Question

Given the following parameters for a fluid flow, calculate the appropriate quantities: \[ V_0 = 1 \, \text{m/s}, \quad P_r = 7.01, \quad \nu = 10^{-6} \, \text{m}^2/\text{s} \] \[ S_{hn} = \frac{4.91}{\sqrt{Re_x}}, \quad \Delta x = 0.01 \, \text{m} \]

Hint:

The Reynolds number (\( Re_x \)) is a crucial parameter in fluid dynamics, influencing the heat transfer and the flow regime. The Prandtl number and Nusselt number are also key in determining convective heat transfer in fluid systems.

Answer 1

In this problem, we are given the flow velocity \( V_0 = 1 \, \text{m/s} \), the Prandtl number \( P_r = 7.01 \), the kinematic viscosity \( \nu = 10^{-6} \, \text{m}^2/\text{s} \), and the formula for the Nusselt number \( S_{hn} \) based on the Reynolds number \( Re_x \): \[ S_{hn} = \frac{4.91}{\sqrt{Re_x}} \] We can use the following relation for the Reynolds number: \[ Re_x = \frac{V_0 \cdot x}{\nu} \] Where \( x \) is the characteristic length (given as \( \Delta x = 0.01 \, \text{m} \)). Substituting the known values: \[ Re_x = \frac{1 \cdot 0.01}{10^{-6}} = 10^4 \] Now, substitute \( Re_x = 10^4 \) into the Nusselt number equation: \[ S_{hn} = \frac{4.91}{\sqrt{10^4}} = \frac{4.91}{100} = 0.0491 \] Thus, the Nusselt number \( S_{hn} \) is \( 0.0491 \).