Difference between revisions of "OpenFOAM/C2/2D-Laminar-Flow-in-a-channel/English-timed"
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| 00:01 | | 00:01 | ||
− | | Hello and welcome to the spoken tutorial on ''' Simulating 2D Laminar Flow in a Channel using | + | | Hello and welcome to the '''spoken tutorial''' on ''' Simulating 2D Laminar Flow in a Channel''' using '''OpenFoam'''. |
|- | |- | ||
| 00:09 | | 00:09 | ||
− | | In this tutorial I will show you | + | | In this tutorial, I will show you- |
− | '''2D geometry of channel ''' | + | * '''2D geometry of channel ''' |
− | '''Meshing the Geometry''' | + | * '''Meshing the Geometry''' |
− | '''Solving''' and '''Post Processing results''' in '''Paraview''' and Validation using '''analytic result''' | + | * '''Solving''' and '''Post Processing results''' in '''Paraview''' and |
+ | * Validation using '''analytic result'''. | ||
|- | |- | ||
| 00:25 | | 00:25 | ||
− | | To record this tutorial I am using '''Linux Operating system Ubuntu | + | | To record this tutorial, I am using: |
− | '''OpenFOAM version 2.1.1''' | + | * '''Linux Operating system Ubuntu''' 12.04. |
− | ''' | + | * '''OpenFOAM''' version 2.1.1 |
+ | * '''ParaView''' version 3.12.0 | ||
|- | |- | ||
| 00:39 | | 00:39 | ||
− | |Note that '''OpenFOAM''' version | + | |Note that '''OpenFOAM''' version 2.1.1 is supported on '''ubuntu version''' 12.04. |
|- | |- | ||
| 00:45 | | 00:45 | ||
− | |Hence forth all the tutorials will be covered using '''OpenFOAM version 2.1.1 | + | |Hence forth all the tutorials will be covered using '''OpenFOAM ''' version 2.1.1 and''' ubuntu version''' 12.04. |
|- | |- | ||
| 00:56 | | 00:56 | ||
− | | As a | + | | As a prerequisite for this tutorial, you should know how to create '''geometry''' using '''OpenFOAM'''. |
|- | |- | ||
| 01:03 | | 01:03 | ||
− | |If not, please refer to the | + | |If not, please refer to the relevant tutorials on our website. |
|- | |- | ||
| 01:09 | | 01:09 | ||
− | |we simulate flow in a channel to determine flow development length along the downstream '''Channel flow''' problem description | + | |we simulate flow in a channel to determine flow development length along the downstream '''Channel flow''' problem description. |
|- | |- | ||
| 01:19 | | 01:19 | ||
− | | The '''boundary names''' and the '''inlet conditions''' are shown in this figure | + | | The '''boundary names''' and the '''inlet conditions''' are shown in this figure. |
|- | |- | ||
| 01:26 | | 01:26 | ||
− | | The '''flow develpoment length''' is given by the formula '''L= 0.05 * Re * D''' | + | | The '''flow develpoment length''' is given by the formula '''L= 0.05 * Re * D'''. |
|- | |- | ||
| 01:32 | | 01:32 | ||
− | | | + | | 'Re' which is the '''Reynolds number''' and 'D' which is the '''channel height'''. |
|- | |- | ||
| 01:37 | | 01:37 | ||
− | | Using the ''' | + | | Using the formula, length of the '''channel''' comes out to be 5 meters and height is kept as 1 meter. |
|- | |- | ||
| 01:45 | | 01:45 | ||
− | |The '''Inlet velocity | + | |The '''Inlet velocity''' is 1 meters per second. And, we are solving this for a '''Reynolds number''' '''( Re ) equal 100'''. |
|- | |- | ||
| 01:53 | | 01:53 | ||
− | | This is a '''steady state problem '''.Therefore we are using a '''steady state incompressible''' solver for this case | + | | This is a '''steady state problem '''. Therefore we are using a '''steady state incompressible''' solver for this case. |
|- | |- | ||
| 02:01 | | 02:01 | ||
− | | This is the file structure of our case | + | | This is the file structure of our case. The folder should be created in the '''solver''' type that we choose. I have already created a folder in '''simpleFoam''' folder of''' incompressible flow solvers'''. |
|- | |- | ||
| 02:18 | | 02:18 | ||
− | |The | + | |The folder is named as ''' channel'''. Now, let me switch to the folder. |
|- | |- | ||
| 02:25 | | 02:25 | ||
− | | ''' | + | | Copy '''0, Constant''' and '''System''' folders of any other case file in the '''simpleFoam''' directory. |
|- | |- | ||
| 02:34 | | 02:34 | ||
− | | I have copied the''' file structure''' of the case of''' pitzDaily''' | + | | I have copied the''' file structure''' of the case of''' pitzDaily'''. |
|- | |- | ||
| 02:38 | | 02:38 | ||
− | | Paste it inside the channel folder and make the necessary changes in the '''geometry''','''boundary faces''' and '''boundary condition''' | + | | Paste it inside the '''channel''' folder and make the necessary changes in the '''geometry''','''boundary faces''' and '''boundary condition'''. |
|- | |- | ||
| 02:48 | | 02:48 | ||
− | | Now let me | + | | Now, let me open the command terminal. |
|- | |- | ||
| 02:51 | | 02:51 | ||
− | | To do this press '''Ctrl+Alt +t''' keys simultaneously on your | + | | To do this, press '''Ctrl+Alt +t''' keys simultaneously on your keyboard. |
|- | |- | ||
| 02:57 | | 02:57 | ||
− | | In the terminal | + | | In the terminal, type '''run''' and press '''Enter'''. |
|- | |- | ||
| 03:01 | | 03:01 | ||
− | | | + | | Now type '''cd space tutorials''' and press '''Enter'''. |
|- | |- | ||
| 03:08 | | 03:08 | ||
− | | | + | | Now type '''cd space incompressible''' and press '''Enter'''. |
|- | |- | ||
| 03:15 | | 03:15 | ||
− | | | + | | Type '''cd space simpleFoam''' and press '''Enter'''. |
|- | |- | ||
| 03:20 | | 03:20 | ||
− | | | + | | Now type '''cd channel''' and press '''Enter'''. |
|- | |- | ||
| 03:28 | | 03:28 | ||
− | | | + | | Now, type "ls" and press '''Enter'''. |
|- | |- | ||
| 03:33 | | 03:33 | ||
− | | You will see three folders '''0 , Constant and System''' | + | | You will see three folders '''0, Constant''' and '''System'''. |
|- | |- | ||
| 03:37 | | 03:37 | ||
− | | | + | | Now type '''cd constant''' and press '''Enter'''. |
|- | |- | ||
| 03:48 | | 03:48 | ||
− | | | + | | Now type "ls" and press '''Enter'''. |
|- | |- | ||
| 03:52 | | 03:52 | ||
− | | In this you will see | + | | In this, you will see files containing properties of fluid and a folder named '''polymesh'''. |
|- | |- | ||
| 03:59 | | 03:59 | ||
− | | '''RASProperties''' contains '''Reynolds-averaged stress '''model | + | | '''RASProperties''' contains '''Reynolds-averaged stress '''model. |
|- | |- | ||
|04:03 | |04:03 | ||
− | | '''transportProperties''' | + | | '''transportProperties''' contains the '''transport model '''and '''kinematic viscosity''' that is (nu), in this case is set at 0.001 m²/s. |
|- | |- | ||
| 04:17 | | 04:17 | ||
− | | Now in terminal type '''cd polyMesh and press | + | | Now in terminal, type '''cd polyMesh''' and press '''Enter'''. Now, type "ls" and press '''Enter'''. |
|- | |- | ||
| 04:30 | | 04:30 | ||
− | |You will see the '''blockMeshDict''' file here | + | |You will see the '''blockMeshDict''' file here. |
|- | |- | ||
| 04:33 | | 04:33 | ||
− | | To open up the '''blockMeshDict''' file in the terminal | + | | To open up the '''blockMeshDict''' file, in the terminal, type "gedit blockMeshDict" and press '''Enter''', scroll down. |
|- | |- | ||
| 04:48 | | 04:48 | ||
− | | The | + | | The geometry is in meters. So, the '''convertTometers''' is set to 1. Next, we have defined the vertices of the channel. |
|- | |- | ||
| 04:59 | | 04:59 | ||
− | | We have used a '''100 X 100''' | + | | We have used a '''100 X 100 mesh size''' here and '''cell spacing''' is kept as '''( 1 1 1 )'''. |
|- | |- | ||
| 05:07 | | 05:07 | ||
− | | Next we have setup the '''boundary conditions''' and their types which are '''inlet ,outlet,top and bottom ''' | + | | Next, we have setup the '''boundary conditions''' and their types which are '''inlet, outlet, top and bottom '''. |
|- | |- | ||
| 05:19 | | 05:19 | ||
− | | As this is a | + | | As this is a 2D Geometry, front and Back''' are kept as '''empty'''. |
|- | |- | ||
| 05:27 | | 05:27 | ||
− | | Also this being a | + | | Also, this being a simple geometry, '''mergePatchPair''' and '''edges''' are to be kept '''empty'''. Close the '''blockMeshDict''' file. |
|- | |- | ||
| 05:38 | | 05:38 | ||
− | | In the '''command terminal''' | + | | In the '''command terminal''', type '''cd space ..(dot dot) '''and press '''Enter'''. |
|- | |- | ||
| 05:44 | | 05:44 | ||
− | | Again type '''cd space .. (dot dot)''' and press | + | | Again, type '''cd space .. (dot dot)''' and press '''Enter'''. |
|- | |- | ||
| 05:49 | | 05:49 | ||
− | | Now in the terminal type '''cd | + | | Now. in the terminal. type '''cd space 0 (Zero)''' and press '''Enter'''. Now, type "ls" and press '''Enter'''. |
|- | |- | ||
| 05:58 | | 05:58 | ||
− | | This contains the '''intial boundary conditions ''' and''' wall functions''' for the '''channel case''' | + | | This contains the '''intial boundary conditions ''' and''' wall functions''' for the '''channel case'''. |
|- | |- | ||
| 06:05 | | 06:05 | ||
− | | It should contain various files such as '''epsilon ,k, nut,nuTilda ''' which are the '''wall functions'''and | + | | It should contain various files such as '''epsilon, k, nut, nuTilda ''' which are the '''wall functions'''and 'p' , 'R' and capital 'U' which are '''initial conditions''' of the '''flow'''. |
− | which | + | |
|- | |- | ||
|06:20 | |06:20 | ||
− | |Let me switch back to the slides | + | |Let me switch back to the slides. |
|- | |- | ||
| 06:24 | | 06:24 | ||
− | | ' | + | | Calculate 'k' which is the '''turbulent kinetic energy''' from the formula given in the slide. |
|- | |- | ||
| 06:29 | | 06:29 | ||
− | |Where | + | |Where Ux, Uy and Uz are the '''velocity''' '''components in the x, y and z directions and''' U' ( dash ) = 0.05''' times '''u''' actual. |
|- | |- | ||
| 06:43 | | 06:43 | ||
− | | Calculate '''epsilon''' from the | + | | Calculate '''epsilon''' from the formula given where epsilon is the''' rate of dissipation turbulent energy''', '''C mu''' is a '''constant''' and its value is 0.09. |
|- | |- | ||
| 06:56 | | 06:56 | ||
− | |And''' l''' is the | + | |And''' l''' is the length of the '''channel'''. Let me minimize this. |
|- | |- | ||
| 07:02 | | 07:02 | ||
− | | Change only the '''boundary names''' in each of the above '''folder''' | + | | Change only the '''boundary names''' in each of the above '''folder'''. |
|- | |- | ||
| 07:07 | | 07:07 | ||
− | | Note that the values of '''nut, nuTilda and R ''' are to kept default | + | | Note that the values of '''nut, nuTilda and R ''' are to kept default. |
|- | |- | ||
|07:13 | |07:13 | ||
− | | Rest of the | + | | Rest of the files should contain initial value for each of the '''boundary faces'''. |
|- | |- | ||
| 07:21 | | 07:21 | ||
− | | Now in the terminal | + | | Now, in the terminal, type '''cd (space) ..(dot dot)''' and press '''Enter'''. |
|- | |- | ||
| 07:27 | | 07:27 | ||
− | | There are no | + | | There are no changes to be done in the '''system''' folder. |
|- | |- | ||
| 07:31 | | 07:31 | ||
− | |Now | + | |Now we need to '''mesh''' the geometry. To do this, in the command terminal, type "blockMesh" and press '''Enter'''. |
|- | |- | ||
| 07:40 | | 07:40 | ||
− | |'''Meshing''' is done.Now | + | |'''Meshing''' is done. Now let me switch back to the '''slide'''. |
|- | |- | ||
| 07:45 | | 07:45 | ||
− | | The ''' | + | | The type of '''solver''' we are using here is '''SimpleFoam'''. It is a '''Steady-state''' solver for '''in-compressible, turbulent flow'''. |
|- | |- | ||
| 07:55 | | 07:55 | ||
− | | | + | |Let me minimize this. |
|- | |- | ||
| 07:56 | | 07:56 | ||
− | | In the | + | | In the command terminal, type "simpleFoam" and press '''Enter'''. |
|- | |- | ||
| 08:03 | | 08:03 | ||
− | | '''Iterations | + | | '''Iterations''' running will be seen in the command terminal. |
|- | |- | ||
| 08:07 | | 08:07 | ||
− | | '''Iterations '''running may take some time | + | | '''Iterations '''running may take some time. |
|- | |- | ||
| 08:11 | | 08:11 | ||
− | | The '''iterations''' will stop once the solution is | + | | The '''iterations''' will stop once the solution is converged or it reaches its '''end time value'''. |
|- | |- | ||
| 08:16 | | 08:16 | ||
− | | To view the results in ''' | + | | To view the results in '''paraView''', in the terminal, |
|- | |- | ||
| 08:20 | | 08:20 | ||
− | |type | + | |type "paraFoam" and press '''Enter'''. This will open up the '''paraview''' window. |
|- | |- | ||
| 08:28 | | 08:28 | ||
− | | On | + | | On left hand side of the '''paraView''' window, click '''Apply'''. The geometry can be seen here. |
|- | |- | ||
| 08:35 | | 08:35 | ||
− | | On top of '''active variable control | + | | On top of '''active variable control''' menu, change the drop down menu from '''solid color''' to capital '''U'''. |
|- | |- | ||
| 08:50 | | 08:50 | ||
− | | You can see the '''initial state''' of '''velocity magnitude''' at '''inlet.'''. On top of the ''' | + | | You can see the '''initial state''' of '''velocity magnitude''' at '''inlet.'''. On top of the '''paraView''' window, click on the'''play''' button of the '''VCR control'''. |
|- | |- | ||
| 09:00 | | 09:00 | ||
− | |you can see the final value of the '''velocity magnitude''' | + | |you can see the final value of the '''velocity magnitude'''. |
|- | |- | ||
| 09:07 | | 09:07 | ||
− | | Also | + | | Also toggle on the '''color legend''' from the left hand side top of '''active variable control''' menu, click '''APPLY''' again. |
|- | |- | ||
| 09:16 | | 09:16 | ||
− | | Now go to ''' | + | | Now go to '''Display''', scroll down. You can see '''Rescale''', click on it. |
|- | |- | ||
| 09:24 | | 09:24 | ||
− | | We can see that once the '''flow has fully developed | + | | We can see that once the '''flow''' has fully developed, it attains a maximum uniform velocity at the center. Now, let me switch back to the slides. |
|- | |- | ||
| 09:36 | | 09:36 | ||
− | | The results obtained can be | + | | The results obtained can be validated with the analytical solution for '''laminar flow''', in a'''channel''' which is u(max)=1.5 Uavg. |
|- | |- | ||
| 09:46 | | 09:46 | ||
− | |Using ''' | + | |Using '''openFoam''', we obtain a velocity of 1.48 meters per second which is a good match. |
+ | This brings us to the end of the tutorial. | ||
|- | |- | ||
| 09:57 | | 09:57 | ||
− | | In this tutorial we learnt | + | | In this tutorial, we learnt the File structure of '''channel''', |
− | ''' | + | obtained solution using '''steady state solver'''. |
Viewed the geometry in '''paraview ''''''Validation''' with '''analytic results''' | Viewed the geometry in '''paraview ''''''Validation''' with '''analytic results''' | ||
Line 318: | Line 320: | ||
|- | |- | ||
| 10:08 | | 10:08 | ||
− | | As an assignment | + | | As an assignment- |
− | + | solve the problem for '''Reynold Number 1500''' and '''validate''' it with the analytical result. | |
− | + | ||
− | '''validate it with the analytical result | + | |
|- | |- | ||
| 10:17 | | 10:17 | ||
− | | Watch | + | | Watch the video available at this URL: |
+ | http://spoken-tutorial.org/What_is_a_Spoken_Tutorial | ||
+ | It summarizes the Spoken Tutorial project. If you do not have good bandwidth, you can download and watch it. | ||
|- | |- | ||
| 10:28 | | 10:28 | ||
− | | The Spoken Tutorial Project | + | | 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: '''contact@spoken-tutorial.org''' | ||
|- | |- | ||
| 10:42 | | 10:42 | ||
− | | Spoken Tutorials are part of Talk to a Teacher project | + | | '''Spoken Tutorials''' are part of '''Talk to a Teacher''' project. It is supported by the National Mission on Education through ICT, MHRD, Government of India. |
|- | |- | ||
| 10:52 | | 10:52 | ||
− | |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 | ||
|- | |- | ||
| 10:57 | | 10:57 | ||
− | | This is Rahul Joshi from IIT | + | | This is Rahul Joshi from IIT Bombay, signing off. Thanks for joining. |
|} | |} |
Revision as of 13:06, 27 June 2016
Time | Narration |
00:01 | Hello and welcome to the spoken tutorial on Simulating 2D Laminar Flow in a Channel using OpenFoam. |
00:09 | In this tutorial, I will show you-
|
00:25 | To record this tutorial, I am using:
|
00:39 | Note that OpenFOAM version 2.1.1 is supported on ubuntu version 12.04. |
00:45 | Hence forth all the tutorials will be covered using OpenFOAM version 2.1.1 and ubuntu version 12.04. |
00:56 | As a prerequisite for this tutorial, you should know how to create geometry using OpenFOAM. |
01:03 | If not, please refer to the relevant tutorials on our website. |
01:09 | we simulate flow in a channel to determine flow development length along the downstream Channel flow problem description. |
01:19 | The boundary names and the inlet conditions are shown in this figure. |
01:26 | The flow develpoment length is given by the formula L= 0.05 * Re * D. |
01:32 | 'Re' which is the Reynolds number and 'D' which is the channel height. |
01:37 | Using the formula, length of the channel comes out to be 5 meters and height is kept as 1 meter. |
01:45 | The Inlet velocity is 1 meters per second. And, we are solving this for a Reynolds number ( Re ) equal 100. |
01:53 | This is a steady state problem . Therefore we are using a steady state incompressible solver for this case. |
02:01 | This is the file structure of our case. The folder should be created in the solver type that we choose. I have already created a folder in simpleFoam folder of incompressible flow solvers. |
02:18 | The folder is named as channel. Now, let me switch to the folder. |
02:25 | Copy 0, Constant and System folders of any other case file in the simpleFoam directory. |
02:34 | I have copied the file structure of the case of pitzDaily. |
02:38 | Paste it inside the channel folder and make the necessary changes in the geometry,boundary faces and boundary condition. |
02:48 | Now, let me open the command terminal. |
02:51 | To do this, press Ctrl+Alt +t keys simultaneously on your keyboard. |
02:57 | In the terminal, type run and press Enter. |
03:01 | Now type cd space tutorials and press Enter. |
03:08 | Now type cd space incompressible and press Enter. |
03:15 | Type cd space simpleFoam and press Enter. |
03:20 | Now type cd channel and press Enter. |
03:28 | Now, type "ls" and press Enter. |
03:33 | You will see three folders 0, Constant and System. |
03:37 | Now type cd constant and press Enter. |
03:48 | Now type "ls" and press Enter. |
03:52 | In this, you will see files containing properties of fluid and a folder named polymesh. |
03:59 | RASProperties contains Reynolds-averaged stress model. |
04:03 | transportProperties contains the transport model and kinematic viscosity that is (nu), in this case is set at 0.001 m²/s. |
04:17 | Now in terminal, type cd polyMesh and press Enter. Now, type "ls" and press Enter. |
04:30 | You will see the blockMeshDict file here. |
04:33 | To open up the blockMeshDict file, in the terminal, type "gedit blockMeshDict" and press Enter, scroll down. |
04:48 | The geometry is in meters. So, the convertTometers is set to 1. Next, we have defined the vertices of the channel. |
04:59 | We have used a 100 X 100 mesh size here and cell spacing is kept as ( 1 1 1 ). |
05:07 | Next, we have setup the boundary conditions and their types which are inlet, outlet, top and bottom . |
05:19 | As this is a 2D Geometry, front and Back are kept as empty. |
05:27 | Also, this being a simple geometry, mergePatchPair and edges are to be kept empty. Close the blockMeshDict file. |
05:38 | In the command terminal, type cd space ..(dot dot) and press Enter. |
05:44 | Again, type cd space .. (dot dot) and press Enter. |
05:49 | Now. in the terminal. type cd space 0 (Zero) and press Enter. Now, type "ls" and press Enter. |
05:58 | This contains the intial boundary conditions and wall functions for the channel case. |
06:05 | It should contain various files such as epsilon, k, nut, nuTilda which are the wall functionsand 'p' , 'R' and capital 'U' which are initial conditions of the flow. |
06:20 | Let me switch back to the slides. |
06:24 | Calculate 'k' which is the turbulent kinetic energy from the formula given in the slide. |
06:29 | Where Ux, Uy and Uz are the velocity components in the x, y and z directions and U' ( dash ) = 0.05 times u actual. |
06:43 | Calculate epsilon from the formula given where epsilon is the rate of dissipation turbulent energy, C mu is a constant and its value is 0.09. |
06:56 | And l is the length of the channel. Let me minimize this. |
07:02 | Change only the boundary names in each of the above folder. |
07:07 | Note that the values of nut, nuTilda and R are to kept default. |
07:13 | Rest of the files should contain initial value for each of the boundary faces. |
07:21 | Now, in the terminal, type cd (space) ..(dot dot) and press Enter. |
07:27 | There are no changes to be done in the system folder. |
07:31 | Now we need to mesh the geometry. To do this, in the command terminal, type "blockMesh" and press Enter. |
07:40 | Meshing is done. Now let me switch back to the slide. |
07:45 | The type of solver we are using here is SimpleFoam. It is a Steady-state solver for in-compressible, turbulent flow. |
07:55 | Let me minimize this. |
07:56 | In the command terminal, type "simpleFoam" and press Enter. |
08:03 | Iterations running will be seen in the command terminal. |
08:07 | Iterations running may take some time. |
08:11 | The iterations will stop once the solution is converged or it reaches its end time value. |
08:16 | To view the results in paraView, in the terminal, |
08:20 | type "paraFoam" and press Enter. This will open up the paraview window. |
08:28 | On left hand side of the paraView window, click Apply. The geometry can be seen here. |
08:35 | On top of active variable control menu, change the drop down menu from solid color to capital U. |
08:50 | You can see the initial state of velocity magnitude at inlet.. On top of the paraView window, click on theplay button of the VCR control. |
09:00 | you can see the final value of the velocity magnitude. |
09:07 | Also toggle on the color legend from the left hand side top of active variable control menu, click APPLY again. |
09:16 | Now go to Display, scroll down. You can see Rescale, click on it. |
09:24 | We can see that once the flow has fully developed, it attains a maximum uniform velocity at the center. Now, let me switch back to the slides. |
09:36 | The results obtained can be validated with the analytical solution for laminar flow, in achannel which is u(max)=1.5 Uavg. |
09:46 | Using openFoam, we obtain a velocity of 1.48 meters per second which is a good match.
This brings us to the end of the tutorial. |
09:57 | In this tutorial, we learnt the File structure of channel,
obtained solution using steady state solver. Viewed the geometry in paraview 'Validation' with analytic results |
10:08 | As an assignment-
solve the problem for Reynold Number 1500 and validate it with the analytical result. |
10:17 | Watch the video available at this URL:
http://spoken-tutorial.org/What_is_a_Spoken_Tutorial It summarizes the Spoken Tutorial project. If you do not have good bandwidth, you can download and watch it. |
10:28 | The Spoken Tutorial Project team: * Conducts workshops using spoken tutorials.
For more details, please write to: contact@spoken-tutorial.org |
10:42 | Spoken Tutorials are part of Talk to a Teacher project. It is supported by the National Mission on Education through ICT, MHRD, Government of India. |
10:52 | More information on the same is available at the following URL link: |
10:57 | This is Rahul Joshi from IIT Bombay, signing off. Thanks for joining. |