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#include <stdio.h>
#include <stdlib.h>
// HEAT TRANSFER SIMULATION
//
// Simple physical simulation of a rod connected at the left and right
// ends to constant temperature heat/cold sources. All positions on
// the rod are set to an initial temperature. Each time step, that
// temperature is altered by computing the difference between a cells
// temperature and its left and right neighbors. A constant k
// (thermal conductivity) adjusts these differences before altering
// the heat at a cell. Use the following model to compute the heat
// for a position on the rod according to the finite difference
// method.
//
// left_diff = H[t][p] - H[t][p-1];
// right_diff = H[t][p] - H[t][p+1];
// delta = -k*( left_diff + right_diff )
// H[t+1][p] = H[t][p] + delta
//
// Substituting the above, one can get the following
//
// H[t+1][p] = H[t][p] + k*H[t][p-1] - 2*k*H[t][p] + k*H[t][p+1]
//
// The matrix H is computed for all time steps and all positions on
// the rod and displayed after running the simulation. The simulation
// is run for a fixed number of time steps rather than until
// temperatures reach steady state.
int main(int argc, char **argv)
{
int max_time = 50; // Number of time steps to simulate
int width = 20; // Number of cells in the rod
double initial_temp = 50.0; // Initial temp of internal cells
double L_bound_temp = 20.0; // Constant temp at Left end of rod
double R_bound_temp = 80.0; // Constant temp at Right end of rod
double k = 0.5; // thermal conductivity constant
double **H; // 2D array of temps at times/locations
// Allocate memory
H = malloc(sizeof(double *) * max_time);
int t, p;
for (t = 0; t < max_time; t++)
{
H[t] = malloc(sizeof(double *) * width);
}
// Initialize constant left/right boundary temperatures
for (t = 0; t < max_time; t++)
{
H[t][0] = L_bound_temp;
H[t][width - 1] = R_bound_temp;
}
// Initialize temperatures at time 0
t = 0;
for (p = 1; p < width - 1; p++)
{
H[t][p] = initial_temp;
}
// Simulate the temperature changes for internal cells
for (t = 0; t < max_time - 1; t++)
{
for (p = 1; p < width - 1; p++)
{
double left_diff = H[t][p] - H[t][p - 1];
double right_diff = H[t][p] - H[t][p + 1];
double delta = -k * (left_diff + right_diff);
H[t + 1][p] = H[t][p] + delta;
}
}
// Print results
printf("Temperature results for 1D rod\n");
printf("Time step increases going down rows\n");
printf("Position on rod changes going accross columns\n");
// Column headers
printf("%3s| ", "");
for (p = 0; p < width; p++)
{
printf("%5d ", p);
}
printf("\n");
printf("%3s+-", "---");
for (p = 0; p < width; p++)
{
printf("------");
}
printf("\n");
// Row headers and data
for (t = 0; t < max_time; t++)
{
printf("%3d| ", t);
for (p = 0; p < width; p++)
{
printf("%5.1f ", H[t][p]);
}
printf("\n");
}
return 0;
}
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