Outcome 2

Babies, and especially premature babies, have particularly large surface area relative to their body mass as compared with adults. That makes them especially susceptible to hypothermia.  Incubators are used to help reduce the heat loss rate in such cases.  What are the basic features of an incubator and how do they reduce heat loss by each of the following:

Thermal Radiation

Conduction

Forced Convection

Evaporation

Outcome 1

Human body temperature is 98.6 °F. Convert this to Celsius.

Convert body temperature to Kelvin.

Outcome 3

The surface area of a premature baby can be calculated according to the formula of Haycock et. al.^[1]

Surface Area  = M 0.5378  x L 0.3964  x 0.024265

The result give are in m², but length (L) is input in cm and mass (M) is input in kg

Calculate the surface area for a premature baby with weight of 3.5 lbs (a mass of 1.8 kg)  and length 42 cm.

Use the surface area and body temperature you found above to calculate the rate at which the baby loses thermal energy to the environment by thermal radiation if the room is at a temperature of 75 °F (23.9 °C). The emissivity of human skin is typically 0.98. Don’t forget convert the room temperature to Kelvin.

Calculate the heat loss rate by conduction to the table if the baby is laying on a mattress 5 cm thick with thermal conductivity of .04 W/ (m °C). Use the same body temperature and room temperature as in the previous calculations. Assume only the back half of the body is experiencing conduction (use half the surface area).

Calculate the heat loss rate by forced convection for an air speed of 0.5 m/s is caused by the ventilation system and movement of people in the room etc. Use the same body temperature and room temperature as in the previous calculations. Assume only the front half of the body is experiencing forced convection (use half the surface area).

If the room is at 50 % relative humidity the air speed of of 0.5 m/s will result in an evaporation from the baby’s moist skin at a rate described by the equation below (we didn’t talk about determining evaporation rate so if you want to understand this equation talk with you instructor, but for now just use it).

Rate of evaporation in kg/s  = 0.000097 x surface area.

Calculate the rate of evaporation of water from the baby’s skin.

What is the rate at which this evaporation removes thermal energy from the baby? (Hint: How much energy is lost for each kg of water that evaporates?)

Add up all of these heat loss rates to get the total rate of heat loss.

Assuming the baby is mostly water, (use the specific heat of water) calculate the rate at which the temperature of the baby will change in C° per second. Use the baby mass from above.

How many degrees would the baby’s body temperature lower in 10 minutes at this rate?

Connecting Concepts: Metabolism, Thermal Power, Heat

Let’s imagine that we thought the baby could handle generating the thermal energy needed to replace the heat loss you calculate above by simply converting food Calories into thermal energy. In that case we wouldn’t need an incubator, we would just need to keep the baby well fed.  How much breast milk would the baby need to drink each day? Let’s find out.

Breast milk has 700 Calories (kcal) per kg. ^[2] How many kg/s of milk would the baby need to drink to intake the same energy as what is lost?

How many kg/hour is this?

How many kg/day is that?

How does that compare to the baby’s mass?

Does this seem reasonable? Explain.