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721-283 Transport Phenomena (Part 2 Heat Transfer) Dr.Jutarut Tasara

1

1 (Principle of steady state heat )

1.1. (Introduction)

(Temperature gradient) (Temperature different) (Driving force) (Temperature gradient)

(1.1)

1.1 (Temperature

Gradient) (Conduction) (Convection) (Radiation)

1.1


2

(Steady state and Unsteady state) (Steady state)

T/t = 0

X X (Control volume) X X (Unsteady state Transient state)

T/t 0 1.2. (Conduction heat transfer)

(Temperature gradient ) A

(1.2)

(1.3)

qcond = (Wall or J/s) A = (m2) T = (K) X =


3

(Thermal Conductivity) k W/m K

(1.4)

(1.4) (Fouriers law of conduction)

X (1.4) (k) k k k k k k (conductor) k (insulator) k 1-1 1-1

(k), W/mK 35-430 20-200 9-90 () 0.2-2.0 () 0.02-20 0.02-0.40 0.002-0.2


4

a) (Conduction in plane walls)

+

(1.5)

1) Steady-state:

0 2) Transient, no heat generation: 0 3) Steady-state, no heat generation:

Steady state Fouriers law (1.6)

1.2 k A (boundary condition) T = T1 X = 0 T = T2 X = L

(1.7)

(1.7)

(1.8)

R= x/kA K/W h F/btu

Rate of heat conduction in the wall -

Rate of heat conduction out the wall

+ Rate of heat

generation inside the wall =

Rate of change of the energy content of the

wall

(1.6)


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b) (plane walls in series)

1.3 (1.9)

(1.9)

T2 T3 (1.105)

(1.10)

c) (Conduction in hollow cylinder) (r) 1.4

Rate of heat conduction in the wall -

Rate of heat conduction out the wall

+ Rate of heat

generation inside the wall =

Rate of change of the energy content of the

wall

1.3


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1.4

Steady state k Ar Fouriers law 1.11

(1.11)

Ar = 2rL

(1.12)

Boundary condition; Ti T0

(1.13)

d) (Multilayer cylinder) 1.5 Resistance 1.14

(1.14)


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(1.15)

(1.16)

(1.17)

1.5

e) (Conduction in hollow spheres) A =4r2

(1.18)

Boundary condition;

(1.19)

(1.20)


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f) Combined convection and conduction and overall coefficients

A Tw Tf 1.9

(1.21)

(1.22)

(1.23)

(

) (1.24)

(1.25)

Ai = 2Lri () , AA lm=log mean area of the tube A0 overall heat transfer coefficient (U) Ai Ao

(1.26)


9

(1.27)

(1.28)

1.6 (a) (b)

g) (Critical Thickness of Insulation)

() r1 T1 thermal conductivity (k) r2 T2 1.7 (1.29) T0

(1.29)

Thermal resistance Thermal resistance


10

Critical radius

1.7

1.3. Steady state conduction and shape factor

1.3.1. Introduction and graphical method for Two-dimensional conduction

Graphical method ( isotherm) 2 2 (steady-state)

maintained T1 maintained T2 (isotherm) heat flow line sketches Heat flow curvilinear-square (b) Fourier 1

(1.31)

This heat flow heat flow section heat flow lane Total heat flow

lane x y, heat flow T element T element heat flow lane T element

(1.33)

Critical radius

(1.30)

Critical radius

(1.31)


11

N is the number of temperature increments between the inner and outer surfaces Heat flow lane x y lane x y total heat transfer

(1.34)

M heat flow lane l

heat transfer curvilinear-square plots x y temperature increments (N) heat flow lanes (M)

1.8 Graphical curvilinear square method for two-dimensional heat conduction in a

rectangular flue

1.3.2. (shape factor in conduction)

(1.34) S=M/N

(1.35)

S


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S S 1-2

1-2 Conduction shape factor for

Cylinder of length L in a square

0

Horizontal buried cylinder of length L

Two parallel cylinders of length L

[

]

Sphere buried

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