Question

The convection heat transfer coefficient for a clothed person while walking in still air at a velocity of \(0.5\) to \(2 \mathrm{~m} / \mathrm{s}\) is given by \(h=8.6 V^{0.53}\), where \(V\) is in \(\mathrm{m} / \mathrm{s}\) and \(h\) is in \(\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Plot the convection coefficient against the walking velocity, and compare the convection coefficients in that range to the average radiation coefficient of about $5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$.

Short answer

Based on the plotted graph, describe the relationship between the convection coefficients and the radiation coefficient for a clothed person walking in still air, and discuss how convection coefficients change as the walking velocity increases.

Step-by-step solution

Prepare the data for plotting

Create a table with two columns: walking velocity (\(V\)) and convection coefficients (\(h\)). Calculate the convection coefficient corresponding to each velocity in the range \(0.5 \, \mathrm{m} / \mathrm{s}\) to \(2 \, \mathrm{m} / \mathrm{s}\) with increments of your choice (for example, every \(0.1 \mathrm{m} / \mathrm{s}\)).

Plot the convection coefficient against the walking velocity

Using the table you've created, plot the convection coefficient (\(h\)) on the vertical axis and the walking velocity (\(V\)) on the horizontal axis. Connect the points with a smooth curve. You can use any plotting software/ tool or graph paper to create the plot.

Compare convection coefficients to the average radiation coefficient

To compare the convection coefficients to the average radiation coefficient of \(5\,\mathrm{W}/\mathrm{m}^{2}\cdot \mathrm{K}\), plot a horizontal line on the graph at the level of \(h=5\). Observe and analyze the relationship between the convection coefficients and the radiation coefficient.

Discuss the comparison

Describe the relationship between the convection coefficients and the radiation coefficient. Explain how the convection coefficients change as the walking velocity increases and compare those values to the average radiation coefficient.