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Estimating Skin Temperature of a Bald Head Under Convective Conditions: A Calculator Tool

This calculator, developed by Jess Rose and Jeff Amelang in Winter 2009, estimates the skin temperature of a bald head under three distinct convective conditions: free convection, forced convection (windy), and forced convection with a beanie. By modeling the head as a sphere with constant temperature and assessing thermal properties through one-dimensional radial conduction, the tool aids in understanding thermal dynamics. Notable findings reveal that under convective heating, a beanie may surprisingly keep skin temperatures lower than expected, emphasizing the importance of thermal conductivity in tissue.

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Estimating Skin Temperature of a Bald Head Under Convective Conditions: A Calculator Tool

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  1. Bald Head Convective Calculator Jess Rose Jeff Amelang Winter 2009

  2. Calculator Functionality Goal: Create a calculator that estimates skin temperature of a bald head under three different convective conditions: • Free convection • Forced convection (windy) • Forced convection with a beanie

  3. Basic Assumptions • Head is modeled as a sphere of constant temperature with a layer of tissue • Steady state • One Dimensional Radial Conduction • Constant Properties • Neglect Radiation • Properties calculated using the source code of the thermal properties calculator tissue T_c = 98°F T = 0.25 in T_inf D = 7 in

  4. Free Convection Convective coefficient is calculated using Free convection on a sphere Total thermal circuit Partial thermal circuit

  5. Forced Convection (windy) Convective coefficient is calculated using Forced convection on a sphere Total thermal circuit Partial thermal circuit Includes Free Convection if .1 < abs(Gr/Re^2 ) < 10

  6. Forced Convection with Beanie Convective coefficient is calculated using Forced convection on a sphere Y Total thermal circuit Partial thermal circuit Assumptions: • Two parallel thermal circuits • Infinite Contact Resistance between hemispheres

  7. The Calculator

  8. Improvements • Approximate head with volumetric head generation instead of a constant temperature • Eliminate assumption of infinite contact resistance between hemispheres with beanie • Include radiation

  9. Conclusions • When there is convective heating of Charlie Brown’s head, the beanie keeps the skin surface temperature lower, oddly enough. • Changing the conductive coefficient of the tissue has a significant effect on the temperature of the skin.

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