Question

The _____ number is a significant dimensionless parameter for forced convection, and the ___________ number is a significant dimensionless parameter for natural convection. (a) Reynolds, Grashof (b) Reynolds, Mach (c) Reynolds, Eckert (d) Reynolds, Schmidt (e) Grashof, Sherwood

Short answer

(a) Reynolds, Grashof (b) Mach, Eckert (c) Reynolds, Schmidt (d) Grashof, Sherwood (e) Mach, Sherwood Answer: (a) Reynolds, Grashof

Step-by-step solution

Identifying Forced Convection Dimensionless Parameter:

Forced convection occurs when a fluid flows over a surface due to external forces such as pumps, fans, or the wind. The Reynolds number is a dimensionless quantity that describes the relationship between inertial forces and viscous forces in a fluid flow. It is used to predict the onset of turbulence in forced convection, so it is the correct dimensionless parameter for forced convection.

Identifying Natural Convection Dimensionless Parameter:

Natural convection occurs when fluid flow is driven by buoyancy forces caused by temperature differences in the fluid. We should now examine the other dimensionless parameters mentioned in the options to identify the appropriate parameter for natural convection. (a) Grashof number: This dimensionless quantity represents the ratio of buoyancy forces to viscous forces in a fluid. It characterizes the flow in natural convection and is used to predict the onset of free convection. (b) Mach number: This dimensionless quantity represents the ratio of the flow velocity to the speed of sound in the fluid. It is not related to natural convection. (c) Eckert number: This parameter represents the ratio of kinetic energy to the enthalpy difference in the fluid. It is used in studies of viscous dissipation but is not specifically related to natural convection. (d) Schmidt number: This dimensionless quantity is used in mass transfer studies, where it represents the ratio of momentum diffusivity to mass diffusivity. It is not related to natural convection. (e) Sherwood number: This parameter is used in mass transfer studies, representing the ratio of convective mass transfer to diffusive mass transfer. It is not related to natural convection.

Conclusion:

Based on the analysis above, the correct answer is: (a) Reynolds, Grashof The Reynolds number is a significant dimensionless parameter for forced convection, and the Grashof number is a significant dimensionless parameter for natural convection.