CHEMICAL ENGINEERING

SECTION 9

Heat Transfer

PROBLEM 9.1

Calculate the time taken for the distant face of a brick wall, of thermal diffusivity,DHD
0 .0042 cm^2 /s and thicknesslD 0 .45 m, initially at 290 K, to rise to 470 K if the near
face is suddenly raised to a temperature of^0 D870 K and maintained at that temperature.
Assume that all the heat flow is perpendicular to the faces of the wall and that the distant
face is perfectly insulated.

Solution

The temperature at any distancexfrom the near face at timetis given by:

D

N∑D1

ND 0

 1 N^0 ferfc[ 

2 lNCx/

 2

p

DHt]Cerfc[2

NC 1 lx/

 2

p

DHt]g

(equation 9.37)
and the temperature at the distant face is:

D

N∑D1

ND 0

 1 N^0 f2 erfc[ 

2 NC 1 l]/

 2

p

DHtg

Choosing the temperature scale such that the initial temperature is everywhere zero,

/ 2 ^0 D 

470  290 / 2

870  290 D 0. 155

DHD 0 .0042 cm^2 /sor4. 2 ð 10 ^7 m^2 /s,

p

DHD 6. 481 ð 104 and lD 0 .45 m

Thus: 0. 155 D

N∑D1

ND 0

 1 erfc 347 

2 NC 1 /t^0.^5

Derfc 

347 t^0.^5 erfc 

1042 t^0.^5 Cerfc 

1736 t^0.^5

Considering the first term only, 347t^0.^5 D 1 .0andtD 1. 204 ð 105 s
The second and higher terms are negligible compared with the first term at this value
oftand hence:tD 0 .120 Ms(33.5 h)

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