A1 1DUnsteady Heat Conduction Physics Based Approach(1)

of 3

Department of Mechanical Engineering

Indian Institute of Technology Bombay

ME415: Computational Fluid Dynamics & Heat Transfer

Assignment # 1: 1D Unsteady Computational Heat Conduction for Cartesian Geometry

on a Uniform Grid: Physics based Approach

Instructor: Prof. Atul Sharma

Date Posted: 31/01/2015 Due Date: 04/02/15

ONLINE SUBMISSION THROUGH MOODLE ONLY (No late submission allowed): Create a

single zipped file consisting on (a) filled-in answer sheet of this doc file converted into a pdf file and

(b) all the computer programs. The name of the zipped file should be rollnumber_A1

Note: Both problem and answer sheet are provided below. SCILAB or MATLAB should be used

for programming as well as generating graphical results.

Refer http://spoken-tutorial.org/tutorial-search/?search_foss=Scilab&search_language=English, for

getting started to SCILAB for programming as well as generating graphical results. To save figure:

Go to “Graphic window number”, click on “File”, then click on “Export to”, select “Windows BMP

image” in the “Files of type”. Make sure to save the file in the same location where you have this

file. More details are given in the next page.

1. 1-D Computational Heat Conduction (CHC) :

Consider a 1D Cartesian computational domain of size L=1 cm, for CHC transient simulation in a thin (in x-

direction) long steel sheet (density: 7750 kg/m3, specific-heat: 500 J/Kg K, thermal-conductivity: 16.2 W/m-K.

The sheet is taken from a furnace at a temperature of 270C (initial-condition) and is subjected to various thermal

boundary conditions and volumetric heat generation; shown in a table below.

Using the physics based FVM as well as solution methodology, develop a computer program

“A1_1DConduction” for the above problem, run the code for four different boundary-conditions (Cases), given

as:

Cases Boundary Conditions Volumetric Heat

Generation (W/m3) Left Right

A 00C 100

0C 0

B 1000C

h=100W/m2.K, T∞=30

0C

0

C 00C 100

0C 30,000

D 1000C

h=100W/m2.K, T∞=30

0C

30,000

Take the maximum number of grid points in x-and y-direction as imax=12 and convergence criteria (for steady

state) as 0.000001.

Report the results as

a) Plot the steady state temperature profiles for the different cases (4 figures).

b) Discuss the effect of volumetric heat generation on the results for both the types of BCs.

BEST OF LUCK

Keep Playing with the codes in future also.

http://spoken-tutorial.org/tutorial-search/?search_foss=Scilab&search_language=English

of 3

NOTE: CODE EXECUTION IN SCILAB

To open a Scilab console:

Linux: Applications→Programming→Scilab or Applications→Science→Scilab

Windows: Start→All programs→Scilab→Scilab.exe

To load a source code (or a Scinote file):

In the Scilab console, go to top menu bar

File→Open a file…→(Browse for the *.sci file path)

The source code opens in a new Scinote window.

NOTE: Once this window is open, subsequent loading of a new *.sci file will open a new tab in

the same Scinote window.

To execute a program written in Scinote:

In the Scinote window (with the desired program tab open), go to top menu bar

Execute→…file with no echo (please do not select …file with echo)

The execution begins in the Scilab console window.

NOTE: Only one Scilab code can be executed at a time. Once an execute command is given

and the code is to be stopped at an intermediate stage, use the method given below. If another execute

command is given without completing/aborting the previous run, erroneous results may be produced.

To abort a running program:

Go to the Scilab console window and press CTRL+C. This interrupts the code execution. A prompt

appears asking for user input. Enter “abort” here to stop the code execution.

MULTIPLE SCINOTE TABS

of 3

Answer Sheet

Problem # 1: 1-D Computational Heat Conduction (CHC) :

a) Plot the steady-state temperature profile (T(x)) for the different cases (4 figures).

b) Discuss the effect of volumetric heat generation on the results for both the types of BCs.

i) BC 1(No convection): The volumetric heat generation makes heat flux dependent on the x coordinate

of the sheet. It makes heat flow from the point where temperature is maximum within the sheet in both

+x and –x direction. It makes the steady state temperature profile parabolic which was linear in the

absence of heat generation.

ii) BC 2(convection in right end): The volumetric heat generation sets the temperature at the convection

end as Ts=Tinf + (qgen*L/h), where L here is the distance from the maximum temperature point to the

right end. It makes the steady state temperature profile parabolic which was linear in the absence of

heat generation. It makes heat flow from the point where temperature is maximum within the sheet in

both +x and –x direction.

(a)

(b)

(c)

(d)

Fig. 2.1: Steady state temperature profile obtained on the 1D domain for (a) Case A, (b) Case B,

(c) Case C and (d) Case D

A1 1DUnsteady Heat Conduction Physics Based Approach(1)

Documents

Transcript of A1 1DUnsteady Heat Conduction Physics Based Approach(1)