thermoserial.h File Reference

This file contains the implementation of the serial version of the heat transfer simulation in 1D and 2D. More...

#include "thermoutils.h"

Go to the source code of this file.

Functions
long double	_get_value_1D (double time_step, double space_step, long long x, unsigned long long t, long long precision)
	This is a function calculates the value of specific point in the space at specific time in 1D.
long double	_get_value_2D (double time_step, double length, double space_step_x, double width, double space_step_y, long long x, long long y, unsigned long long t, long long precision)
	This is a function calculates the value of specific point in the space at specific time in 2D.
char *	_simulate_heat_transfer_1D_serial (double time_step, double time_limit, double space_step, long long precision)
	This is a function that simulates the heat transfer in 1D object as wire, and write the result to a file.
char *	_simulate_heat_transfer_2D_serial (double time_step, double time_limit, double space_step_x, double space_step_y, long long precision)
	This is a function that simulates the heat transfer in 2D object, and write the result to a file.
double	_execution_time_heat_transfer_1D_serial (double time_step, double time_limit, double space_step, long long precision)
	This is a function that simulates the heat transfer in 1D object as wire, and return the execution time without I/O.
double	_execution_time_heat_transfer_2D_serial (double time_step, double time_limit, double space_step_x, double space_step_y, long long precision)
	This is a function that simulates the heat transfer in 2D object, and return the execution time without I/O.

Detailed Description

This file contains the implementation of the serial version of the heat transfer simulation in 1D and 2D.

In the 1D heat equation, we make a model that thermal energy flow in a 1D object so we place the object along the x-axis. We show that an object has a fixed length and lies along an interval [0, 1] under the condition of both time and thermal energy we have some conditions that affect the temperature that is time and point of x on the object. We also have thermal diffusivity that shows the rate of the temperature to be transferred to the object(how quickly the heat moves throw the object) As, we separated variables of the thermal energy problem to calculate u(x, t) we make this function separated to the function of x-axis X(x) and function of time T(t) u(x, t) = X(t) T(t) Then, we calculate the change throw the time t to get the equation u(x,t)= ∑b(n) * sin(nΠx/L) b(n)= (2/L) ∫f(x)*sin(nΠx/L)dx

In the 2D heat equation, we make a model that thermal energy flow in a 2D object, so we place the object on xy-plane under the condition of time. We represent the object by [0, a] x [0, b] as a is the length on x-axis and b is the width on y-axis, so, the tempertaure affected by function of x-axis X(x) and and y-axis Y(y) and time T(t). represented by u(x, y, t) = X(x) Y(y) T(t) Then, we separated the variables as 1D to get in each one of them the constant change as we get u(t) by using the diffusivity on u(xx) and u(yy) u(t) = c^2 (u(xx) + u(yy)) So, we get final equation to be as u(x,y,t)= ∑∑A(mn) sin(μ(m)x)sin(υ(n)y) exp(-λ(mn)t) μ(m)= mΠ/a , υ(n)=nΠ/b , λ(mn) = c√μ(m)^2 + υ(n)^2 A(mn)= 4/ab∫∫f(x,y)sin(μ(m)x)sin(υ(n)y) dy dx

Function Documentation

_execution_time_heat_transfer_1D_serial()

double _execution_time_heat_transfer_1D_serial	(	double	time_step,
		double	time_limit,
		double	space_step,
		long long	precision
	)

This is a function that simulates the heat transfer in 1D object as wire, and return the execution time without I/O.

In this simulation, we simulate heat propagation in 1D object as wire and the change in its tempreture over time using fourier transform.

Parameters

time_step	The rate of change of the time.
time_limit	The time that we want to measure the temperature of the object after.
space_step	The rate of change of the space.
precision	The number of vectors we use in the calculations.

Returns

execution time without I/O if there is no error happened interrupted the calculations.

_execution_time_heat_transfer_2D_serial()

double _execution_time_heat_transfer_2D_serial	(	double	time_step,
		double	time_limit,
		double	space_step_x,
		double	space_step_y,
		long long	precision
	)

This is a function that simulates the heat transfer in 2D object, and return the execution time without I/O.

In this simulation, we simulate heat propagation in 2D object as square or rectangle and the change in its tempreture over time using fourier transform.

Parameters

time_step	The rate of change of the time.
time_limit	The time that we want to measure the temperature of the object after.
space_step_x	The rate of change of the space in x-axis.
space_step_y	The rate of change of the space in y-axis.
precision	The number of vectors we use in the calculations.

Returns

execution time without I/O if there is no error happened interrupted the calculations.

_get_value_1D()

long double _get_value_1D	(	double	time_step,
		double	space_step,
		long long	x,
		unsigned long long	t,
		long long	precision
	)

This is a function calculates the value of specific point in the space at specific time in 1D.

In this function, we calculate the temperature of point x at time t given the rate of change of x and t, using fourier transform and the number of times we sum the series depend on the number of precision provided.

Parameters

time_step	The rate of change of the time.
space_step	The rate of change of the space.
x	The point we want to calculate the temperature at.
t	The current time we are at.
precision	The number of vectors we use in the calculations.

Returns

sum we calculated.

_get_value_2D()

long double _get_value_2D	(	double	time_step,
		double	length,
		double	space_step_x,
		double	width,
		double	space_step_y,
		long long	x,
		long long	y,
		unsigned long long	t,
		long long	precision
	)

This is a function calculates the value of specific point in the space at specific time in 2D.

In this function, we calculate the temperature of point x and y at time t given the rate of change of x, y and t, using fourier transform and the number of times we sum the series depend on the number of precision provided.

Parameters

time_step	The rate of change of the time.
length	The length of the object.
space_step_x	The rate of change of the space in x-axis.
width	The width of the object.
space_step_y	The rate of change of the space in y-axis.
x	The point in x-axis we want to calculate the temperature at.
y	The point in y-axis we want to calculate the temperature at.
t	The current time we are at.
precision	The number of vectors we use in the calculations.

Returns

sum we calculated.

_simulate_heat_transfer_1D_serial()

char * _simulate_heat_transfer_1D_serial	(	double	time_step,
		double	time_limit,
		double	space_step,
		long long	precision
	)

This is a function that simulates the heat transfer in 1D object as wire, and write the result to a file.

In this simulation, we simulate heat propagation in 1D object as wire and the change in its tempreture over time using fourier transform.

Parameters

time_step	The rate of change of the time.
time_limit	The time that we want to measure the temperature of the object after.
space_step	The rate of change of the space.
precision	The number of vectors we use in the calculations.

Returns

0 if there is no error happened interrupted the calculations, and write the output to text file named simulate_heat_transfer_1D_serial_ + current time, the row represent the time, and the column represent the temperature at this point at that time.

_simulate_heat_transfer_2D_serial()

char * _simulate_heat_transfer_2D_serial	(	double	time_step,
		double	time_limit,
		double	space_step_x,
		double	space_step_y,
		long long	precision
	)

This is a function that simulates the heat transfer in 2D object, and write the result to a file.

In this simulation, we simulate heat propagation in 2D object as square or rectangle and the change in its tempreture over time using fourier transform.

Parameters

time_step	The rate of change of the time.
time_limit	The time that we want to measure the temperature of the object after.
space_step_x	The rate of change of the space in x-axis.
space_step_y	The rate of change of the space in y-axis.
precision	The number of vectors we use in the calculations.

Returns

0 if there is no error happened interrupted the calculations, and write the output to text file named simulate_heat_transfer_2D_serial_ + current time, the output file contains paragraphs each one represent the time slot, each row represent the temperature at this point of the 2D object on x-axis (length), and the column represent the temperature at this point at that time on y-axis (width). The number of rows in each paragraph (time slot) equals length* space_step_x, and the number of columns equals width* space_step_y.