[PDF] Heat Transfer conduction and convection



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Steady Heat Transfer February 14, 2007

ME 375 - Heat Transfer1

Steady Heat Transfer with Steady Heat Transfer with

Conduction and Convection

Conduction and Convection

Larry Caretto

Mechanical Engineering 375

Heat TransferHeat Transfer

February 14, 2007

2

Outline

• Review last lecture • Equivalent circuit analyses - Review basic concept - Application to series circuits with conduction and convection - Application to composite materials - Application to other geometries • Two-dimensional shape factors 3

Review Steady, 1-D,

• Rectangular• Cylindrical shell 1212
ln2 r rTTk

LQ• Spherical shell

2112
/1/14 rrTTkQ L TTk A Qq L0 is an average thermal conductivity (or a constant value) if k is constantk T 0 , T L = temperatures at x = 0,L; T 1 , T 2 temperatures at inner (r 1 ) and outer(r 2 ) radii 0e gen

4Review Heat Generation

• Various phenomena in solids can generate heat • Define as the heat generated per unit volume per unit time gen e

Figure 2-21 from Çengel,

Heat and Mass Transfer

222
2 A I LAALI V RIe gen 5

Review Heat Generation II

• Temperature and heat flux equations L

TTkLxeq

Lgen 0 22
L xTT k xLe k xeTT

Lgengen

02 0 22

Lxgenx

QEQ 0

6Plot of (T - T0)/(TL - T0) for Heat Generation in a Slab

00.20.40.60.811.21.41.61.82

0 0.10.20.30.40.50.60.70.80.9 1

x/L

TemperatureDifference Ratio

H = 0

H = .01

H = .1

H = 1 H = 2 H = 5

H = 10

02

TTkeLH

Lgen

Steady Heat Transfer February 14, 2007

ME 375 - Heat Transfer2

7

Steady Heat Transfer Definition

• In steady heat transfer the temperature and heat flux at any coordinate point do not change with time • Both temperature and heat transfer can change with spatial locations, but not with time • Steady energy balance (first law of thermodynamics) means that heat in plus heat generated equals heat out 8

Rectangular Steady Conduction

Figure 2-63 from Çengel,

Heat and Mass TransferFigure 3-2 from

Çengel, Heat

and Mass

Transfer

The heat

transfer is constant in this 1D rectangle for both constant & variable k dxdTkqA Q 9

Thermal Resistance

• Heat flow analogous to current • Temperature difference analogous to potential difference • Both follow Ohm's law with appropriate resistance term 10

Thermal Resistance II

• Conduction kALRRTTQLTTAkQ cond cond 2121
• Convection hARRTTQTThAQ conv convfs fs 1 • Radiation radrad hATTTTTTAR

12211223231121

11 F 11

Where Does the Heat Go?

Energy conservation

requires that conduction heat through wall equals the heat leaving the wall by convection and radiation 321
QQQ

Figure 1-18 from

Çengel, Heat and

Mass Transfer

12

Where Does the Heat Go? II

Figure 1-18

from Çengel,

Heat and

Mass

Transfer

Figure 3-5 from Çengel,

Heat and Mass Transfer

Steady Heat Transfer February 14, 2007

ME 375 - Heat Transfer3

13

Parallel Resistances (T

= T surr radconvtotal

RRR111

radsconvs total hAhAR1 surr TT

Define total heat transfer

coefficient, h total radconv totalstotal hhRAh1

Figure 3-5

from Çengel,

Heat and

Mass Transfer

14

Combined Modes

Convection or

convection plus radiationConvection or convection plus radiation

Conduction

11 TThq L TTkq 21
L

All values are the same

q 22
TThq

Figure 3-6 from

Çengel, Heat and

Mass Transfer

15

Combined Modes II

1,1,2121

convwallconvtotal RRRTT RTTQ 2121
2121
1111
hkL hTT AQq AhkAL AhTTQ L

A is area normal

to heat flow

Series

Resistance

Formula

Figure 3-6 from

Çengel, Heat and

Mass Transfer

16

Combined Modes III

2121
11 hkL hTT AQq L

A is area normal

to heat flow

If you know h

1 , h 2 , L, k, T 1 and T 2 , but you do not know T 1 and T 2 , can you find the heat flux?

Once you found the heat flux from the

information give, can you find T 1 and T 2 222
111
hqTThqTT

Figure 3-6 from

Çengel, Heat and

Mass Transfer

17

Problem

A house has a 4 in thick brick wall with k = 0.6

Btu/hr·ft·

o

F. The interior temperature is 70

o F and the exterior temperature is 0 o

F. The inside and

outside convection plus radiation coefficients are

3 Btu/hr·ft

2 o

F and 4 Btu/hr·ft

2 o

F, respectively.

Find the heat flux through the wall.

Given:Wall with L = 4 in = 4/12 ft and k =0.6

Btu/hr·ft·

o

F has convection on two sides. T

1 70
o F, T 2 = 0 o F, h 1 = 3 Btu/hr·ft 2 o

F and h

2 = 4

Btu/hr·ft

2 o F. Find: AQq 18

Solution

L

A is area normal

to heat flow

BtuFfthr

BtuFfthrftBtuFfthrFF

hkL hTT AQq ooooo

46.0124

3070
11 22
2121

Figure 3-6 from

Çengel, Heat and

Mass Transfer

2 5.61 fthrBtu AQq

Find values of T

1 and T 2 . Can you check these values?

Steady Heat Transfer February 14, 2007

ME 375 - Heat Transfer4

19

Solution II

L

A is area normal

to heat flow F

FfthrBtufthrBtu

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