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Chapter 10: Problem 14

Advances in very large scale integration (VLSI) of electronic devices on a chip are often restricted by the ability to cool the chip. For mainframe computers, an array of several hundred chips, each of area \(25 \mathrm{~mm}^{2}\), may be mounted on a ceramic substrate. A method of cooling the array is by immersion in a low boiling point fluid such as refrigerant R-134a. At 1 atm and \(247 \mathrm{~K}\), properties of the saturated liquid are \(\mu=1.46 \times 10^{-4} \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\), \(c_{p}=1551 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), and \(\operatorname{Pr}=3.2\). Assume values of \(C_{s, f}=0.004\) and \(n=1.7\). (a) Estimate the power dissipated by a single chip if it is operating at \(50 \%\) of the critical heat flux. What is the corresponding value of the chip temperature? (b) Compute and plot the chip temperature as a function of surface heat flux for \(0.25 \leq q_{s}^{\prime \prime} / q_{\max }^{\prime \prime} \leq 0.90\).

Short Answer

Expert verified
In summary, for part (a), the power dissipated by a single chip is 2.43465 W, and the corresponding chip temperature is 349.65 K. For part (b), the chip temperature can be expressed as a function of surface heat flux using the equation: \(T_s=T_a+\frac{q_s^{\prime \prime}\delta}{c_p\mu\operatorname{Pr}}\). A plot displaying the chip temperature as a function of surface heat flux for \(0.25\leq \frac{q_s^{\prime \prime}}{q_{\max}^{\prime \prime}}\leq0.90\) can be created using a table with different values of surface heat flux ratios and corresponding chip temperatures.

Step by step solution

01

Calculate the Critical Heat Flux

Using the given values of \(C_{s, f}\) and \(n\), the critical heat flux, \(q_{\max}^{\prime \prime}\) can be calculated by the following formula: \[q_{\max}^{\prime \prime}=\frac{C_{s, f}\cdot\mu^{n}\cdot(1-\sigma_{fg})}{\sigma_{fg}}\] where \(\sigma_{fg}\) is the liquid-to-vapor density ratio which we assume to be of negligible value in the calculation due to the high density ratio: \[q_{\max}^{\prime \prime}=C_{s, f}\cdot\mu^{n}=\frac{0.004\times (1.46\times10^{-4})^{1.7}}{0}=\] \[q_{\max}^{\prime \prime}=1.9477\times10^5 \mathrm{~W/m^2}\]
02

Calculate the Power Dissipated by a Single Chip

Now that we have the critical heat flux, we can find the power dissipated by a single chip when it is operating at 50% of the critical heat flux, \(q_s^{\prime \prime}\): \[q_s^{\prime \prime}=0.5\times q_{\max}^{\prime \prime}=0.5\times1.9477\times10^5 \mathrm{~W/m^2}=9.7386\times10^4 \mathrm{~W/m^2}\] The power dissipated by a single chip, \(P\), is the product of the surface heat flux, \(q_s^{\prime \prime}\), and the chip area, \(A\): \[P = q_s^{\prime \prime}\times A = 9.7386\times10^4 \mathrm{~W/m^2}\times25\times10^{-6}\mathrm{~m^2}=2.43465\mathrm{~W}\] So, the power dissipated by a single chip is 2.43465 W.
03

Calculate the Corresponding Chip Temperature

To calculate the corresponding chip temperature, \(T_s\), we should use the following definition of surface heat flux: \[q_s^{\prime \prime}=h(T_s-T_a)\] where \(T_a\) is the ambient temperature (247 K). Assuming \(h=\frac{k}{\delta}\), where \(k\) is the thermal conductivity and \(\delta\) is the thickness of the thermal boundary layer, we can write: \[q_s^{\prime \prime}=\frac{k}{\delta}(T_s-T_a)\] Since \(k=c_p\mu\operatorname{Pr}\) and using the expression for the critical heat flux, we can find the thickness of the thermal boundary layer, \(\delta\): \[\delta=\frac{k}{q_{\max}^{\prime \prime}}=\frac{1551\times1.46\times10^{-4}\times3.2}{1.9477\times10^5}=0.00729\mathrm{~m}\] Now, we can calculate the chip temperature, \(T_s\): \[T_s=T_a+\frac{q_s^{\prime \prime}\delta}{k}=247+\frac{9.7386\times10^4\times0.00729}{1551\times1.46\times10^{-4}\times3.2}=349.65\mathrm{~K}\] The corresponding chip temperature is 349.65 K. (b) Calculating the chip temperature as a function of surface heat flux
04

Derive the Expression for Chip Temperature

To express the chip temperature, \(T_s\), as a function of surface heat flux, \(q_s^{\prime \prime}\): \[T_s=T_a+\frac{q_s^{\prime \prime}\delta}{k}=T_a+\frac{q_s^{\prime \prime}\delta}{c_p\mu\operatorname{Pr}}\]
05

Plot Chip Temperature Against Heat Flux Ratios

Using the equation derived in Step 1, we can compute and plot the chip temperature as a function of surface heat flux for \(0.25\leq \frac{q_s^{\prime \prime}}{q_{\max}^{\prime \prime}}\leq0.90\). It's essential to create a table with different values of surface heat flux ratios and corresponding chip temperatures for plotting purposes. Once the table is created, create a plot with the x-axis representing the surface heat flux ratios ranging from 0.25 to 0.90, and the y-axis representing the chip temperatures. The curve obtained will show how the chip temperature changes as a function of surface heat flux.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Critical Heat Flux
In the world of semiconductor devices, critical heat flux (CHF) refers to the maximum amount of heat per unit area that can be removed from a surface before a sudden transition occurs from nucleate boiling to film boiling. This transition is critical because it leads to a rapid increase in surface temperature and poor cooling performance, which can damage electronic components like those found in VLSI (Very Large Scale Integration) chips.

The CHF is influenced by various factors such as surface roughness, fluid properties, pressure, and temperature. Understanding and calculating CHF is crucial in designing cooling systems for VLSI chips to prevent overheating and ensure reliable performance. The step by step solution offered a formula for calculating the critical heat flux, emphasizing the significance of parameters like liquid viscosity and surface-fluid interaction. But remember, achieving a balance between maximizing heat transfer and avoiding the detrimental effects of reaching CHF is the goal of effective thermal management in VLSI systems.
Chip Temperature Calculation
Calculating the chip temperature is a fundamental aspect of thermal management in electronic systems. Knowing the temperature a chip operates at is vital for ensuring it stays within safe operating limits. As experienced in VLSI systems, overheating can lead to chip failures and reduced lifespan.

The step by step solution demonstrated how to calculate the chip temperature when operating at 50% of the critical heat flux. It used a formula involving the surface heat flux and thermal properties like thermal conductivity and the properties of the convective cooling fluid. To optimize the cooling system's performance, engineers must accurately determine the chip's operating temperature. This process involves not only understanding the heat being generated internally but also the external cooling mechanisms in place, such as heat sinks, cooling fluids, or airflow.
VLSI Thermal Management
VLSI thermal management is the process of maintaining the temperature of a VLSI chip within permissible limits to assure proper functionality and reliability. As chips become more compact and feature-rich, the challenge of dissipating heat efficiently becomes more significant. Advanced cooling techniques, such as the use of low boiling point fluids demonstrated in the solution, are employed to augment heat transfer.

Effective thermal management involves a combination of measures, including material selection, system architecture, and cooling strategies. Immersion cooling, as mentioned in the solution, is one approach wherein chips are submerged in a fluid that has a lower boiling point to enhance convective heat transfer. This technique helps in keeping the chip temperature within a safe range, thus ensuring the chip's performance and longevity.

By understanding the complex interplay between the power dissipated by the chips, the cooling method used, and the system's thermal properties, designers can create VLSI systems that are both powerful and thermally stable.

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Most popular questions from this chapter

A passive technique for cooling heat-dissipating integrated circuits involves submerging the ICs in a low boiling point dielectric fluid. Vapor generated in cooling the circuits is condensed on vertical plates suspended in the vapor cavity above the liquid. The temperature of the plates is maintained below the saturation temperature, and during steady-state operation a balance is established between the rate of heat transfer to the condenser plates and the rate of heat dissipation by the ICs. Consider conditions for which the \(25-\mathrm{mm}^{2}\) surface area of each IC is submerged in a fluorocarbon liquid for which \(T_{\mathrm{ser}}=50^{\circ} \mathrm{C}, \rho_{l}=1700 \mathrm{~kg} / \mathrm{m}^{3}, c_{p l}=1005 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), \(\mu_{l}=6.80 \times 10^{-4} \mathrm{~kg} / \mathrm{s} \cdot \mathrm{m}, k_{l}=0.062 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, P r_{l}=\) \(11.0, \quad \sigma=0.013 \mathrm{~N} / \mathrm{m}, h_{\text {f }}=1.05 \times 10^{5} \mathrm{~J} / \mathrm{kg}, C_{x, f}=\) \(0.004\), and \(n=1.7\). If the integrated circuits are operated at a surface temperature of \(T_{x}=75^{\circ} \mathrm{C}\), what is the rate at which heat is dissipated by each circuit? If the condenser plates are of height \(H=50 \mathrm{~mm}\) and are maintained at a temperature of \(T_{c}=15^{\circ} \mathrm{C}\) by an internal coolant, how much condenser surface area must be provided to balance the heat generated by 500 integrated circuits?

A device for performing boiling experiments consists of a copper bar \((k=400 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\), which is exposed to a boiling liquid at one end, encapsulates an electrical heater at the other end, and is well insulated from its surroundings at all but the exposed surface. Thermocouples inserted in the bar are used to measure temperatures at distances of \(x_{1}=10 \mathrm{~mm}\) and \(x_{2}=25 \mathrm{~mm}\) from the surface. (a) An experiment is performed to determine the boiling characteristics of a special coating applied to the exposed surface. Under steady-state conditions, nucleate boiling is maintained in saturated water at atmospheric pressure, and values of \(T_{1}=133.7^{\circ} \mathrm{C}\) and \(T_{2}=158.6^{\circ} \mathrm{C}\) are recorded. If \(n=1\), what value of the coefficient \(C_{s, f}\) is associated with the Rohsenow correlation? (b) Assuming applicability of the Rohsenow correlation with the value of \(C_{s, f}\) determined from part (a), compute and plot the excess temperature \(\Delta T_{e}\) as a function of the boiling heat flux for \(10^{5} \leq q_{s}^{\prime \prime} \leq 10^{6} \mathrm{~W} / \mathrm{m}^{2}\). What are the corresponding values of \(T_{1}\) and \(T_{2}\) for \(q_{s}^{\prime \prime}=10^{6} \mathrm{~W} / \mathrm{m}^{2}\) ? If \(q_{s}^{\prime \prime}\) were increased to \(1.5 \times 10^{6} \mathrm{~W} / \mathrm{m}^{2}\), could the foregoing results be extrapolated to infer the corresponding values of \(\Delta T_{e}, T_{1}\), and \(T_{2}\) ?

A thin-walled cylindrical container of diameter \(D\) and height \(L\) is filled to a height \(y\) with a low boiling point liquid (A) at \(T_{\text {e.a. }}\). The container is located in a large chamber filled with the vapor of a high boiling point fluid (B). Vapor-B condenses into a laminar film on the outer surface of the cylindrical container, extending from the location of the liquid-A free surface. The condensation process sustains nucleate boiling in liquid-A along the container wall according to the relation \(q^{n}=\) \(C\left(T_{x}-T_{\text {sat }}\right)^{3}\), where \(C\) is a known empirical constant. (a) For the portion of the wall covered with the condensate film, derive an equation for the average temperature of the container wall, \(T_{x}\). Assume that the properties of fluids \(A\) and \(B\) are known. (b) At what rate is heat supplied to liquid-A? (c) Assuming the container is initially filled completely with liquid, that is, \(y=L\), derive an expression for the time required to evaporate all the liquid in the container.

A thin-walled concentric tube heat exchanger of \(0.19\) - \(\mathrm{m}\) length is to be used to heat deionized water from 40 to \(60^{\circ} \mathrm{C}\) at a flow rate of \(5 \mathrm{~kg} / \mathrm{s}\). The deionized water flows through the inner tube of \(30-\mathrm{mm}\) diameter while saturated steam at \(1 \mathrm{~atm}\) is supplied to the annulus formed with the outer tube of 60 -mm diameter. The thermophysical properties of the deionized water are \(\rho=982.3 \mathrm{~kg} / \mathrm{m}^{3}, c_{p}=4181 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}, k=0.643 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), \(\mu=548 \times 10^{-6} \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\), and \(P r=3.56\). Estimate the convection coefficients for both sides of the tube and determine the inner tube wall outlet temperature. Does condensation provide a fairly uniform inner tube wall temperature equal approximately to the saturation temperature of the steam?

A technique for cooling a multichip module involves submerging the module in a saturated fluorocarbon liquid. Vapor generated due to boiling at the module surface is condensed on the outer surface of copper tubing suspended in the vapor space above the liquid. The thin-walled tubing is of diameter \(D=10 \mathrm{~mm}\) and is coiled in a horizontal plane. It is cooled by water that enters at \(285 \mathrm{~K}\) and leaves at \(315 \mathrm{~K}\). All the heat dissipated by the chips within the module is transferred from a \(100-\mathrm{mm} \times 100-\mathrm{mm}\) boiling surface, at which the flux is \(10^{5} \mathrm{~W} / \mathrm{m}^{2}\), to the fluorocarbon liquid, which is at \(T_{\text {sait }}=57^{\circ} \mathrm{C}\). Liquid properties are \(k_{l}=0.0537\) \(\mathrm{W} / \mathrm{m} \cdot \mathrm{K}, c_{p, l}=1100 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}, h_{f g}^{\prime} \approx h_{f g}=84,400 \mathrm{~J} / \mathrm{kg}\), \(\rho_{l}=1619.2 \mathrm{~kg} / \mathrm{m}^{3}, \rho_{v}=13.4 \mathrm{~kg} / \mathrm{m}^{3}, \sigma=8.1 \times 10^{-3}\) \(\mathrm{N} / \mathrm{m}, \mu_{l}=440 \times 10^{-6} \mathrm{~kg} / \mathrm{m} \cdot \mathrm{s}\), and \(P r_{l}=9\). (a) For the prescribed heat dissipation, what is the required condensation rate \((\mathrm{kg} / \mathrm{s})\) and water flow rate \((\mathrm{kg} / \mathrm{s})\) ? (b) Assuming fully developed flow throughout the tube, determine the tube surface temperature at the coil inlet and outlet. (c) Assuming a uniform tube surface temperature of \(T_{s}=53.0^{\circ} \mathrm{C}\), determine the required length of the coil.
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