state distribution for the state variable 0 was unique and stable. When the exponent becomes less than - 1, nevertheless, bistability occurs if the steady-state solution exists. Linear stability analysis shows that the lower branch solution on the fin efficiency/effectiveness versus branching number plot was stable, whereas the upper solution was unstable to small perturbations.