


PROBLEM Description
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/* This program works for two dimensional heat conduction problem with constant thermal conductivity*/


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# The length of the domain along X direction = 1 meter 
# The length of the domain along Y direction = 0.2 meter 
# Thermal conductivity = (Conductivity/(Density*Specific_heat)) = (43/(7800*473)) watts per meter centigrade 
# Number of nodes in X direction = 20 
# Number of nodes in Y direction = 10
# End Simulation time is taken = 1.0
# Maximum number of iterations = 6000
Boundary Condition:
# Temperature at left edge =  80 centigrade
# Temperature at Right edge =  20 centigrade
# Temperature at Bottom edge =  30 centigrade
# Temperature at Top edge =  60 centigrade



Note: The Temperature at the corner nodes are set as averages of both sides

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Note:Input Minimum number of threads=2 and Maximum number of threads=8


 How to compile and run the program in Linux:

 If its a GNU compiler:
$ g++ -lm -o omp2d  -fopenmp omp_heat-equation-2d.cpp
 $ ./omp2d

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If its a Intel compiler:
$ icc  -o omp2d -openmp omp_heat-equation-2d.cpp
 
$ ./omp2d
 
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Output:
It prints the number of iterations and the maximum wall time taken for the program to execute. 
On execution the tempareture value for the corresponding (i,j) node (where i is between 0 to 19 and j is between 0-9) be printed in "output_test.dat" file"omp_2D_Heat_Equation.dat".In  file. In "omp_2D_Heat_Equation.dat" it prints . 
In "omp_output_iter.txt" it prints the iteration.
In  "output_test.dat" in the first column it prints the discretized length along X and in the next column it prints the temperature at(i,5) where i is between 0-19. This values are validated with the standard Open source CFD s/w OpenFOAM temperature values in "Heat_2D.txt" file.

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