Final answer:
The Reynolds number is significant for forced convection, indicating whether flow is laminar or turbulent, while the Grashof number is significant for natural convection, related to density differences caused by temperature gradients.
Step-by-step explanation:
The correct answer to the question "The ___ number is a significant dimensionless parameter for forced convection and the ___ number is a significant dimensionless parameter for natural convection" is B. Reynolds, Grashof. The Reynolds number is a critical dimensionless parameter that helps predict whether a fluid flow will be laminar or turbulent. It is calculated based on factors like fluid density, speed, viscosity, and characterizing length or radius of the conduit through which the fluid is moving. For a flow in a tube, for instance, a Reynolds number (NR) below about 2000 indicates laminar flow, whereas a value above about 3000 suggests turbulent flow. The transition region between laminar and turbulent flow, which is unstable, occurs between these two values.
On the other hand, the Grashof number is a dimensionless parameter that is crucial for natural convection, which occurs due to density differences within the fluid owing to temperature gradients, unlike forced convection which involves external forces such as a pump or a fan.