Temperature regulation can be a particular challenge in newborn infants due to t

Question

Temperature regulation can be a particular challenge in newborn infants due to their small size coupled with their inability to significantly regulate their skin temperature by altering blood flow (we will discuss this in class some time next week - it is not needed for this problem). Evaluate the comfort temperature for a newborn baby with W = 3 kg. Assume that the skin temperature is 37 degree C and that the only mechanisms for heat loss are convection (with no air velocity) and radiation. The area of the baby can be estimated by assuming that A scales as W^2/3 where W is the body mass of a person (or baby). Think carefully about how to scale the mass transfer coefficients needed to describe the newborn. Repeat the calculations in part (A) for a baby wrapped in a thin blanket with a heat transfer coefficient of 4 kcal/(hr-m^2_degree K). By how much would the baby need to increase his / her metabolism so that the comfort temperature were 21 degree C. i.e. what is the value

Explanation / Answer

ASSUMPTION:- Convective heat transfer coefficient of baby(h) = 6.5 W/m2K & Typical heat loss from baby's body = 13 Watts (Experimental standard)

SOLUTION:- (A) Tsurface = Ts = 37C = 310.15K, Surface area of baby = A = W^2/3 = 3^2/3 = 2.09 m2,

By formula P = h x A x (Ts-Tc)

i.e. 13 = 6.5 x 2.09 x (310.15 - Tc) i.e. Tc = 310.15 - 0.96 = 309.19 K

Comforting temperature Tc = 309 K = 36C (ANSWER)

(B) Now h = 4 kcal/hr.m2.K = 1.11 W/m2K

Again By formula 13 = 1.11 x 2.09 x (310.15 - Tc) i.e. Tc = 304.55 K = 31.4 C (ANSWER)

(C) For Tc = 21C = 294.15K

13 = 6.5 x A x (310.15 - 294.15) i.e. A = 0.125 m2 and Since A = Wc^2/3, So Wc = A^3/2 = 0.125^3/2

So Wc = 0.045 kg So M = W - Wc = 3 - 0.045 = 2.95 kg

M = 2.95 kg (ANSWER)

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