Experiment #1:Experiment #1:

Measurements of Thermal ConductivityMeasurements of Thermal Conductivity

• OBJECTIVE

To measure the thermal conductivity of two materials (steel and brass).

• What is heat transfer?

Heat transfer is thermal energy in transit due to a temperaturedifference.

• What is thermal energy?Thermal energy is associated with the translation, rotation,vibration and electronic states of the atoms and moleculesthat comprise matter. It represents the cumulative effect ofmicroscopic activities and is directly linked to the temperatureof matter.

• THEORETICAL CONSIDERATIONS

Heat Transfer and Thermal Energy

• What is heat transfer?

Heat transfer is thermal energy in transit due to a temperaturedifference.

• What is thermal energy?Thermal energy is associated with the translation, rotation,vibration and electronic states of the atoms and moleculesthat comprise matter. It represents the cumulative effect ofmicroscopic activities and is directly linked to the temperatureof matter.

Heat Transfer and Thermal Energy (cont.)

Quantity Meaning Symbol Units

Thermal Energy+ Energy associated with microscopic behavior of matter

Temperature A means of indirectly assessing the amount of thermal energy stored in matter

Heat Transfer Thermal energy transport due to temperature gradients

Heat Amount of thermal energy transferred over a time interval t 0

Heat Rate Thermal energy transfer per unit time

Heat Flux Thermal energy transfer per unit time and surface area

or U u J or J/kg

T

Q J

q W

q 2W/m

+ Thermal energy of system

Thermal energy per unit mass of systemUu

DO NOT confuse or interchange the meanings of Thermal Energy, Temperature and Heat Transfer

K or ℃

Modes of Heat Transfer

Conduction: Heat transfer in a solid or a stationary fluid (gas or liquid) due to the random motion of its constituent atoms, molecules and /or electrons.

Convection: Heat transfer due to the combined influence of bulk and random motion for fluid flow over a surface.

Radiation: Energy that is emitted by matter due to changes in the electron configurations of its atoms or molecules and is transported as

electromagnetic waves (or photons).

• Conduction and convection require the presence of temperature variations in a material medium.

• Although radiation originates from matter, its transport does not require a material medium and occurs most efficiently in a vacuum.

Modes of Heat Transfer

Heat Transfer Rates: Conduction

2 1x

T TdTq k kdx L

1 2x

T Tq k

L (1.2)

Heat rate (W): x xq q A

Application to one-dimensional, steady conduction across aplane wall of constant thermal conductivity:

Conduction:

General (vector) form of Fourier’s Law:

Heat flux

q k T

Thermal conductivity Temperature gradient2W/m W/m K °C/m or K/m

Heat Transfer Rates

℃/

Heat Transfer Rates: Convection

Convection

Relation of convection to flow over a surface and developmentof velocity and thermal boundary layers:

Newton’s law of cooling:

h sq T T (1.3a)

2Convection heat transfer coefficih : (W/ment K)

Heat Transfer Rates

Heat Transfer Rates: Radiation

Radiation Heat transfer at a gas/surface interface involves radiation emission from the surface and may also involve theabsorption of radiation incident from the surroundings(irradiation, ), as well as convection if .sT T

Energy outflow due to emission:4

b sE E T (1.5)

emissiv: Surface 0ity 1 blackbody: Emissive power of a (the perfect emit r ) tebE

2Emissive powe: r W/mE

-8 2 4: Stefan-Boltzmann constant 5.67×10 W/m K

Energy absorption due to irradiation:absG G

2: incident Absorbed radiatio (W )n /mabsG

absorpti: Surfa vityce 0 1 2Irradiation: W/mG

G

Heat Transfer Rates

Heat Transfer Rates Radiation (Cont.)

Irradiation: Special case of surface exposed to large surroundings of uniform temperature, surT

4sur surG G T

4 4

If , the from the surface due to exchange with the surroundings is

net radiation heat flux:

rad b s s surq E T G T T

(1.7)

Heat Transfer Rates

Heat Transfer Rates: Radiation (Cont.)

Alternatively,

2

2 2

Radiation heat transfer coefficient

h

h : W/m K

h

rad r s sur

r

r s sur s sur

q T T

T T T T

(1.8)

(1.9)

For combined convection and radiation,

conv rad s r s surq q q h T T h T T

(1.10)

Heat Transfer Rates

Schematic:

Problem 1.73(a): Process identification for single-and double-pane windowsProcess Identification

Convection from room air to inner surface of first pane,1convqNet radiation exchange between room walls and inner surface of first pane ,1radqConduction through first pane,1condqConvection across airspace between panes,conv sqNet radiation exchange between outer surface of first pane and inner surface of second pane (across airspace),rad sq

Conduction through a second pane,2condqConvection from outer surface of single (or second) pane to ambient air,2convq

Net radiation exchange between outer surface of single (or second) pane and surroundings such as the ground,2radqIncident solar radiation during day; fraction transmitted to room is smaller for double panesq

Problem 1.31: Power dissipation from chips operating at a surface temperature of 85C and in an enclosure whose walls and air are at 25C for (a) free convection and (b) forced convection.

q rad

q conv

Air

= 25oC

orh = 4 .2(T - )s

1/4

W /m -K2 L = 15 m m

T = 85 C, = 0 .60s o

C hip, P elec

SubstrateT = 25 C sur

oSchematic:

Assumptions: (1) Steady-state conditions, (2) Radiation exchange between a small surface and a large enclosure, (3) Negligible heat transfer from sides of chip or from back of chip by conduction through the substrate.Analysis:

elec conv radP q q

(a) If heat transfer is by natural convection,

5 / 4 5/42 5/4 -4 2

-4 2 -8 2 4 4 4 4

=4.2W/m K 2.25×10 m 60K =0.158W

0.60 2.25×10 m 5.67×10 W/m K 358 -298 K =0.065W

0.158W+0.065W=0.223W

conv s

rad

elec

q CA T T

q

P

(b) If heat transfer is by forced convection,

2 -4 2h =250W/m K 2.25×10 m 60K =3.375W

3.375W+0.065W=3.44Wconv s

elec

q A T T

P

4 4h s s surA T T A T T

22 -4 2= 0.015m =2.25×10 mA L

Problem: Electronic Cooling

We know from Heat Transfer, that if a plane wall of thickness (Δx) and a We know from Heat Transfer, that if a plane wall of thickness (Δx) and a cross sectional area (A) is maintained at two different temperatures at both cross sectional area (A) is maintained at two different temperatures at both ends of (Δx) with a temperature difference of (ΔT), then the heat transfer ends of (Δx) with a temperature difference of (ΔT), then the heat transfer per unit time (q) will be proportional to the cross-sectional area (A) and the per unit time (q) will be proportional to the cross-sectional area (A) and the

corresponding negative corresponding negative temperature gradienttemperature gradient (-dT/dx= ΔT/Δx), i.e.: (-dT/dx= ΔT/Δx), i.e.:

qq

Δx

T2

T1 ΔT=T1-T2dT/dxdT/dx

dT/dx= ΔT/ΔxdT/dx= ΔT/Δxq

AA

Heat flow can be modelled by analogy to an electrical circuit where heat Heat flow can be modelled by analogy to an electrical circuit where heat flow is represented by current, temperatures are represented by voltages, flow is represented by current, temperatures are represented by voltages, heat sources are represented by constant current sources, thermal heat sources are represented by constant current sources, thermal resistances are represented by resistors and thermal capacitances by resistances are represented by resistors and thermal capacitances by capacitors. capacitors.

Ohm’s Law:

V1 V2

I

R

VIR

Thermal resistanceThermal resistance Fourier’s law: Fourier’s law:

From the above equation, we have,From the above equation, we have,

where is called thermal resistance.where is called thermal resistance.

dT Tq kA kAdx x

T Tq x RkA

xRkA

Equivalent Thermal Circuits

Δx

T2

T1 ΔT=T1-T2dT/dxdT/dx

-dT/dx= ΔT/Δx-dT/dx= ΔT/Δxq

T1 T2

xRkA

q

A

The heat flow will be in the perpendicular-to-the-cross-section direction, The heat flow will be in the perpendicular-to-the-cross-section direction, i.e. one-dimensional. The coefficient of proportionality is (k) and is called i.e. one-dimensional. The coefficient of proportionality is (k) and is called

the the ""coefficient of thermal conductivitycoefficient of thermal conductivity" " or simply or simply ""thermal conductivitythermal conductivity."." Thermal conductivityThermal conductivity, k, is the , k, is the property of a material that indicates its abil of a material that indicates its ability to conduct ity to conduct heat. .

It may be easily determined if all the above quantities are known (measured),

i.e.:

k =(q / A)/(ΔT/Δx)

All quantities in the above equation have coherent units (SI units in this experiment): k [W/m/ K]; Q [W]; A [m2]; ΔT [K or °C], because this is temperatures difference, so [K] or [°C] will give the same result; and Δx [m].

• APPARATUS

Heater

Thermocouples

Test Section

Cooling Water Intlet

Heater Control Knob

Power (On/Off)

Record the readings of temperatures

Knob (adjust to show the temperaturesat various locations)

(PID Function Controller)

(Rct is the thermal contact resistance)

''q

10.

10.