What is the average heat dissipation from a normal desktop computer?

Question

Please also specify the heat dissipated from a normal human being occupying a room. I have to design an air conditioning system. I need the total heat evolved into the room.

Answer 1

You left out lots of stuff, how big of a computer? By how big i mean how many watts is the power supply. From experience I know that my 500w power supply puts out lots of heat. Same thing with the CPU and video cards. How big is the volume of the room that needs air conditioning? And here is a tricky one that ill bet you haven't even thought of.... how cold does the room need to be kept? because the colder the room, the more heat that the human will put out to compensate for the air temp. :P

Answer 2

The upper limit is usually quoted at 250 watts. You need to design an air conditioning system around the maximum load (i.e. with some excess capacity). The nominal value for a human beings heat output is about 100W. If you need more detail you should go to the ASHRAE (American society for heating and refrigeration engineers, http://www.ashrae.org/). Also note that a good estimate of the heat load on any structure can be calculated directly from the electrical consumption (lighting, computers, office equipment, etc.) plus the average amount of sunlight coming into the building through windows at a given latitude and time of year. This really can't be explained in a short discussion, you should get a book or browse several environmental science websites.

Answer 3

not much.. YOu've got some solid state stuff there with sinks on them and blah blah blah.. YOu're probably looking at about 125 watts total..

Howere.. This is for a normal computer.. Computers with autism exude a lot less energy but those with split personalities have a total emission as a factor above the normal by the number of personalities found in the computer.



I really hope this has cheered you up as you asked a very sad question!!!

Answer 4

Open the case and blow out any/all dust that has accumulated (turn off the computer first). Especially the fans (fan for the video card also). If this doesn't help, then you may need to get a new cooling fan for the video card (or just replace the video card).

Answer 5

It must be close to the same as having 2 or 3 people in the room.

Answer 6

Mobile Networks and Applications 4 (1999) 3–13 3

Heat dissipation in wearable computers aided by thermal coupling

with the user

Thad Starner and Yael Maguire

Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Wearable computers and PDA’s are physically close to, or are in contact with, the user during most of the day. This proximity

would seemingly limit the amount of heat such a device may generate, conflicting with user demands for increasing processor speeds

and wireless capabilities. However, this paper explores significantly increasing the heat dissipation capability per unit surface area of a

mobile computer by thermally coupling it to the user. In particular, a heat dissipation model of a forearm-mounted wearable computer

is developed, and the model is verified experimentally. In the process, this paper also provides tools and novel suggestions for heat

dissipation that may influence the design of a wearable computer.

1. Introduction: Heat dissipation for body-centered

devices

Demand for higher computational power in notebook

computers has forced hardware designers to plan processor

heat dissipation carefully. However, as owners of high-end

laptops will testify, the surface of the machine may still

reach uncomfortable temperatures, especially upon momentary

contact. As high-end computers are incorporated into

smaller form factors, this problem will worsen. Wearable

computers would seem to have particular difficulties since

the computer housing may be in prolonged contact with

skin. However, this paper suggests that wearable computers

may provide a better form factor than today’s notebooks

in regard to heat dissipation.

An obvious approach to the problem of heat generation

is to decrease the power required for high-end CPUs

through higher integration, optimized instruction sets, and

more exotic techniques such as “reversible computation”

[42]. However, profit margins, user demand, and backwards

compatibility concerns are pushing industry leaders

to concentrate on processors requiring more than 5 W. In

addition, the explosion of mobile peripherals, such as wireless

Internet radios, video cameras, sound cards, body networks,

scanners, and global positioning system (GPS) units

creates an ever higher heat load as functionality increases.

An example of this effect is the U.S. Army’s modern (late

1990’s) soldier, who is expected to dissipate 30 W on communications

gear alone! Thus, even with improved technology,

heat dissipation will continue to be an issue in the

development of mobile devices.

Current systems try to insulate the user from heat

sources, slowing or shutting down when internal temperatures

get too high. However, the human body is one of

the most effective and complex examples of thermoregulation

in nature, capable of dissipating well over 2700 W

of heat [10]. Thus, the human body itself might be used

to help dissipate heat. To take advantage of this system,

some background knowledge is necessary. The next section

discusses the fundamentals of human heat regulation

and thermal comfort, but for a more thorough discussion

see [10,37]. Those readers who are familiar with the principles

of thermoregulation should skip to the next section.

2. Thermoregulation in humans

In the extremes, the human body generates between

80 W to 10,000 W of power [27,36]. With proper preparation,

it can survive in the hot Saharan desert or on the ice

in Antarctica for extended periods. Yet, the body maintains

its “core” temperature (the upper trunk and head regions) at

37 C, only varying 2 C while under stress (in medical

extremes, 5 C may be observed) [10]. Obviously, the

human body can be an excellent regulator of heat. However,

the sedate body is comfortable in a relatively narrow

range of environmental temperatures. Even so, the amount

of heat that is exchanged in this comfort range can be significant

when all the different modes are considered. Heat

balance in the human body can be expressed by

M0 􀀀W0 = Q0evap + Q0conv + Q0rad + Q0cond + Q0stor, (2.1)

whereM0 is the rate of heat production (due to metabolism),

W0 is the rate of useful mechanical work, Q0evap is the rate

of heat loss due to evaporation, Q0conv is the rate of heat

gained or lost (exchanged) due to convection, Q0rad is the

rate of heat exchanged by radiation, Q0cond is the rate of

heat exchanged by conduction, and Q0stor is the rate of heat

storage in the body. Thus, total body heat may increase or

decrease resulting in changes in body temperature [10].

Body heat exchange is very dependent on the thermal

environment. The thermal environment is characterized by

ambient temperature (C), dew point temperature (C) and

ambient vapor pressure (kgm􀀀1 s􀀀2), air or fluid velocity

(m s􀀀1), mean radiant temperature (C) and effective radiant

field (Wm􀀀2), clothing insulation (clo), barometric

Ó Baltzer Science Publishers BV

4 T. Starner, Y. Maguire / Heat dissipation in wearable computers

pressure (kgm􀀀1 s􀀀2), and exposure time. Ambient temperature

is simply the temperature of the environment outside

of the influence of the body. The dew point temperature

is the temperature at which condensation first occurs

when an air-water vapor mixture is cooled at a constant

pressure. Ambient vapor pressure is also a measure of humidity

and, for most cases, is the pressure exerted by the

water vapor in the air. Air and fluid movement are the result

of free buoyant motion caused by a warm body in cool

air, forced ventilation of the environment, or body movement.

Mean radiant temperature and the effective radiant

field describe radiant heat exchange. Mean radiant temperature

(MRT) is the temperature of an imaginary isothermal

“black” enclosure in which humans would exchange the

same amount of heat by radiation as in the actual nonuniform

environment. Effective radiant field (ERF) relates the

MRT or the surrounding surface temperatures of an enclosure

to the air temperature. The “clo” is a unit of clothing

insulation which represents the effective insulation provided

by a normal business suit when worn by a resting person

in a comfortable indoor environment. It is equivalent to a

thermal resistance of 0.1547 m2 CW􀀀1 or a conductance

of 6.46 Wm􀀀2 C􀀀1. Barometric pressure is caused by the

atmosphere and usually expressed in kPa (1000 kgm􀀀1 s􀀀2)

or torr. While the following sections will address these variables

where appropriate, the reader is encouraged to read

[20] and [10] for a more extensive treatment.

For most discussions, the outer skin is considered to be

the heat exchange boundary between the body and the thermal

environment. Heat exchange terms reflect this, having

units of Wm􀀀2. A good approximation of an individual’s

skin surface area is given by the Dubois formula

AD = 0:202m0:425H0:725, (2.2)

where AD is the surface area in square meters, mis the body

mass in kilograms, and H is the height in meters [20]. For

convenience, we assume a user with a skin surface area of

1.8 m2 and a mass of 70 kg.

2.1. Convection

In an environment where air temperature is cooler than

that of the skin or clothing surface, the air immediately next

to the body surface becomes heated by direct conduction.

As the air heats, it becomes less dense and begins to rise.

This occurs everywhere about the body and forms a microenvironment

where heat is transferred by convection. This

air flow is called the natural convection boundary layer

[10].

Due to the complexity of the problem, a mathematical

analysis of convection heat loss on the human body has not

been developed. However, experimental approximations

have been proposed. For natural convection in both seated

and standing positions, Fanger [18] presents a convection

coefficient hc of

hc = 2:68(tcl 􀀀 ta)0:25 (2.3)

in units of Wm􀀀2 C􀀀1, where tcl is the clothing surface

temperature and ta is the ambient temperature.

Convection also occurs when a breeze is present. For

uniform forced air flows under 2:6 ms􀀀1, Fanger [18] suggests

an approximation of

hc = 12:1pV , (2.4)

where V is air velocity. When a slight breeze is present

both the natural and forced air convection formulas should

be calculated and the larger value used. In his book, Clark

[10] presents a different experimental formula of

hc = 8:3pV (2.5)

without providing a constraint on air flow speed. In addition,

Clark states that hc is doubled when the air flow

is turbulent based on experimental evidence with appropriately

human-sized and instrumented heated cylinders.

2.2. Radiation

Heat can be exchanged between two bodies by electromagnetic

radiation, even through large distances. For the

purposes of heat exchange to and from the human body,

this paper is concerned with radiation from sources cooler

than 100 C. The Stefan–Boltzmann formula can be used

to determine the total emissive power of a wavelength at

absolute temperature T

Wb = T 4, (2.6)

where is the emittance of the body, and is the Stefan–

Boltzmann constant (5:7 10􀀀8Wm􀀀2 K􀀀4). The emittance

of an object is the ratio of the actual emission of heat

from a surface to that of a perfect black body, equally capable

of emitting or absorbing radiation at any wavelength.

The emittance for human skin and clothing are quite high in

the longer wavelengths mainly involved at these temperatures,

around 0:98 and 0:95, respectively. The units for Wb

are Wm􀀀2, so to calculate the heat energy emitted by the

human body, again assuming 33 C mean skin temperature

and 1:8 ms􀀀2 surface area,

􀀀T 4(AD) = 0:98 5:7 10􀀀8 W

m2 K4

(306 K)41:8

m

s2 = 880 W: (2.7)

In reality, the human body does not radiate this much

heat. Instead it absorbs a portion of its own thermal radiation

and is affected by surrounding surfaces. When calculating

radiant heat transfer from the human body (or small

object) to a surrounding room (or large container), the following

approximation is useful:

R = 1􀀀T 4

1 􀀀 T 4

2 Ar

AD

, (2.8)

where T1 is the absolute temperature of the body, T2 is the

temperature of the room, 1 is the emittance of the body

(approx. 0:98), and the ratio Ar=AD compares the area

T. Starner, Y. Maguire / Heat dissipation in wearable computers 5

exchanging radiative energy with the surroundings (Ar) to

the total body surface area (AD). This ratio is 0:65 for a

body sitting and 0:75 for a body standing. The max value

is 0:95 for a body spread eagled. Thus, for a naked man

sitting in a 25 C room,

Q0rad =1􀀀T 4

1 􀀀 T 4

2 Ar

AD

AD

=5:7 10􀀀8 W

m2 K4 0:98􀀀(33 + 273 K)4

􀀀 (25 + 273 K)40:65(1:8m2) = 58 W: (2.9)

With maximum exposure of the body to the surroundings,

the result becomes 86 W. Similarly, in a 15 C room, 122–

180 W of dissipation may be expected.

Heat may also be re-gained by the body through radiation,

in particular, solar radiation. Human skin and clothing

have variable emissivity for many of the wavelengths generated

by the sun (a 5760 K source). In addition, the angle

of the sun and orientation of the subject have significant effects

on the heat transfer. However, empirical studies have

shown that a semi-nude man walking in a desert has an

effective 233 W solar load. When light colored clothing is

worn, this can be lessened to 117 W [20].

2.3. Conduction

Conduction normally plays a small role in human heat

regulation, except as the first stage of convection. Heat can

be dissipated through contact with shoe soles, doorknobs,

or through the surface underneath a reclining subject. Heat

conduction through a plate of area A and thickness b is

given by

Q0cond =

kA(T1 􀀀 T2)

b

, (2.10)

where k is the thermal conductivity of the plate and T1 and

T2 are the temperatures on either side of the plate. The sign

of Q0cond indicates the direction of heat flow.

2.4. Evaporation

When the body is sedentary, it loses heat during evaporation

of water from the respiratory tract and from diffusion

of water vapor through the skin (insensible or latent heat

loss). When other modes of heat loss are insufficient, the

body sheds excess heat through evaporation of sweat (sensible

heat loss). The rate of heat lost through the evaporation

process can be calculated by

Q0evap = Dm, (2.11)

where Dm is the rate of mass of water lost and is the

latent heat of evaporation of sweat (2450 J g􀀀1). Thus, for

the typical water loss of 0:008 g s􀀀1 through the respiratory

tract, the heat loss is 20W. In hot environments, sweat rates

can be as high as 0:42 g s􀀀1 for unacclimatized persons and

1:11 g s􀀀1 for acclimatized persons, resulting in 1000 W to

2700 W of heat dissipation, respectively [10,39].

2.5. Heat storage

One term in equation (2.1) is still unexamined: Q0stor.

Heat storage in the body takes the form of a higher body

temperature and can be calculated with the formula

S = mCDT , (2.12)

where S is the energy stored, m is the body mass, C is the

specific heat of the body (approx. 3:5 103 J kg􀀀1 C􀀀1),

and DT is the change in body temperature. Thus, for a 1 C

increase in a 70 kg man,

S = 70 kg3:5 103 J

kgC(1 C) = 245, 000 J (2.13)

of heat energy are stored. If this increase occurs over the

course of an hour, the average power absorbed is Q0stor =

68 W. In this way the human body is its own buffer when

adequate heat dissipation is not available or, conversely,

when too much heat is being dissipated.

2.6. Skin temperature, thermal receptors, and damage

Skin temperature may vary wildly depending on the area

measured. For example, while comfortable, a subject may

have temperature readings of 25 C on the toes while the

forehead is 34 C [23]. Even temperatures within a small

region may show significant variation due to air flow [10].

How these temperatures are perceived by the body depends

on the range and the context of the temperatures. Table 1

(adapted from [20]) summarizes typical responses to skin

temperatures. The receptors in the skin are much more sensitive

to changes in temperatures. Thus, momentary contact

with a surface that is warmer than the skin will elicit a sensation

that seems much hotter than would be felt with more

constant contact. This, plus the fact that skin can be quite

cool compared to normal body temperature, corresponds to

the wide bounds on these ranges.

While contact with any surface above 43 C for an extended

period of time risks burning, temporary contact can

be made at higher temperatures. For 10 minutes, contact

with a surface at a temperature of 48 C can be maintained.

Metals and water at 50 C can be in contact with the skin

for 1 minute without a burn risk. In addition, concrete can

be tolerated for 1 minute at 55 C, and plastics and wood

at 60 C. At higher temperatures and shorter contact times,

materials show a higher differentiation of burn risk [23].

Table 1

Skin temperature sensations.

Skin temp., C State

45 tissue damage

43–41 threshold of burning pain

41–39 threshold of transient pain

39–35 hot

37–35 initial sense of warmth

34–33 neutral

33–15 increasing cold

15–5 intolerably cold

6 T. Starner, Y. Maguire / Heat dissipation in wearable computers

3. Thermal regulation in a forearm-mounted wearable

computer

While the previous section discussed rules and principles

in general, this section will concentrate on a specific

example: a forearm-mounted wearable computer (inspired

by BT’s proposed “Office on the Arm” [40]). The goal is

to model how much heat such a computer could generate

if it is thermally coupled to the user. In order to perform

this analysis, several conditions must be assumed.

First, the surface area of the forearm must be approximated.

The forearm is about 3:5% of the body’s surface

area [20] or 0:063 m2 for our assumed user. Note that

this is approximately the surface area of the bottom of a

smaller notebook computer. For convenience, it will be

assumed that the computer fits snugly around the forearm

as a sleeve for near perfect heat conduction and will have

negligible thickness so that inner and outer surface areas

will be approximately equal.

To provide an approximate bound on the amount of heat

the forearm computer can generate, the free air dissipation

of heat through convection and radiation must be calculated.

For practical considerations, the assumed environment will

be a relatively warm, humid day of 31 C (88F), relative

humidity of 80%, and a maximum allowable surface temperature

of the computer of 41:5 C. 41:5 C was chosen as

a “safe” temperature based on a summary of the medical

literature by Lele [7,24], a survey of heat shock protein

(HSP) studies which use > 43 C water baths to encourage

HSP production [16], and many reported physiological experiments

where subjects were immersed in water baths for

several hours at significantly higher temperatures [3,33,38].

Furthermore, similar temperatures can be measured from

the bottom surfaces of modern notebook computers.

Using the guidelines from above

Q0conv = hc(Afore)(Ts 􀀀 Tamb)

= 2:68(41:5 C 􀀀 31 C)0:25􀀀0:063m2 (41:5 C 􀀀 31 C) = 3:2 W: (3.1)

Assuming a surface emittance of 0:95 and 80% of the surface

of the forearm computer “seeing” the environment for

radiative exchange

Q0rad = R Afore, (3.2)

Q0rad =􀀀T 4

1 􀀀 T 4

2 Ar

AD

Afore

=5:7 10􀀀8 W

m2 K4 0:95􀀀(41:5 + 273)4

􀀀 (31 + 273)40:80(0:063m2) = 3:4 W: (3.3)

Thus, in this environment, uncoupled from the body with

no wind and no body motion, the forearm computer is limited

to 6:6 W. From these calculations, a notebook computer

could dissipate 13:2 W, having approximately twice

the surface area. Note that this is in agreement with the

10–14 W heat production characteristic of passively cooled

Table 2

Skin structure.

Depth, mm Structure

0–0.4 epidermis

0.5 superficial venous plexi

0.8 superficial arteriolar plexus

1.4 superficial venous plexi

2.2 subcutaneous fat begins

2.5 subcutaneous arteries

accompanied by venae comitantes

notebook computers common in 1994 and 1995. As an

aside, Intel guidelines increase the heat limit to 23–25 W

for notebook computers with aggressive active cooling [28].

However, once mounted on the arm, heat will be conducted

from the computer to the arm. Most thermal coupling

that must be considered is through the skin to the

surface veins and arteries. Skin has a thermal conductivity

of 0:37 Wm􀀀1 C􀀀1, and the body will maintain a temperature

of 37 C for blood coming from the body’s core.

However, the linear heat conduction equation above is inadequate

for modeling the heat transport of the blood stream.

In order to proceed in creating an appropriate model, the

first step is to determine the rate of blood flow through the

forearm.

The primary means of thermoregulation by the human

body is the rerouting of blood flow from deeper blood vessels

to more superficial skin vessels, or vice versa. Table 2

(from [8]) shows the approximate depths of skin blood vessels.

Skin blood flow is increased to an area when the local

temperature of that part is raised, when an irritant is applied,

or when the body temperature as a whole is elevated [10].

In addition, if there is a sufficient rise in return blood temperature

from a peripheral body part, the body as a whole

will begin heat dissipation measures [4,13]. However, it is

improbable that enough heat would be transfered via one

forearm to incite such a response [21].

Skin blood flow is regulated by vasodilation and vasoconstriction

nerves. Areas that act as heat sinks, like

the hands [22], have almost exclusively vasoconstriction

nerves. In these areas, the arterial flow into the area must

be warm already to cause the relaxation of vasoconstriction.

Larger areas, such as the forearm, have a mixture

of vasodilators and vasconstrictors, making the prediction

of skin blood flow difficult. However, empirical studies

by Taylor et al. [38] suggest that maximum forearm blood

flow occurs when the forearm skin is raised to 42 C for

35–55 minutes. While there can be considerable variability

among subjects depending on age, weight, blood pressure,

and other factors, Taylor et al. found in their measurements

that the average maximum skin blood flow in the forearm

is

21 ml

100 mlfore min

:

This last set of units requires some explanation. In physiology

literature, blood flow is normalized for the volume

of tissue in which it is observed. In this case, the tissue is a

T. Starner, Y. Maguire / Heat dissipation in wearable computers 7

Figure 1. Blood flow geometries in the arm.

volume of the forearm. In many experiments, total forearm

blood flow is measured, which includes blood flow through

both skeletal muscle and skin. However, muscle blood flow

does not change significantly with outside application of

heat to the forearm [12,17,35]. Thus, as above, results are

sometimes given in skin blood flow instead of total blood

flow per volume of forearm [34]. Johnson and Proppe [22]

provide a conversion factor: 100 ml of forearm roughly

corresponds to 0:0050 m2 of skin. Combining this figure

with the specific heat of blood 0:064 W min g􀀀1 C􀀀1 and

its density 1:057 gml􀀀1 [6] yields a striking maximum heat

dissipation capability of the blood in the forearm of

22 ml

100 ml min

100 ml

0:0050m2

1:057 g

ml

0:064

W min

g C

0:063m2 = 18

W

C

: (3.4)

Equally amazing, estimates place total possible body transfer

of heat through skin blood flow at a 1745 W [22]!

Armed with these constants and empirical results, we can

create a model for heat conduction in the forearm.

3.1. Derivation of heat flow in the forearm

We model the arm as a set of four concentric cylinders

of increasing radius, based on the information in table

2 (see [9,31,32] for related bioheat models). Figure 1

demonstrates the variables used in this derivation. Blood

originates from the body (at 37 C), flows through the arterial

layer and returns through the two venous layers. This

model is similar to the double-pipe bayonet heat exchanger

developed by Martin [26].

To begin, we define the fundamental heat flow rates in

the arm.

􀀀M01

cp dT1 = dQ012 􀀀 dQ0in, (3.5)

􀀀M02cp dT2 =􀀀dQ012 + dQ023, (3.6)

􀀀M03

cp dT3 =􀀀dQ023 + dQ0out, (3.7)

where cp is the heat capacity of the blood. We define the

heat flow rates as

dQ012 =k(T1 􀀀 T2) dA2, (3.8)

dQ023 =k(T2 􀀀 T3) dA3, (3.9)

dQ0in =k(TB 􀀀 T1) dA1, (3.10)

dQ0out =k(T3 􀀀 Tarm) dA4 = 0, (3.11)

where TB is the temperature of the external heat bath, Tarm

is the temperature of the inner arm, and T1, T2, and T3

are the blood temperatures between the cylinders. A1, A2,

A3, and A4 are the areas of the outer to inner cylinders,

respectively. dAi is a cylindrical shell of blood layer i of

length z=L over which one considers the differential heat

flow rates across that surface.

Equation (3.11) was set to zero to simplify the calculation.

Since blood mass is conserved, arterial blood flow

must return along the two venous layers. We can thus define

the blood flow rates as

M01

=􀀀M02

=p, (3.12)

M03

=􀀀M02

=q, (3.13)

where 1=p + 1=q = 1.

To ease the computation, the above equations can be

reformulated in terms of dimensionless parameters. Define

N =

kA2

M02

cp

, dAi = Ai

dz

L

, = N

z

L

,

=

A1

A2

, =

A3

A2

,

where L is the total length of the arm. Combining this with

equations (3.5) through (3.13) yields

􀀀

dT1

d

= 􀀀p(T1 􀀀 T2) + p(TB 􀀀 T1), (3.14)

􀀀

dT2

d

= 􀀀(T1 􀀀 T2) + (T2 􀀀 T3), (3.15)

􀀀

dT3

d

= q(T2 􀀀 T3): (3.16)

Let i = (Ti􀀀TB)=(Tin􀀀TB). Tin is a constant to denote

the temperature of the blood in the rest of the body as it

flows into the artery of the arm. The derivative is di =

8 T. Starner, Y. Maguire / Heat dissipation in wearable computers

dTi=(Tin 􀀀 TB). Finally this yields three dimensionless,

coupled differential equations

d1

d

=p1(1 + ) 􀀀 p2, (3.17)

d2

d

=1 􀀀 2(1 + ) + 3, (3.18)

d3

d

=􀀀q(2 􀀀 3): (3.19)

The general solution is of the form

i =

3X

j=1

Ci,jej (3.20)

so

di

d

=

3X

j=1

Ci,jjej: (3.21)

Equations (3.17)–(3.19) can easily be decoupled in a

matrix formalism. Rewriting the right side of equations

(3.17) through (3.19) as a matrix, M, the eigenvalues of

M are the j ’s. Thus, solving the cubic equation



p(1 + ) 􀀀 􀀀p 0

1 􀀀(1 + ) 􀀀

0 􀀀q q 􀀀

(3.22)

will yield each j .

The remaining part of the solution entails applying the

boundary conditions. The boundary conditions are:

The blood entering the artery at the elbow is in contact

with a large heat bath (the body) that maintains the blood

temperature entering down the arm at 37 C.

The blood mixes in the hand such that the blood temperature

at the arm-hand junction is equal in the artery

and two venous layers. In actuality, due to the hand,

the exit temperature of the arterial flow will be slightly

different (warmer) than the return venous flow. This

boundary condition was imposed for simplicity and because

it gives a lower bound on the heat exchange rate

in the arm. (Most literature considers the hand to be a

heat sink, which could significantly increase heat dissipation.

However, Nagasaka et al. [29] provide evidence

that vasoconstriction may occur in the fingers when exposed

to local temperatures greater than body temperature,

limiting the additional heat transfer.)

Mathematically, the first boundary condition can be written

as

2(0) = C2,1 + C2,2 + C2,3 = 1: (3.23)

Including this in equations (3.17) through (3.19) yields

d1

d

(0)= p1(0)(1 + ) 􀀀 p, (3.24)

d2

d

(0)= 1(0) 􀀀 (1 + ) + 3(0), (3.25)

d3

d

(0) =􀀀q(1 􀀀 3(0)): (3.26)

Since, at = 0,

1(0) =

3X

j=1

C1,j , (3.27)

3(0) =

3X

j=1

C3,j (3.28)

and equations (3.24)–(3.26) further simplify to

3X

j=1

C1,j (p(1 + ) 􀀀 j ) = p, (3.29)

3X

j=1

C1,j 􀀀

3X

j=1

C2,jj +

3X

j=1

C3,j = 1 + , (3.30)

3X

j=1

C3,j (q 􀀀 j ) = q: (3.31)

The same can be done with the second boundary condition,

occurring at z = L (and = N),

1(N) = 2(N) = 3(N), (3.32)

which yields

3X

j=1

C1,jejN 􀀀

3X

j=1

C2,jejN =0, (3.33)

3X

j=1

C1,jejN 􀀀

3X

j=1

C3,jejN =0: (3.34)

Combining these results with equations (3.17) through

(3.19) yields

3X

j=1

C1,jejN(j 􀀀 p) =0, (3.35)

3X

j=1

C2,jejN(j ) =0, (3.36)

3X

j=1

C3,jejN(j ) =0: (3.37)

Equations (3.23), (3.29)–(3.31), and (3.33)–(3.37) can be

combined into a matrix to evaluate the constants

M C = B, (3.38)

M =

2666664

0 0 0 1 1 1 0 0 0



1

2

3 0 0 0 0 0 0

1 1 1 􀀀1 􀀀2 􀀀3

0 0 0 0 0 0 1 2 3

1 2 3 􀀀1 􀀀2 􀀀3 0 0 0

1 2 3 0 0 0 􀀀1 􀀀2 􀀀3

11 22 33 0 0 0 0 0 0

0 0 0 11 22 33 0 0 0

0 0 0 0 0 011 22 33

3777775

,

(3.39)

T. Starner, Y. Maguire / Heat dissipation in wearable computers 9

C =

2666666666664

C1,1

C1,2

C1,3

C2,1

C2,2

C2,3

C3,1

C3,2

C3,3

3777777777775

, B =

2666666666664

1

p

1 +

q

0

0

0

0

0

3777777777775

, (3.40)

where j = ejN,

j = p(1 + ) 􀀀 j , j = q 􀀀 j, and

j = j 􀀀 p. The constants become C = M􀀀1 B and a

final solution is obtained.

The actual physical data used to solve this problem are

listed below:

Tin = 37 C, TB = 39 C.

p = q = 2.

k = 0:37 Wm􀀀1 C􀀀1 [1].

d1 = 0:0005 m, d2 = 0:0008 m, and d3 = 0:0014 m.

Average forearm skin surface area is 0.063 m2, and the

average radius of the forearm is 0.035 m [10].

Blood flow was calculated for a few values from the

range of possible blood flows in the arm (5, 10, 15, and

22 ml=(100 mlfore min) [10].

The average power transfer into the arm can be calculated

by taking the mean integral of the temperature distribution

in the outer vein and modifying equation (3.10):

Q0in = k􀀀TB 􀀀 hT1iA1, (3.41)

where

hT1i =

Tin 􀀀 TB

N Z N

0

1 d + TB:

The power results for the different blood flows are shown

in table 3.

While this derivation was performed for an applied temperature

TB = 39 C, the power rating increases linearly

with the difference between the applied temperature and

body temperature. Thus, at the hypothetical 41:5 C, which

should develop very close to maximum skin blood flow, we

expect around 28 W of heat conduction through the forearm.

Table 3

Heat dissipation for various blood flow rates

given a 39 C external heat bath.

Blood flow rate, Power, W

ml=(100mlfore min)

5 2.96

10 5.92

15 8.87

21 12.43

3.2. Verification of the model

To verify the model in the last section, an experiment

was devised to examine the conduction of heat away from

the forearm’s surface. Two open-topped 10 liter styrofoam

containers were filled with water at 48:8 C and placed side

by side in a 25 C temperature-controlled room. Magnetic

stirrers were used to keep the water agitated. Two calibrated

digital thermometers were placed diagonally across

from each other in each bath. When the baths cooled to

43 C, a subject immersed his forearm into the “forearm

bath,” leaving his upper arm and hand out of the bath.

The temperatures of both the forearm and control baths

were recorded every 200 seconds until the baths cooled below

body temperature. The subject was dressed in T-shirt,

jeans, and boots. Before the experiment, the subject indicated

he was overly warm even after remaining seated for

an hour. Before and during the experiment, his body temperature

remained constant and no visible perspiration was

evident, though he claimed his forehead felt moist before

immersion and during the early part of the experiment. This

would seem to indicate the subject was near his physiological

tolerance to heat before resorting to open sweating.

For each 200 second time period, the heat loss of each

bath was calculated using the temperature corrected thermal

capacity of water (approx. 4:179 J g􀀀1 C􀀀1) [41]. The

result can be seen in figure 2. By interpolating the corresponding

heat loss at a given temperature for the control

water bath, the difference in heat loss between the two

baths can be calculated. Figure 3 shows the increase in

heat dissipation caused by conduction through the forearm.

Note that there is a “knee” in the graph at approximately

40:5 C. Above this temperature, the forearm bath seems to

dissipate, on average, 12:8 W more than the control bath.

Under 40 C the forearm bath is actually dissipating less

than the control path. Such a drastic change would be

expected around 37 C, when the body would be heating

the water, but why would such a sudden change happen

around 40 C? First, the amount of blood that is pumped to

the surface veins and arteries of the forearm decreases as

temperature decreases. A similar breakpoint is observed in

the literature [3] for blood flow at this temperature. However,

even given that the blood flow may be significantly

reduced at these temperatures, why should the presence of

the forearm inhibit heat dissipation before the water bath

reaches body temperature? Obviously, since the subject’s

body temperature did not exceed 37 C, the forearm could

not be adding heat to the bath. Instead, the forearm likely

blocked the natural radiative, convective, and evaporative

heat dissipation of the bath. In future experiments, a thermally

neutral dummy arm of the same volume should be

inserted into the control bath, and both baths should be

agitated more aggressively. To compensate for this effect,

the results must be offset by at least the 12 W difference

between the baths at body temperature. Thus, the total heat

conducted away by the forearm is approximately 23 W at

41:5 C. This experimental result is significantly smaller

10 T. Starner, Y. Maguire / Heat dissipation in wearable computers

Figure 2. Heat dissipation from forearm () and control (+) water baths.

Figure 3. Heat conduction through forearm versus water bath temperature.

than the predicted 28 W of the model. However, in the

model we assumed that the interior of the arm would be

held constant at 37 C. In actuality, the interior muscle mass

of the arm will reach 38 C when the forearm is submerged

in water at temperatures above 40 C [3,12]. With this

change, the model predicts approximately 22 W of heat

conduction, which closely matches the experimental data.

Other human limb heat transfer models that include muscle

heating have been published since this paper was in review

[32], but the above model provides a simple predictive tool

and is specifically tailored for this task.

While this experiment involved one subject, the results

coincide with temperature vs. blood flow experiments from

the literature and also correlate nicely with the model proposed

above. Note that since the body is very active in

maintaining its core temperature, similar amounts of heat

dissipation from the forearm may be available in all but

the most adverse conditions. Even at a more conservative

forearm temperature of 39 C, a substantial amount of heat

will be conducted away by the forearm as shown in the

model above.

3.3. Discussion and practical issues

Given the above models and calculations, a forearm

computer may generate up to

Q0tot = Q0conv + Q0rad + Q0cond = 30 W (3.42)

in warm, still air and without body motion. This is summarized

in figure 4 and is significantly higher heat dissipation

per surface area than that of a normal passively

T. Starner, Y. Maguire / Heat dissipation in wearable computers 11

Figure 4. Forearm computer heat dissipation.

cooled notebook computer (approximately 450 Wm􀀀2 versus

100 Wm􀀀2). Unfortunately, this calculation ignores

several practical factors. The wearable would need to monitor

its surface temperature to avoid exceeding the 41:5 C

limit, but would the user feel that 41:5 C is too high a

temperature for a sheath on the forearm? A simple way to

address this problem is to provide the user with a physical

knob to adjust the maximum operating temperature of

the computer (up to safe limits) and a meter showing the

fraction of full functionality available in current conditions.

This interface makes the trade-off between heat generation

and functionality explicit and accessible to the user.

Another concern is sweating under the sleeve due to exertion.

Without a way for sweat to be released, the user may

experience discomfort, similar to the sensation of sweating

in rubber gloves. To alleviate this problem, a thin layer

of heat conducting fabric can be used to “wick” the water

trapped under the computer sleeve. Slits should be designed

into the computer to allow evaporation of the water. The resulting

evaporation will increase user comfort and increase

cooling. The slits also provide the benefit of adding more

surface area to the forearm computer, increasing cooling.

The above analysis assumed good thermal contact between

the electronics and the forearm. In reality this may

prove difficult given the obvious constraint of the user’s

comfort. A carefully chosen material for the wicking layer

and a custom-fitted forearm sleeve may be sufficient for

the needed heat conduction. In more exotic applications,

phase-change materials might be used in the sleeve. However,

the wearable computer will have “hot spots” which

could cause discomfort [2,25]. A variant of a self-contained

fluid heat-pipe may be needed to even out the temperature

gradient. Forced air could also be used to transfer heat to

the forearm. In practice, the actual computer in the forearm

sheath may be the size of a credit card with the rest of

the casing dedicated to the distribution of heat. By making

these sections modular, upgrades are trivial, and the user

could have fashionable casings designed to complement his

or her wardrobe.

A side benefit to thermally coupling the computer to the

user’s forearm is that intermittent contacts of the surface

with other body parts may be better tolerated. The user

would have an innate sense that the computer cannot be

burning him or else his forearm would be uncomfortable.

This helps offset the effects of different relative temperatures

of the skin surface. Careful selection of the computer

casing material will also help this problem [23].

Previous sections assumed a static, reasonably constrained

environment. In actuality, the user’s thermal environment

will change, often to the benefit of the computer.

Small amounts of air flow can significantly increase heat

dissipation. While walking, the air flow about the arm is

significantly enhanced by the pendulum-like movement of

the arm. In fact, the air flow along the forearm is turbulent

for many situations, effectively doubling the heat dissipation

of calmer air movement [10]. In addition, changes

in ambient and skin temperature and the cooling effects of

the user’s sweating may be exploited in many cases (for

example, when a sweating user enters an air conditioned

building). With sensing of skin temperature and sweating,

the forearm computer can regulate its own heat production

according to the thermal environment. The temperature

feedback mechanisms already common in microprocessor

design suggest such a trend.

Mounting the computer on the forearm has many advantages

including convenient access, higher availability

of turbulent air flow due to the pendulum effect, and heat

exchange through the hand. However, there are many potential

mounting locations. The legs have a similar set of

advantages as the arms with an even larger surface area but

12 T. Starner, Y. Maguire / Heat dissipation in wearable computers

with less ease of access. Mounting on the head has the

advantage of faster natural convective air flow while the

user is sedentary and a constant flow of forced air while

walking. Unfortunately, hair impedes heat conduction to

the skin. Mounting the computer on “core” body areas is

also a possibility, but it would result in lesser heat gradients

in many instances. While the system analyzed above

operates with skin regions at body temperature, the limbs

are often colder due to lower ambient conditions, which

increases their temporary heat storage capacity.

More aggressive systems might employ thermal regulation

via active thermal reservoirs. For example, the heat

capacity of the computer’s batteries might be exploited.

While charging, batteries could be chilled so that heat can

be transferred into them during use [19]. The computer’s

heating of the batteries while running may also provide the

benefit of increased battery life. In addition, by employing

active cooling elements such as Peltier junctions, the

computer might cool the batteries or components during

times of low ambient temperature. Thus, the computer has

access to a thermal reservoir during times of heat stress.

Similarly, a water reservoir, perhaps stored in a sponge,

could be used for evaporative cooling. Finally, software

applications can be written with heat dissipation in mind.

Disk maintenance, downloads, and batch jobs can be delayed

until the computer senses a cooler environment. In

this manner, performance is reserved for user interactions,

and the effective average heat dissipation can be higher.

4. Conclusion

This paper provides first-order heat dissipation guidelines

for developing wearable computer prototypes and introduces

an unconventional way of thinking about cooling.

By thermally coupling a forearm wearable computer with

the user, heat dissipation can be significantly increased from

today’s industry limits, even in warm environments. The

effective heat generation limit may be further increased by

aggressive active management of thermal reservoirs such

as the computer casing and batteries, monitoring of user

and environmental conditions, software scheduling of background

processes, and making the trade-off between heat

generation and functionality explicit to the user.

Acknowledgements

We would like to thank the reviewers for their extremely

helpful suggestions; Tavenner Hall for initial help in editing

this paper and producing figures; Dr. Shuguang Zhang for

his help in procuring the temperature controlled room and

laboratory equipment; Keith Starner, Dr. H.F. Bowman, Dr.

A. Pentland, Dr. R. Gonzalez, Dr. M. Kolka, and the members

of the Natick Army Research Labs for help in finding

background resources in these fields; BT for inspiring novel

ways of approaching wearables; the wearables mailing list

for commentary and encouragement; and Walter Bender for

the prodding to substantiate an off-hand comment with research.

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Thad Starner is a final-term doctoral student at

the MIT Media Laboratory where he co-founded

the Wearable Computing Project. A USAF Laboratory

Graduate Fellow, Thad has received MIT

degrees in computer science, brain and cognitive

science, and media arts and sciences and is an Associate

Scientist in the Speech Systems Group at

Bolt, Beranek, and Newman (BBN). Mr. Starner

is in his sixth year of incorporating wearable computing

with his everyday life. His research interests

include user modeling, augmented memory, augmented reality,

human-powered wearable computers, sign language recognition, handwriting

recognition, and face recognition.

E-mail: [e-mail]

http://wearables.www.media.mit.edu/projects/wearables/

Yael Maguire is an M.S. degree candidate and research

assistant in the Physics and Media Group at

the MIT Media Laboratory. He received a B.Sc.

in engineering physics from Queen’s University,

Canada, in 1997. Mr. Maguire’s current research

is on experimental methods of quantum computation

using Nuclear Magnetic Resonance (NMR).

E-mail: [e-mail]