Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
k) Now, we can prepare a plot of T_2 vs epsilon, in EXCEL:
=
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
2. Calculate temperatures at various rs:
Note the eqn entered at cell D8 in the Formula bar.
Also note that max. temp (

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About MS EXCEL Spreadsheet
We see that E11 is 140.459296.
Now, we apply Solver.
Click on Data-Solver. We get:
Target cell is E11.
Equal to: Click on Min.i.e. Target cell will be minimized

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About MS EXCEL Spreadsheet
Now, drag-copy to calculate all values of y, i.e. upto cell D26:
Now, find out the area of first trapezoid: A1 = (y1 + y0)/2)* x, as shown below:
100
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Software Solutions
to Problems on Heat Transfer
Vol. I: CONDUCTION
by
Dr. M. Thirumaleshwar
Professor,
Dept. of Mechanical Engineering,
St. Joseph Engineering College,
Vamanjoor, Mangalore 575 028, India
formerly:
(i) Principal, Vivekananda College of Eng

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
=
Solve the above Problem with EXCEL:
Following are the steps:
1. Set up the EXCEL worksheet as shown below. Enter the

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About Mathcad
Sum(10)=55 .sum of first ten terms
Sum(50) = 1.275.103 .sum of first fifty terms
Sum(100) 5.05.103
.sum of first hundred terms
Note how brief and succinct is the program.

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
About Mathcad
To extract elements of a matrix:
Matrix rows and columns are generally numbered starting from 1. However, default origin of Mathcad
starts from 0. So, we change the origin to

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About MS EXCEL Spreadsheet
c) And, then copy-drag C4 to complete the calculations:
d) Now, we need dT/dx at x = 0. To get this:
At x = 0, i.e. between rows 4 and 5, insert another row, a

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About Finite Element Heat Transfer (FEHT)
Note that we have chosen the height of the section arbitrarily as 10 cm. By default, depth
perpendicular to paper is 1 m.
5. Now, specify the mat

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About MS EXCEL Spreadsheet
c) Click on Scatter with smooth lines, i.e. 2nd button from top in the left column under Scatter,
shown highlighted in the above fig.). We get:
d) Now, we have

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About MS EXCEL Spreadsheet
We have to find out x1, x2 and x3, satisfying these equations:
Set up the EXCEL Worksheet as follows:
Here x_1, x_2 and x_3 are allocated with trial values of 1

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
125
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
2. Do the preliminary calculations as sown; again name these new cells:
Note in the above fig. that the formulas used i

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
3. Now, enter the equation for Tx in cell D8, and then drag-copy it up to cell D18.
Immediately, the values of Tx are c

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
.
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
To plot Q_heater vs. k of the cryocooler rod for a detector temp of 190 K:
First construct a parametric Table as shown b

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
Mathcad Solution:
159
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
Mathcad Solution:
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
About MS EXCEL Spreadsheet
8. Integration in EXCEL:
If y = f(x) is plotted, area under the curve is obtained by integration. Numerical integration is adopted
when the function to be integ

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
Prob. 1A.7. An IR detector is cooled by keeping it on the top of a cryocooler rod 5 mm in diameter
and 70 mm long. The l

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
c) Click on Record Macro. We get:
In the above, Macro Name: we have left the default value viz. Macro1
Short cut key: W

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About MS EXCEL Spreadsheet
There are several options for curve fit; Select polynomial, order 5:
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
Results:
Thus:
T_ 2 = 293.9 K. Ans.
Q_conduction = 147 W/m^2.Ans.
Develop the tools we need for Life Science
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Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
Note that cell E20 is not exactly equal to zero, but has converged to -7.00492E-08, almost equal to zero;
it is good eno

Software Solutions to Problems on Heat Transfer
Conduction: Part I
Fouriers Law and Heat conduction equation,
multimode heat transfer:
And the average temp of cylinder is calculated as:
i.e. Tavg = 308.427 deg.C. (See the formula in cell G91 in the Formul

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About Finite Element Heat Transfer (FEHT)
7. Next, click: (Run Calculate):
You get:
Click: Continue
8. Now, view Results: Click on: (View Temperatures) or (View Temp contours) or (View

Software Solutions to Problems on Heat Transfer
Conduction: Part I
About Mathcad
1 About Mathcad
(Ref: Mathcad software and some Mathcad functions useful for heat transfer calculations Part-I,
by M. Thirumaleshwar, The Indian Jl. of Technical Education,