Chapter 6

Thermo-mechatronics

Contents

• Heat flowing model and simulation• Remote temperature monitoring

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

• In compact form

• Boundary conditions – Are specific to cases • Insulated surface

– Initial condition

simulation of spatial temperature variation of SRAM

• SRAM is memory used in PC• Influence of hot spots

Example

• 2D heat flow problem for thin plate of 1m by 1m

• Boundary condition – Temp is fixed at zero at edges

• internal heat source

• 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);

00.2

0.40.6

0.81

0

0.5

10

5

10

15

20

25

30

Direct simulation

• For the direct simulation, proposed solution

• For homogenous case

• Re writing

• Separating into first order equations

• , 1 and 2 are constants

• Using Fourier series expansion

• The solution will be

• Substituting the expression for T

• Re-writing

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

Spatial distribution of temp vs time

0

0.5

1

1.5

0

0.5

1

1.5

2-5

0

5

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

Three important cases are

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

Remote sensing contd…

• Boundary conditions

Remote sensing contd…

• Solution using Fourier series expansion

• qest(0,t) is the estimated heat at distance 0 • Xm is the measurement point