6. Cooling of a silicon chip [35 points]: A silicon chip measuring 551mm is embedded in a
substrate as in the figure. The chip generates an amount of waste heat Q=0.03W. Although the
bottom and sides of the chip are insulated, the top surface is exposed to air flow and subject to
both radiation and convective heat transfer. The radiation heat transfer Jrad (W) can be
determined using the StefanBoltzmann law: Jrad=A(T4Ts4). Additionally, the convective heat J
covv(W) is given by: Jconv=hA(TTs). Note that: A is the area in m2. is the emissivity and here is
taken to be 0.9 . is the Stefan-Boltzmann constant which is 5.67108W/m2K4. T is the ambient
temperature which is 293.15K. Ts is the surface temperature of the chip and here is unknown. h is
the convective heat transfer coefficient and is 50W/m2K. Under steady state conditions we can
write the following balance equation Q=Jrad+Jconv. [Hint: Q has to be substituted as -0.03 since it
is loss to the environment]. You are asked to find the value of the surface temperature using both
fixed point iteration and Newton-Raphson methods employing MATLAB functions which you will
develop for this problem. The user specifies two initial guesses and a stopping eriterion and the
function then: 2 (i) determines the surface temperature Ts using both methods. (ii) It should report
the number of iterations of each method. (iii) Plots the approximate percent relative error using
both methods as a function of the number of iterations. Add labels and legends. Also make sure
the y-axis is logarithmic. (iv) Perform a test case using 340K and 350K as initial guesses and 106
% as a stopping criterion..
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6 Cooling of a silicon chip 35 points A silicon chip mea.pdf
1. 6. Cooling of a silicon chip [35 points]: A silicon chip measuring 551mm is embedded in a
substrate as in the figure. The chip generates an amount of waste heat Q=0.03W. Although the
bottom and sides of the chip are insulated, the top surface is exposed to air flow and subject to
both radiation and convective heat transfer. The radiation heat transfer Jrad (W) can be
determined using the StefanBoltzmann law: Jrad=A(T4Ts4). Additionally, the convective heat J
covv(W) is given by: Jconv=hA(TTs). Note that: A is the area in m2. is the emissivity and here is
taken to be 0.9 . is the Stefan-Boltzmann constant which is 5.67108W/m2K4. T is the ambient
temperature which is 293.15K. Ts is the surface temperature of the chip and here is unknown. h is
the convective heat transfer coefficient and is 50W/m2K. Under steady state conditions we can
write the following balance equation Q=Jrad+Jconv. [Hint: Q has to be substituted as -0.03 since it
is loss to the environment]. You are asked to find the value of the surface temperature using both
fixed point iteration and Newton-Raphson methods employing MATLAB functions which you will
develop for this problem. The user specifies two initial guesses and a stopping eriterion and the
function then: 2 (i) determines the surface temperature Ts using both methods. (ii) It should report
the number of iterations of each method. (iii) Plots the approximate percent relative error using
both methods as a function of the number of iterations. Add labels and legends. Also make sure
the y-axis is logarithmic. (iv) Perform a test case using 340K and 350K as initial guesses and 106
% as a stopping criterion.
![6. Cooling of a silicon chip [35 points]: A silicon chip measuring 551mm is embedded in a
substrate as in the figure. The chip generates an amount of waste heat Q=0.03W. Although the
bottom and sides of the chip are insulated, the top surface is exposed to air flow and subject to
both radiation and convective heat transfer. The radiation heat transfer Jrad (W) can be
determined using the StefanBoltzmann law: Jrad=A(T4Ts4). Additionally, the convective heat J
covv(W) is given by: Jconv=hA(TTs). Note that: A is the area in m2. is the emissivity and here is
taken to be 0.9 . is the Stefan-Boltzmann constant which is 5.67108W/m2K4. T is the ambient
temperature which is 293.15K. Ts is the surface temperature of the chip and here is unknown. h is
the convective heat transfer coefficient and is 50W/m2K. Under steady state conditions we can
write the following balance equation Q=Jrad+Jconv. [Hint: Q has to be substituted as -0.03 since it
is loss to the environment]. You are asked to find the value of the surface temperature using both
fixed point iteration and Newton-Raphson methods employing MATLAB functions which you will
develop for this problem. The user specifies two initial guesses and a stopping eriterion and the
function then: 2 (i) determines the surface temperature Ts using both methods. (ii) It should report
the number of iterations of each method. (iii) Plots the approximate percent relative error using
both methods as a function of the number of iterations. Add labels and legends. Also make sure
the y-axis is logarithmic. (iv) Perform a test case using 340K and 350K as initial guesses and 106
% as a stopping criterion.](https://image.slidesharecdn.com/6coolingofasiliconchip35pointsasiliconchipmea-230321055539-f45c0515/85/6-Cooling-of-a-silicon-chip-35-points-A-silicon-chip-mea-pdf-1-320.jpg)
