ME 259 - IHT: Interactive Heat Transfer Computer Exercises
1. Basic Equation Solving
Suppose you wish to solve the following set of equations, where q1, q2, q3, and T are unknowns:
q1 = 0.35(1000-T)
q2 = 5.6710-8(T4-3004)
q3 = 1.4(T-300)4/3
q1 = q2 + q3
Note that two equations are nonlinear and the system cannot be solved analytically.
STEP 1 - Preprocessing
Simply type the equations as given onto the IHT workspace as shown below. You may insert comments or
headings by preceding text lines with a double slash // or by bracketing long sections of text with /* ……. */.
// Nonlinear Equation System Example
q1 = 0.35*(1000-T)
q2 = 5.67E-08*(T^4-300^4)
q3 = 1.4*(T-300)^(4/3)
q1 = q2 + q3
STEP 2 - Solving
Click the Solve button to prepare the solver. If your equations have syntax errors, an error warning will
appear - click OK and usually the solver will highlight the word or equation that contains the error. If you do
not supply enough equations for the number of unknowns, another error warning will appear - click OK and a
summary of equations and unknowns will appear to help you determine what is missing.
If there are no syntax or number of equations errors, an Initial Guesses table appears. Initial guesses are
required for each unknown and the solver uses a value of 1 as a default guess. You may change these
guesses, however, the default values are often satisfactory. You may also insert Minimum and Maximum
solution values if you know the range of possible solution values. For example, we know that temperature in
Kelvin can never be less than zero; so inserting a minimum value of 0 for a temperature unknown will
accelerate convergence since the solver will then only search for positive values. In this example, set the
minimum value for T to 300 (why?).
After initial guesses have been set, click OK and wait for the Data Browser table to appear. (Note: if a
previous dataset exists, the solver will ask you whether you want to save it or discard it.) If the message
"Equation set successfully solved" appears in the Data Browser, then the values for q1, q2, q3, and T
represent a valid solution. In general, there may exist several valid solution sets for a system of nonlinear
equations. The particular solution found by the solver depends upon the initial guesses and the search
algorithm. In this example, only one valid solution set exists since the equations are based upon a physical
problem:
T
q1
q2
q3
322.1
237.3
150.7
86.59
STEP 3 - Postprocessing
Once a valid solution has been found, you may want to copy it to the clipboard for pasting. Highlight the
solution by clicking the upper left rectangle in the table and then click Copy. Options are available for
transposing rows/columns and including variable names. It is suggested that you paste your solution to the
bottom of your equation worksheet before printing a hardcopy. This is done by locating the cursor at the
bottom and then clicking Paste from the Edit menu. Also, be sure to type in appropriate units next to each
solution value. You can now print your entire problem by clicking Print from the File menu. If you wish to have
greater control of how your page looks in terms of font style/size, organization, bold/italic/underline, etc., copy
and paste your entire worksheet to Notepad or Microsoft Word.
Performing parametric studies and plotting results are possible using the Explore and Graph functions.
These features will be used in the next example.
2. Solving a Heat Transfer Problem: Insulated Steam Pipe Undergoing Convection and Radiation
The following worksheet example shows how to set up a typical heat transfer problem. Note that through the
use of commenting, the problem can be presented in a structured format where the given information and
knowns are segregated from the equations and unknowns. The solver recognizes any variable that is set to a
numerical value as a known. You may use any alphanumeric name for a variable, however, please try to be
conventional. There are the usual intrinsic functions such as pi, sqrt, exp, ln, sin, cos, tan, etc. Refer to the
Help Index for a complete listing of the intrinsic functions. Also, IHT does not keep track of dimensional units
– you must make sure that consistent units are used.
// ME 259 Class Example
// Given: Insulated steam pipe undergoing convection and radiation
ri = 0.05
// m
ro = 0.075
// m
L = 25
// m
Ti = 423.15
// K
To = 298.15
// K
hi = 100
// W/m2-K
ho = 10
// W/m2-K
eps = 0.8
sigma = 5.67E-08 // W/m2-K4
// Find:
//
//
//
a) Total heat loss from pipe (q)
b) Outside surface temperature of insulation (Ts)
c) Effect of varying ro from 0.06 to 0.25 m
d) Effect of varying eps from 0.05 to 1.0
// Assumptions:
//
//
//
//
i) steady-state conditions
i) one-dimensional radial conduction through insulation
iii) constant properties
iv) large surroundings, Tsur = To
v) pipe wall has negligible thermal resistance
// Properties:
// 85% magnesia insulation at 360 K, from Table A.3, p.835
kins = 0.055 // W/m-K
// ANALYSIS:
// Thermal resistances
Rtotal = Rconvi + Rins + Rconvo*Rrado/(Rconvo+Rrado)
Rconvi = 1/(hi*2*pi*ri*L)
Rins = ln(ro/ri)/(2*pi*kins*L)
Rconvo = 1/(ho*2*pi*ro*L)
Rrado = 1/(hr*2*pi*ro*L)
hr = eps*sigma*(Ts^2+To^2)*(Ts+To)
// Heat rate & temperature equations
q = (Ti-To)/Rtotal
q = (Ti-Ts)/(Rconvi+Rins)
Ts_C = Ts - 273.15
The solution to this problem is given below:
Rconvi
Rconvo
Rins
Rrado
Rtotal
Ts
Ts_C
hr
q
0.001273
0.008488
0.04693
0.01654
0.05381
311.2
38.03
5.133
2323
K/W
K/W
K/W
K/W
K/W
K
C
W/m2-K
W
Now, try performing a parametric study where you vary the insulation thickness (i.e., the value of ro) over the
range of 0.06 to 0.25 m in steps of 0.01 m To do this, click on Explore and choose the Variable to Sweep as
ro and input the range parameters. Then click OK and wait for the Data Browser to appear. Here, you will see
the results corresponding to each value of ro. Suppose you are interested in the effect of ro on the heat loss,
q. This is best viewed by plotting q vs. ro. Click on Graph, then select ro as coordinate X and q as coordinate
Y1. Click OK and a plot should appear. You can add titles, change scales, change lines, change data
markers, and add a legend if you wish. The graph can be printed as a full page or copied, sized, and pasted
to your worksheet. Next, try plotting Ts versus ro and then repeat for a parametric study with 0.05 < eps < 1.
There are many other features in IHT, including 1st-order differential equations, integrals, material property
functions, user-defined functions, and pre-written heat transfer correlations, special equations, and models
(see Help menu). Not bad for a $15 program !!
Effect of insulation thickness on heat loss from steam pipe
4500
4000
3500
Heat loss (W)
3000
2500
2000
1500
1000
500
0
0.05
0.075
0.1
0.125
0.15
0.175
Outside insulation radius (m)
0.2
0.225
0.25