# (567bu) Damped Wave Conduction and Relaxation Effects On Human Anatomical Temperature

- Conference: AIChE Annual Meeting
- Year: 2010
- Proceeding: 2010 AIChE Annual Meeting
- Group: Food, Pharmaceutical & Bioengineering Division
- Session:
- Time:
Wednesday, November 10, 2010 - 6:00pm-8:00pm

The heat generated within the human anatomy on account of several metabolic reactions and the heat transfer to the surroundings can be described using the bioheat transfer equation introduced by Pennes [1998]. The energy balance equation is combined with the damped wave conduction and relaxation equation and the governing equation of transient temperature can be written. The heat generated per unit volume on account of metabolism and heat removed oer unit volumeby blood flow is also included in the governing equation. Thermal peclect number, relaxation number are defined. The non-Fourier effects can become significant in the times associated with heat transfer between the tissue and blood. Consider a rod of length l with one end maintained at O K. At time t = 0, the entire rod is at 0 K. For times greater than o, a temperature dependent heat source is allowed to heat the rod. The transient temperature distribution in the rod is made note of. When S = U* the governing equation reverts to wave equation. Steady state and transient state solutions for temperature in the rod are presented. Special case solutions for U* =1 and S = U* are developed. A critical point of null heat transfer can be identified. The temperature overshoot found can be explained by the temperature dependent heat source. The maxima in temperature occurs at X = 1.5. Reversal of heat flow can be expected. The heat will back flow from X = 1.5 to X = 0. Expressions for heat flux are derived.