Difference between revisions of "OpenFOAM/C2/Supersonic-flow-over-a-wedge/English-timed"

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|-
 
|-
 
| 00:01
 
| 00:01
−
| Hello and welcome to the spoken tutorial on '''Supersonic flow over a wedge using OpenFOAM'''
+
| Hello and welcome to the '''spoken tutorial''' on '''Supersonic flow over a wedge''' using '''OpenFOAM'''.
  
 
|-
 
|-
 
| 00:07
 
| 00:07
−
| In this tutorial I will show you How to solve a '''compressible flow''' problem of '''supersonic flow over a wedge ''' How to post process the results in '''paraView'''.
+
| In this tutorial, I will show you: * How to solve a '''compressible flow''' problem of '''supersonic flow over a wedge '''  
 +
* How to postprocess the results in '''paraView'''.
  
 
|-
 
|-
 
| 00:18
 
| 00:18
−
| To record this tutorial I am using''' Linux Operating system Ubuntu version 10.04'''
+
| To record this tutorial, I am using:
−
'''OpenFOAM version 2.1.0'''
+
* '''Linux Operating system Ubuntu''' version 10.04
−
'''ParaView version 3.12.0'''
+
* '''OpenFOAM''' version 2.1.0
 +
* '''ParaView''' version 3.12.0
  
 
|-
 
|-
 
| 00:30
 
| 00:30
−
| To practice this tutorial a learner should have some basic knowledge of '''Compressible flows''' and'''Gas Dynamics'''
+
| To practice this tutorial, a learner should have some basic knowledge of '''Compressible flows''' and'''Gas Dynamics'''.
  
 
|-
 
|-
 
| 00:38
 
| 00:38
−
| Let us now solve '''supersonic flow''' over a '''wedge''' using '''OpenFOAM''' and see the '''shock structure''' formed using '''paraview'''
+
| Let us now solve '''supersonic flow''' over a '''wedge''' using '''OpenFOAM''' and see the '''shock structure''' formed using '''paraview'''.
  
 
|-
 
|-
 
| 00:47
 
| 00:47
−
| The problem consists of a wedge with '''semi-angle of 15 degrees''' kept in a '''uniform supersonic flow'''
+
| The problem consists of a wedge with a '''semi-angle''' of 15 degrees kept in a uniform '''supersonic flow'''.
  
 
|-
 
|-
 
| 00:55
 
| 00:55
−
|The Inlet velocity is '''5 meters per second'''
+
|The Inlet velocity is 5 meters per second.
  
 
|-
 
|-
 
| 01:00
 
| 01:00
−
| The '''boundary condition'''s are set as shown in the figure
+
| The '''boundary condition'''s are set as shown in the figure.
  
 
|-
 
|-
 
| 01:05
 
| 01:05
−
| The type of solver I am using here is '''rhoCentralFoam'''
+
| The type of '''solver''' I am using here is '''rhoCentralFoam'''.
  
 
|-
 
|-
 
| 01:10
 
| 01:10
−
| It is a '''Density'''-based '''compressible flow solver''' It is based on '''central- upwind''' '''schemes of Kurganov and Tadmor '''
+
| It is a '''Density'''-based '''compressible flow solver'''. It is based on '''central- upwind''' '''schemes of Kurganov and Tadmor'''.
  
 
|-
 
|-
 
| 01:21
 
| 01:21
−
| Open a '''command terminal ''' to do this press '''ctrl +alt+ t''' keys '''simultaneously''' on your keyboard
+
| Open a '''command terminal '''. To do this, press '''ctrl +alt+ t''' keys simultaneously on your keyboard.
  
 
|-
 
|-
 
| 01:28
 
| 01:28
−
| In the command '''terminal''' type path for '''supersonic flow''' over a '''wedge'''
+
| In the command terminal, type the path for '''supersonic flow''' over a '''wedge'''.
  
 
|-  
 
|-  
 
|01:35
 
|01:35
−
|In the terminal Type ''''run' and press enter'''
+
|In the terminal, type "run" and press '''Enter'''.
  
 
|-
 
|-
 
| 01:40
 
| 01:40
−
|  '''cd tutorial - ''' and Press Enter '''cd compressible - ''' and Press Enter '''cd rhoCentralFoam - ''' and Press Enter
+
|  '''cd space tutorials''' and press '''Enter'''.
 +
'''cd space compressible ''' and press '''Enter'''.
 +
'''cd space rhoCentralFoam''' and press '''Enter'''.
  
 
|-
 
|-
 
|02:02
 
|02:02
−
| '''cd wedge15Ma5 '''
+
| '''cd space wedge15Ma5'''
  
 
|-
 
|-
 
| 02:13
 
| 02:13
−
| This is the name of the folder of '''supersonic flow''' over a wedge in '''rhoCentralFoam''' and press enter'''
+
| This is the name of the folder of '''supersonic flow''' over the wedge in '''rhoCentralFoam''' and press '''Enter'''.
  
 
|-
 
|-
 
| 02:21
 
| 02:21
−
| Now type''' ls''' and press enter
+
| Now, type "ls" and press '''Enter'''.
  
 
|-
 
|-
 
| 02:24
 
| 02:24
−
| You will see '''three folders''' : '''0,constant and system.'''
+
| You will see three folders: '''0, constant''' and '''system'''.
  
 
|-
 
|-
 
| 02:29
 
| 02:29
−
| Now open the '''blockMeshDict file''',to do this  
+
| Now, open the '''blockMeshDict file'''. To do this,
  
 
|-
 
|-
 
|02:34
 
|02:34
−
|type '''cd '''space '''constant''' and press enter
+
|type '''cd space constant''' and press '''Enter'''.
  
 
|-
 
|-
 
| 02:41
 
| 02:41
−
| '''cd '''space '''polyMesh''' note that '''M''' here is capital and press enter
+
| '''cd space polyMesh''' note that 'M' here is capital and press '''Enter'''.
  
 
|-
 
|-
 
| 02:49
 
| 02:49
−
| Now type '''ls''' and press enter you can see the '''blockMeshDict file'''
+
| Now type "ls" and press '''Enter'''. You can see the '''blockMeshDict file'''.
  
 
|-
 
|-
 
| 02:54
 
| 02:54
−
| To view'''blockMeshDict file''' type '''gedit''' space''' blockMeshDict''' note that '''M and D '''here are capital press enter
+
| To view the '''blockMeshDict''' file, type '''gedit space blockMeshDict'''. Note that 'M' and 'D' here are capital, press '''Enter'''.
  
 
|-
 
|-
 
| 03:08
 
| 03:08
−
| let me drag this to the '''capture area''' scroll down
+
| Let me drag this to the '''capture area''', scroll down.
  
 
|-
 
|-
 
| 03:14
 
| 03:14
−
| In this you need to '''calculate''' the '''co-ordinate''' for the wedge
+
| In this, you need to calculate the co-ordinates for the wedge.
  
 
|-
 
|-
 
| 03:20
 
| 03:20
−
| This has been already '''calculated''' and set up in the problem
+
| This has been already calculated and set up in the problem.
  
 
|-
 
|-
 
| 03:23
 
| 03:23
−
| The rest of the data remains the same
+
| The rest of the data remains the same.
  
 
|-
 
|-
 
|03:29
 
|03:29
−
| In '''boundary patches'''  boundaries are set as shown in the figure  
+
| In '''boundary patches''', boundaries are set as shown in the figure.
  
 
|-
 
|-
 
| 03:33
 
| 03:33
−
| Close  '''blockMeshDict file'''
+
| Close  '''blockMeshDict''' file.
  
 
|-
 
|-
 
| 03:36
 
| 03:36
−
| in the '''command terminal''' type '''cd ..(dot dot)''' '''twice'''  to return back to '''wedge folder'''
+
| In the command terminal, type '''cd space ..(dot dot)''' twice to return back to '''wedge''' folder.
  
 
|-
 
|-
 
| 03:45
 
| 03:45
−
| Now Open the '''0 folder '''
+
| Now open the 0 (zero) folder.
  
 
|-
 
|-
 
| 03:51
 
| 03:51
−
| To do this type '''cd '''space''' 0 and press enter'''
+
| To do this, type '''cd space 0''' and press '''Enter'''.
  
 
|-
 
|-
 
| 03:58
 
| 03:58
−
| '''Type ls and press enter'''
+
| Type "ls" and press '''Enter'''.
  
 
|-
 
|-
 
| 04:02
 
| 04:02
−
| This contains the initial boundary condition for '''pressure,velocity and Temperature'''
+
| This contains the initial boundary condition for pressure, velocity and Temperature.
  
 
|-
 
|-
 
| 04:10
 
| 04:10
−
| Type '''cd .. (dot dot)''' and press enter.Now we need to '''mesh the geometry'''
+
| Type '''cd space .. (dot dot)''' and press '''Enter'''. Now we need to '''mesh''' the geometry.
  
 
|-
 
|-
 
| 04:19
 
| 04:19
−
| To do this in the '''command terminal''' type '''blockMesh''' and Press Enter '''Meshing''' has been done
+
| To do this, in the '''command terminal''', type "blockMesh" and press '''Enter'''. '''Meshing''' has been done.
  
 
|-
 
|-
 
| 04:32
 
| 04:32
−
| Now to view the geometry in the ''' command terminal ''' type '''paraFoam''' and press enter This will open the '''paraview''' window
+
| Now, to view the geometry- in the command terminal,  type "paraFoam" and press '''Enter'''. This will open the '''paraview''' window.
  
 
|-
 
|-
 
| 04:45
 
| 04:45
−
| On the left hand side of '''object inspector menu''' click '''APPLY'''
+
| On the left hand side of '''object inspector''' menu, click '''APPLY'''.
  
 
|-
 
|-
 
| 04:53
 
| 04:53
−
| In this you can see the '''geometry''' in which the '''rectangular''' '''section upstream'''  changes to a '''wedge downstream''' Close the '''paraview''' window
+
| In this, you can see the geometry in which the rectangular  section '''upstream'''  changes to a '''wedge downstream'''. Close the '''paraview''' window.
  
 
|-
 
|-
 
| 05:05
 
| 05:05
−
| Now run the solver ''''rhoCentralFoam''''  
+
| Now, '''run''' the '''solver''' '''rhoCentralFoam'''.
  
 
|-
 
|-
 
| 05:11
 
| 05:11
−
| To do this in the '''command terminal''' type '''rhoCentralFoam''' and Press Enter
+
| To do this, in the command terminal, type "rhoCentralFoam" and press '''Enter'''.
  
 
|-
 
|-
 
| 05:20
 
| 05:20
−
| The '''iterations''' running can be seen in the '''terminal window'''
+
| The '''iterations''' running can be seen in the terminal window.
  
 
|-
 
|-
 
| 05:24
 
| 05:24
−
| '''Iterations running''' will stop after it '''converges '''or at the end of the time step Now the''' solving''' has been done
+
| '''Iterations''' running will stop after it converges or at the end of the time steps. Now, the solving has been done.
  
 
|-
 
|-
 
| 05:34
 
| 05:34
−
| To '''visualise''' these results let us open the '''paraview window''' once again
+
| To visualize these results, let us open the '''paraview''' window once again.
  
 
|-
 
|-
 
| 05:40
 
| 05:40
−
| In the '''command terminal''' type “'''paraFoam” '''and press Enter
+
| In the '''command terminal''', type “paraFoam” and press Enter.
  
 
|-
 
|-
 
| 05:49
 
| 05:49
−
| Again on the left hand side of '''object inspector menu click '''APPLY'''
+
| Again on the left hand side of '''object inspector''' menu, click '''APPLY'''.
  
 
|-
 
|-
 
| 05:56
 
| 05:56
−
| On the left hand side top in '''active variable control menu''''''you will see a drop down menu showing solid color.''' Now click on it  '''And change from solid color to capital U'''
+
| On the left hand side top, in '''active variable control''' menu, you will see a drop-down menu showing '''solid color'''. Now, click on it  and change from '''solid color''' to capital 'U'.
  
 
|-
 
|-
 
| 06:14
 
| 06:14
−
| Now make the '''color legend ON''' by clicking on the left hand side top of '''active variable control menu''' and make the '''color legend ON''' '''click on it'''
+
| Now, make the '''color legend ON''' by clicking on the left hand side top of '''active variable control''' menu and make the '''color legend 'ON''''. Click on it.
  
 
|-
 
|-
 
| 06:28
 
| 06:28
−
| On top of the '''Paraview window''' you can see the '''VCR control''' Click on '''PLAY'''
+
| On top of the '''Paraview''' window, you can see the '''VCR control'''. Click on '''PLAY'''.
  
 
|-
 
|-
 
| 06:37
 
| 06:37
−
| You can see the final results of '''U velocity'''
+
| You can see the final results of '''U velocity'''.
  
 
|-
 
|-
 
| 06:42
 
| 06:42
−
| Now scroll down the  '''properties''' in '''object inspector menu''' on the left hand side Now click on '''display''' besides '''properties'''
+
| Now, scroll down the  properties in '''object inspector menu''' on the left hand side. Now click on '''Display''' besides '''Properties'''.
  
 
|-
 
|-
 
| 06:56
 
| 06:56
−
| Scroll down and click on '''Rescale to Size''' You can see the final value of '''Velocity magnitude'''
+
| Scroll down and click on '''Rescale to Size'''. You can see the final value of '''Velocity, magnitude'''.
  
 
|-
 
|-
 
| 07:05
 
| 07:05
−
| Similarly you can select '''pressure'''You can see the final result of '''pressure''' Now close the '''paraview window'''
+
| Similarly, you can select '''pressure'''. You can see the final result of '''pressure'''. Now, close the '''paraView''' window.
  
 
|-
 
|-
 
| 07:16
 
| 07:16
−
| You can also calculate the '''Mach''' number for the flow To do this we can use the '''Openfoam '''utility by '''typing Mach in the command terminal '''
+
| You can also calculate the '''Mach''' number for the flow. To do this, we can use the '''Openfoam '''utility by typing "Mach" in the command terminal.
  
 
|-
 
|-
 
| 07:26
 
| 07:26
−
| Type '''Mach'''
+
| Type '''Mach'''.
  
 
|-
 
|-
 
|07:29  
 
|07:29  
−
| Note that '''M''' here is '''capital''' and press enter.You can see that '''Mach number''' is calculated for each time step
+
| Note that 'M' here is capital and press '''Enter'''. You can see that '''Mach number''' is calculated for each time step.
  
 
|-
 
|-
 
| 07:36
 
| 07:36
−
| Now again open the '''paraview window'''.By typing in the '''command terminal paraFoam'''and press enter
+
| Now, again open the '''paraview ''' window by typing in the command terminal "paraFoam" and press '''Enter'''.
  
 
|-
 
|-
 
| 07:48
 
| 07:48
−
| Click '''APPLY''' scroll down.In '''volume fields''' '''Check''' the '''Ma''' box and again click '''APPLY'''
+
| Click '''APPLY''', scroll down. In '''volume fields''', check the 'Ma' box and again click '''APPLY'''.
  
 
|-
 
|-
 
| 08:04
 
| 08:04
−
| On top of the''' active variable control menu''' click on '''Solid Color''' and change it to '''Ma'''
+
| On top of the''' active variable control''' menu, click on '''Solid Color''' and change it to 'Ma'.
  
 
|-
 
|-
 
| 08:11
 
| 08:11
−
| In the '''VCR control''' menu again click on '''PLAY''' and make the '''color legend ON'''
+
| In the '''VCR control''' menu, again click on '''PLAY''' and make the '''color legend 'ON''''.
  
 
|-
 
|-
 
| 08:21
 
| 08:21
−
| You can see the '''Mach number''' in the''' color legend''' and '''corresponding colours'''
+
| You can see the '''Mach number''' in the''' color legend''' and the corresponding colours.
  
 
|-
 
|-
 
| 08:29
 
| 08:29
−
| We notice here that when the wedge is kept in supersonic flow it produce a shock across which the flow properties like temprature, pressure  
+
| We notice here that when the '''wedge''' is kept in '''supersonic flow''', it produces a '''shock''' across which the flow properties like temprature, pressure  
−
and density drastically changes
+
and density drastically change.
  
 
|-
 
|-
 
|08:43
 
|08:43
−
| Now Let me switch back to the '''slides''' The solved tutorial can be '''validated''' with '''exact ''''''solution''' 
+
| Now, let me switch back to the '''slides'''. The solved tutorial can be '''validated''' with exact solution available in basic books of '''Aerodynamics''' by John D Anderson.
−
'''available '''in basic books of '''Aerodynamics''' by '''John D Anderson'''
+
  
 
|-
 
|-
 
| 08:55
 
| 08:55
−
| In this tutorial we learnt: '''Solving a compressible flow problem'''
+
| In this tutorial, we learnt: * '''Solving a compressible flow problem'''
−
'''Velocity''' and '''pressure contour''' for the wedge
+
* '''Velocity''' and '''pressure contour''' for the wedge and
−
'''OpenFOAM utility''' for calculating the '''Mach number'''
+
* '''OpenFOAM utility''' for calculating the '''Mach number'''.
  
 
|-
 
|-
 
| 09:06
 
| 09:06
−
| As an Assignment Vary the '''wedge angle between 10 ° to 15 ° ''' to view the''' shock characteristic''' for the flow
+
| As an Assignment, vary the wedge angle between 10 ° to 15 ° to view the''' shock characteristic''' for the flow.
  
 
|-
 
|-
 
| 09:14
 
| 09:14
−
| This bring us to the end of tutorial watch The video available at this URL: http://spoken-tutorial.org/What_is_a_Spoken_Tutorial  
+
| This brings us to the end of the tutorial. Watch the video available at this URL:
 +
http://spoken-tutorial.org/What_is_a_Spoken_Tutorial  
  
 
|-
 
|-
Line 279: Line 283:
 
|-
 
|-
 
| 09:28
 
| 09:28
−
| The Spoken Tutorial Project Team Conducts workshops using spoken tutorials  
+
| The Spoken Tutorial Project team:
−
Gives certificates to those who pass an online test For more details,  
+
* Conducts workshops using spoken tutorials  
−
please write to us at contact@spoken-tutorial.org
+
* Gives certificates to those who pass an online test.
 +
For more details, please write to us at '''contact@spoken-tutorial.org'''
  
 
|-
 
|-
 
| 09:41
 
| 09:41
−
| Spoken Tutorials project is  part of Talk to a Teacher project, It is supported by the National Mission on Education through ICT, MHRD, Government of India.
+
| '''Spoken Tutorials''' project is  part of '''Talk to a Teacher''' project. It is supported by the National Mission on Education through ICT, MHRD, Government of India.
−
More information on the same is available at the following URL link http://spoken-tutorial.org/NMEICT-Intro
+
More information on the same is available at the following URL link:
 +
http://spoken-tutorial.org/NMEICT-Intro
  
 
|-
 
|-
 
| 09:56
 
| 09:56
−
| This script has been contributed by Arvind M and this is Rahul Joshi from IIT BOMBAY signing off.Thanks for joining.
+
| This script has been contributed by Arvind M and this is Rahul Joshi from '''IIT Bombay''', signing off. Thanks for joining.
  
 
|}
 
|}

Revision as of 11:47, 27 June 2016

Time Narration
00:01 Hello and welcome to the spoken tutorial on Supersonic flow over a wedge using OpenFOAM.
00:07 In this tutorial, I will show you: * How to solve a compressible flow problem of supersonic flow over a wedge
  • How to postprocess the results in paraView.
00:18 To record this tutorial, I am using:
  • Linux Operating system Ubuntu version 10.04
  • OpenFOAM version 2.1.0
  • ParaView version 3.12.0
00:30 To practice this tutorial, a learner should have some basic knowledge of Compressible flows andGas Dynamics.
00:38 Let us now solve supersonic flow over a wedge using OpenFOAM and see the shock structure formed using paraview.
00:47 The problem consists of a wedge with a semi-angle of 15 degrees kept in a uniform supersonic flow.
00:55 The Inlet velocity is 5 meters per second.
01:00 The boundary conditions are set as shown in the figure.
01:05 The type of solver I am using here is rhoCentralFoam.
01:10 It is a Density-based compressible flow solver. It is based on central- upwind schemes of Kurganov and Tadmor.
01:21 Open a command terminal . To do this, press ctrl +alt+ t keys simultaneously on your keyboard.
01:28 In the command terminal, type the path for supersonic flow over a wedge.
01:35 In the terminal, type "run" and press Enter.
01:40 cd space tutorials and press Enter.

cd space compressible and press Enter. cd space rhoCentralFoam and press Enter.

02:02 cd space wedge15Ma5
02:13 This is the name of the folder of supersonic flow over the wedge in rhoCentralFoam and press Enter.
02:21 Now, type "ls" and press Enter.
02:24 You will see three folders: 0, constant and system.
02:29 Now, open the blockMeshDict file. To do this,
02:34 type cd space constant and press Enter.
02:41 cd space polyMesh note that 'M' here is capital and press Enter.
02:49 Now type "ls" and press Enter. You can see the blockMeshDict file.
02:54 To view the blockMeshDict file, type gedit space blockMeshDict. Note that 'M' and 'D' here are capital, press Enter.
03:08 Let me drag this to the capture area, scroll down.
03:14 In this, you need to calculate the co-ordinates for the wedge.
03:20 This has been already calculated and set up in the problem.
03:23 The rest of the data remains the same.
03:29 In boundary patches, boundaries are set as shown in the figure.
03:33 Close blockMeshDict file.
03:36 In the command terminal, type cd space ..(dot dot) twice to return back to wedge folder.
03:45 Now open the 0 (zero) folder.
03:51 To do this, type cd space 0 and press Enter.
03:58 Type "ls" and press Enter.
04:02 This contains the initial boundary condition for pressure, velocity and Temperature.
04:10 Type cd space .. (dot dot) and press Enter. Now we need to mesh the geometry.
04:19 To do this, in the command terminal, type "blockMesh" and press Enter. Meshing has been done.
04:32 Now, to view the geometry- in the command terminal, type "paraFoam" and press Enter. This will open the paraview window.
04:45 On the left hand side of object inspector menu, click APPLY.
04:53 In this, you can see the geometry in which the rectangular section upstream changes to a wedge downstream. Close the paraview window.
05:05 Now, run the solver rhoCentralFoam.
05:11 To do this, in the command terminal, type "rhoCentralFoam" and press Enter.
05:20 The iterations running can be seen in the terminal window.
05:24 Iterations running will stop after it converges or at the end of the time steps. Now, the solving has been done.
05:34 To visualize these results, let us open the paraview window once again.
05:40 In the command terminal, type “paraFoam” and press Enter.
05:49 Again on the left hand side of object inspector menu, click APPLY.
05:56 On the left hand side top, in active variable control menu, you will see a drop-down menu showing solid color. Now, click on it and change from solid color to capital 'U'.
06:14 Now, make the color legend ON by clicking on the left hand side top of active variable control menu and make the color legend 'ON'. Click on it.
06:28 On top of the Paraview window, you can see the VCR control. Click on PLAY.
06:37 You can see the final results of U velocity.
06:42 Now, scroll down the properties in object inspector menu on the left hand side. Now click on Display besides Properties.
06:56 Scroll down and click on Rescale to Size. You can see the final value of Velocity, magnitude.
07:05 Similarly, you can select pressure. You can see the final result of pressure. Now, close the paraView window.
07:16 You can also calculate the Mach number for the flow. To do this, we can use the Openfoam utility by typing "Mach" in the command terminal.
07:26 Type Mach.
07:29 Note that 'M' here is capital and press Enter. You can see that Mach number is calculated for each time step.
07:36 Now, again open the paraview window by typing in the command terminal "paraFoam" and press Enter.
07:48 Click APPLY, scroll down. In volume fields, check the 'Ma' box and again click APPLY.
08:04 On top of the active variable control menu, click on Solid Color and change it to 'Ma'.
08:11 In the VCR control menu, again click on PLAY and make the color legend 'ON'.
08:21 You can see the Mach number in the color legend and the corresponding colours.
08:29 We notice here that when the wedge is kept in supersonic flow, it produces a shock across which the flow properties like temprature, pressure

and density drastically change.

08:43 Now, let me switch back to the slides. The solved tutorial can be validated with exact solution available in basic books of Aerodynamics by John D Anderson.
08:55 In this tutorial, we learnt: * Solving a compressible flow problem
  • Velocity and pressure contour for the wedge and
  • OpenFOAM utility for calculating the Mach number.
09:06 As an Assignment, vary the wedge angle between 10 ° to 15 ° to view the shock characteristic for the flow.
09:14 This brings us to the end of the tutorial. Watch the video available at this URL:

http://spoken-tutorial.org/What_is_a_Spoken_Tutorial

09:21 It summarizes the Spoken Tutorial project. If you do not have good bandwidth, you can download and watch it.
09:28 The Spoken Tutorial Project team:
  • Conducts workshops using spoken tutorials
  • Gives certificates to those who pass an online test.

For more details, please write to us at contact@spoken-tutorial.org

09:41 Spoken Tutorials project is part of Talk to a Teacher project. It is supported by the National Mission on Education through ICT, MHRD, Government of India.

More information on the same is available at the following URL link: http://spoken-tutorial.org/NMEICT-Intro

09:56 This script has been contributed by Arvind M and this is Rahul Joshi from IIT Bombay, signing off. Thanks for joining.

Contributors and Content Editors

DeepaVedartham, PoojaMoolya, Pratik kamble, Sandhya.np14

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