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The Maurice Herzog problem 1

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(1)

How long can you stand on top of Annapurna without gloves ? (no wind)

The Maurice Herzog problem 1

use the 1D bioheat equation to determine the temperature in Maurice’s fingers (5mm of tissue between bone and skin) at steady state

what are the characteristic lengths involved in the problem ? estimate the time required to reach this steady state

blood flow rate per unit volume of tissue: Vb ~ 10-4 s-1 or 2 X 10-4 s-1 blood density: ρb ~ 1000 kg/m3

blood specific heat: Cb ~ 3600 J/kg.K blood temperature Tb = 37°C

thermal conductivity of tissue: λ ~ 0.5 W/m.K

metabolic heat generation rate: qm ~ 0 in fingers (no muscles) outside temperature: Ta = -20°C

heat transfer coefficient with air: h ~ 2 W/m2.K

steady state 1D diffusion + source term

(2)

Steady state solution of

@

2

✓

@ x

2

⇢

b

C

b

V

b

✓ = 0

T = T b + Ta Tb

cosh(xS/lb) + /(hlb) sinh(xS/lb) cosh(x/lb)

✓ = T T

b

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