Question

Nusselt number is a function of:

• A. Heat capacity
• B. Conductivity only
• C. Grashof and Prandtl numbers
• D. Reynolds number only

Hint:

In forced convection, the Nusselt number is a function of the Reynolds number and Prandtl number, whereas in natural convection, it is influenced by the Grashof and Prandtl numbers.

Answer 1

The Correct Option is C

The Nusselt number (Nu) is a dimensionless quantity that relates the convective heat transfer to the conductive heat transfer in a fluid flow. It is used to characterize the efficiency of heat transfer in forced or natural convection. The Nusselt number is defined as: \[ Nu = \frac{h L}{k} \] Where:
- \( h \) is the convective heat transfer coefficient,
- \( L \) is the characteristic length,
- \( k \) is the thermal conductivity of the fluid.
The Nusselt number is typically a function of several dimensionless numbers, including the Reynolds number (Re), the Prandtl number (Pr), and the Grashof number (Gr). These numbers help determine the nature of the fluid flow (laminar or turbulent) and the relative importance of convective versus conductive heat transfer.
- The Grashof number (Gr) characterizes the relative importance of buoyancy forces to viscous forces in natural convection.
- The Prandtl number (Pr) is a dimensionless number that relates the momentum diffusivity (kinematic viscosity) to the thermal diffusivity.
- The Reynolds number (Re) is important in determining whether the flow is laminar or turbulent, but it is not directly related to the Nusselt number in the way the Grashof and Prandtl numbers are in natural convection.
Thus, the Nusselt number is primarily a function of the Grashof and Prandtl numbers in natural convection problems.