Temperature Distribution. The temperature distribution in a thin metal plate wit

Question

Temperature Distribution. The temperature distribution in a thin metal plate with constant (or isothermal) termperatures on each side can be modeled using a two-dimensional grid. Typically, the number of points in the grid are specified, as are the constant temperatures on the four sides. The temperatures of the interior points are usually initialized to zero, but they change accordng to the temperatures around them. Assume that the temperature of an interior point can be computed as the average of the four adjacent temperatures. Each time that the temperature of an interior point changes, the temperatures of the points adjacent to it change. These changes continue until a thermal equilibrium is achieved and all temperatures become constant.

- Write a program to model this temperature distribution for a grid with six rows and eight columns. Allow the user to enter the temperatures for the four sides. Use one grid to store the temperatures. Thus, when a point is updated, its new value is used to update the next point. Continue updating the points, moving across the tolerance value. Use the vector class to implement the grid.

Explanation / Answer

main()
readfile()
writefile()
SetBoundary()

Following getting a lineup of functions you'll need, you need to attain the temperature equation. An iterative scheme will have something like this

T = T + dT

dT will be positive or negative based on your boundary conditions, but you will need to choose an expression for dT. usually the simplest for that I use is a central differencing method.

in 1D with equal grid spacing is something like this.

dT(i) = [ T(i-1) - 2*T(i) + T(i+1) ] / 2*dx

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.