Question

Which dimensionless number characterizes the ratio of convective to conductive heat transfer in a fluid?

• A. Reynolds number
• B. Prandtl number
• C. Nusselt number
• D. Grashof number

Hint:

Do not confuse the Nusselt number ($Nu$) with the Biot number ($Bi$).
Both have the form $\frac{hL}{k}$, but $k$ in $Nu$ is the fluid thermal conductivity, whereas $k$ in $Bi$ is the solid thermal conductivity.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question asks for the dimensionless parameter in heat transfer that measures the ratio of heat transfer by convection to heat transfer by conduction.

Step 2: Key Formula or Approach:
The Nusselt number ($Nu$) is defined as:
\[ Nu = \frac{h \cdot L_c}{k} \]
where:
$h$ is the convective heat transfer coefficient,
$L_c$ is the characteristic length, and
$k$ is the thermal conductivity of the fluid.

Step 3: Detailed Explanation:

• The physical significance of the Nusselt number can be understood by looking at heat transfer across a fluid layer of thickness $L$.

• Convective heat flux is given by $q_{\text{conv}} = h \Delta T$.

• Conductive heat flux across the same fluid layer, if static, is $q_{\text{cond}} = \frac{k \Delta T}{L}$.

• The ratio of these two modes of heat transfer is:
\[ \frac{q_{\text{conv}}}{q_{\text{cond}}} = \frac{h \Delta T}{\frac{k \Delta T}{L}} = \frac{h L}{k} = Nu \]

• A Nusselt number close to $1$ indicates pure conduction, while higher values signify enhanced heat transfer due to convection (fluid motion).

Step 4: Final Answer:
The dimensionless number that characterizes this ratio is the Nusselt number.