Heat Transfer and The Human Head

1. Heat Transfer and The Human Head Brad Elmer John Pearson

2. Introduction • Problem • Find the effects of wearing a beanie on a bald head • Varying wind speeds in cold weather

3. Assumptions • Average Head Circumference 58cm (www.thehatesite.com) • Radiation neglected (same for all cases) • Flesh Properties Same as Water • Constant Core Temperature • Transition region where hat ends very small

4. Setup • Conditions • Air at 20° F • Core at 97.8° F • Test 1 • Bald, no wind • w/Beanie, no wind • Test 2 • Bald, 20 mph wind • w/Beanie, 20 mph wind • Test 3 • Bald, category 5 hurricane 156mph wind • w/Beanie, category 5 hurricane 156mph wind

5. Solution • Test 1 • Free convection • Gr >>Re2 • Test 2 • Forced convection • Some error expected • Re > 7.6e4 • Test 3 • Forced convection • Some error expected • Re > 7.6e4

6. Results Head Surface Temperatures

7. Recommendations • Wear a beanie especially when there are category five hurricane winds and it’s 20°F outside • Do not shave your head bald in a cold climate

8. Appendix • Formulas used • Free convection • 9.12 • 9.25 • 9.35 • Forced convection • 7.56

9. Appendix