Question

An average man has a body surface area of \(1.8 \mathrm{~m}^{2}\) and a skin temperature of \(33^{\circ} \mathrm{C}\). The convection heat transfer coefficient for a clothed person walking in still air is expressed as $h=8.6 V^{0.53}\( for \)0.5

Short answer

Answer: To find the rate of heat loss for each walking velocity, first calculate the convection heat transfer coefficient (h) using the formula \(h = 8.6 V^{0.53}\) for each velocity (V). Next, use the heat transfer equation \(q = hA(T_{s} - T_{\infty})\) with the calculated h values and given surface area (A), surface temperature (\(T_{s}\)), and air temperature (\(T_{\infty}\)) to determine the rate of heat loss (q) for each walking velocity.

Step-by-step solution

Define known parameters

In this problem, we are given the body surface area (A = 1.8 m²), air temperature (\(T_{\infty}\) = 7°C), and surface temperature (\(T_{s}\) = 30°C).

Calculate the convection heat transfer coefficient (h)

Having the given formula for the convection heat transfer coefficient: \(h = 8.6 V^{0.53}\), we will calculate h for each walking velocity: (a) 0.5 m/s, (b) 1 m/s, (c) 1.5 m/s, (d) 2 m/s.

Calculate the rate of heat loss q

Now, we will use the formula \(q = hA(T_{s} - T_{\infty})\) to calculate the rate of heat loss for each walking velocity using the calculated h values from step 2. 3a. For \(V = 0.5\) m/s: Calculate h: \(h = 8.6 (0.5)^{0.53}\) Then calculate q: \(q = h(1.8)(30 - 7)\) 3b. For \(V = 1.0\) m/s: Calculate h: \(h = 8.6 (1)^{0.53}\) Then calculate q: \(q=h(1.8)(30-7)\) 3c. For \(V = 1.5\) m/s: Calculate h: \(h = 8.6 (1.5)^{0.53}\) Then calculate q: \(q=h(1.8)(30-7)\) 3d. For \(V = 2.0\) m/s: Calculate h: \(h = 8.6 (2)^{0.53}\) Then calculate q: \(q=h(1.8)(30-7)\) After calculating the rate of heat loss (q) for each walking velocity in step 3, we have found the solution for each part of this exercise.