Advanced Mechatronics, thermo mechatronics, thermal conductivity, heat transfer, mode of heat transfer, convection, conduction and radiation

1. Chapter 6
Thermo-mechatronics

2. Contents
• Heat flowing model and simulation
• Remote temperature monitoring

3. Heat flowing model and simulation
• For 2D forced heat flow
• Where u(x,y,t) is temperature at x,y at time t
and k is diffusivity given by

4. • In compact form
• Boundary conditions
– Are specific to cases
• Insulated surface
– Initial condition

5. simulation of spatial temperature
variation of SRAM
• SRAM is memory used in PC
• Influence of hot spots

6. Example
• 2D heat flow problem for thin plate of 1m by
1m
• Boundary condition
– Temp is fixed at zero at edges
• internal heat source

7. • MATLAB code
• x=0:0.01:1;
• y=0:0.01:1;
• for i=1:length(x);
• for j=1:length(y) ;
• if ((x(i)<0.5) && (y(j)<0.5))
• F(i,j)=30*sin(2*pi*x(i))*sin(2*pi*y(j));
• else
– F(i,j)=0;
• end
• end
• Mesh(x,y,F);

8. 0
0.2
0.4
0.6
0.8
1
0
0.5
30
25
20
15
10
5
0
1

9. Direct simulation
• For the direct simulation, proposed solution
• For homogenous case

10. • Re writing
• Separating into first order equations
• l, l1 and l2 are constants

11. • Using Fourier series expansion
• The solution will be
• Substituting the expression for T

12. • Re-writing

13. Example 2
• Unknown heat source located at center of
rectangular plate
• Source – fast heat source-pulse
– 0.2m diameter
– Q=106 MW heat for t<1sec
• Plate 1.2m by 2m
• Boundary condition
– Initial temperature 0 degree Celsius
– Outer boundary is thermally insulated

14. Spatial distribution of temp vs time
0
0.5
1
1.5
0
0.5
1
1.5
5
0
-5
2

15. Remote temperature monitoring
• Estimation of internal variables of a system
from measurement in the boundary
• Sensing and data acquisition from multiple
sensors
• Modeling of the field propagation of signals
and power from the input to the sensors
• Explosion sensing

16. Three important cases are

17. Estimation of heat flux input from
temperature measurement
• For single dimensional case
• Where u(x,t) is temperature at x at time t
• Exact measurement of temperature at xm at
time t

18. Remote sensing contd…
• Boundary conditions

19. Remote sensing contd…
• Solution using Fourier series expansion
• qest(0,t) is the estimated heat at distance 0
• Xm is the measurement point