well explained but there is one thing that doesn't add up. you're saying that if Nu = 1, there is no convection. this can't be mathematically correct cuz if Nu = Q_conv / Q_cond, then Nusselt is also 0 if convection is zero. could you explain this please.
Many thanks for your interesting question, you know the ratio of convection over conduction is only a physical interpretation of Nusselt and not a mathematical and exact meaning of Nusselt. By the way, in micro scale always there is motion between molecules of a fluid.
If there is no convection, q̇_conv is not zero. It is in fact just equal to q̇_cond, because as you can imagine, if the fluid is not moving, it just like a solid body and therefore like a solid body. Hence, if there is no flow, then q̇_”conv” = q̇_cond.
*keep in mind that q̇_conduc is just a theoretical/comparative value, but the real heat flow is q̇_convec - so its not just the convective parts of our flow, but the entire reallife flow, which might be convective.
