8/2/2019 Week2 Tutorial

1/3

MIET1081 Tutorials Semester 1, 2012

Week 2 Tutorial Thermal Resistance Approach

Pre Tutorial Preparation

1. An important class of heat transfer problems for which simple solutions are obtainedencompasses those involving two surfaces maintained atconstanttemperatures T1 and T2.

The steady rate of heat transfer between these two surfaces is expressed as

where Sis the conduction shape factor, which has the dimension oflength,and kis the

thermal conductivity of the medium between the surfaces. The conduction shape factor

depends on thegeometryof the system only.

A 5-m-wide, 4-m-high and 40-m-long kiln used to cure concrete pipes is made of 20-cm-

thick concrete walls (k=0.9 W/m.oC). The kiln is maintained at 40oC by injecting hot steam

into it. The convection heat transfer coefficients on the inner and the outer surfaces of the

kiln are 3000 W/m2.oC and 25 W/m2.oC, respectively. Determine the rate of heat loss from

the kiln when the ambient air is at -4 oC using the shape factor method.

2. Fill in the gaps

What is 2 in terms of0?

Consider this:

Enter the numerical values:

atx= 0, 0 = 3

and so atx= 2,

2 =

2

3

4

5

6

7

8

0 0.5 1 1.5 2

Q

x

0 2

8/2/2019 Week2 Tutorial

2/3

MIET1081 Tutorials Semester 1, 2012

So 2 can be defined in terms of0 as an equation as:

This is saying the initial value at plus the rate of change over (or multiplied by) the distanceit changes. Substitute in the values and check the answer!

Now rewrite the conservation of energy in thex-coordinate from:

=

Substitute in

What is your final equation? You have just derived the heat conduction equation in thex-

direction

___________________________

In class tutorial problems and discussion

1. Consider two cold canned drinks, one wrapped in a blanket 10-mm thick and the otherplaced on a table in the same room. Which drink will warm up faster?

What phenomena occurs when the blanket thickness is extremely large, say 100mm?

2. There are many ways to solve heat transfer problems. In thehomework problem, we can also use the conventional plane

wall method, where you need to determine the correct surface

area to use. You should use the outer surface area for outer

convection resistance, the inner surface area for inner

convection resistance, and the average area for the conduction

resistance.

3.

A 3.3-m-high and 6.0-m-wide wall consists of a long 18-cm x30-cm cross-section of horizontal bricks, surrounded by

plaster layers. There is also 2-cm-thick rigid foam on the inner

side of the wall. The inner and outer temperatures are 22oC

in out

8/2/2019 Week2 Tutorial

3/3

MIET1081 Tutorials Semester 1, 2012

and -4oC and the convection heat transfer coefficients on the inner and the outer surfaces

are h1=10W/m2.oC and h2=20 W/m2.oC, respectively. Assuming heat transfer through the

wall is one-dimensional and heat transfer by radiation is disregarded calculate the rate of

heat transfer through the entire wall.Properties The thermal conductivities are given to be k

= 0.72 W/mC for bricks, k= 0.22 W/mC for plaster layers, and k= 0.026 W/mC for the

rigid foam.

Suggested Homework Problems:

Cengel&Turner4thEd: 17-33,17-51,17-57

Cengel&Turner3rdEd: 17-36,17-53,17-59

Cengel&Turner2ndEd: 17-35,17-57,17-68

Solutions to Wk 1 Tutorial

1.) The inner and outer surfaces of a 0.5-cm-thick glass (k 0.78 W/m.oC) window per unit

area (e.g. Area 1m2

are maintained at specified temperatures (Tin 10o

C, Tout3o

C). Theamount of heat transfer through the glass in 5 h is to be determined.

For 5 hours

2.) The inner and outer surfaces of a 2x2m square silicon plate (k 20 W/m.oC) with thicknessof 1m are maintained at 30oC and 20oC respectively. What is the heat transfer rate by

conduction and what is the amount of heat transfer through the plate in a 5 hour period? Whatwould the heat transfer be if the plate thickness is doubled?

For 5 hours

if the plate thickness is doubled, then Q is halved and

3.) Integrate the one-dimensional Laplace equation twice to get the general solution.

Assuming the solid material is copper, k 400 W/moC. Solve for the constants by definingeither a temperature boundary condition Tleft100oC Tright50oC

and

What heat flux value imposed at the left wall would give the same physical behavior?