/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 54 A computer consists of an array ... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 54

A computer consists of an array of five printed circuit boards (PCBs), each dissipating \(P_{h}=20 \mathrm{~W}\) of power. Cooling of the electronic components on a board is provided by the forced flow of air, equally distributed in passages formed by adjoining boards, and the convection coefficient associated with heat transfer from the components to the air is approximately \(h=200 \mathrm{~W} / \mathrm{m}^{2}\). \(\mathrm{K}\). Air enters the computer console at a temperiture of \(T_{6}=20^{\circ} \mathrm{C}\), and flow is driven by a fin whese power consumption is \(P_{f}=25 \mathrm{~W}\). Iniet ain \(\forall_{1} T_{i}\) (a) If the tempensture rise of the air flow. \(\left(T_{e}-T_{i}\right)_{\text {is }}\) is ot to exceed \(15^{\circ} \mathrm{C}\), what is the minimum allowable volumetric flow rate \(\forall\) of the air? 'The density and specific heat of the air may be approximated is \(\rho=1.161\) \(\mathrm{kg} / \mathrm{m}^{3}\) and \(c_{p}=1007 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), respectively. (b) The component that is most suncejtible to thermal failure dissipates I W/cm \({ }^{2}\) of surface area. To minimive the potential for thermal failure, where should the component be installed on a PCB? What is its surface lemperature at this location?

Short Answer

Expert verified
The minimum allowable volumetric flow rate is 0.00715 m鲁/s. The most reliable position for the component is near the air inlet, with a surface temperature of 70掳C.

Step by step solution

01

Calculate Total Power Dissipation

The total power dissipated by the five PCBs is given by \[ P_{total, PCB} = 5 imes P_{h} = 5 imes 20 \mathrm{W} = 100 \mathrm{W}. \] Adding the fan power,\[ P_{total} = P_{total, PCB} + P_{f} = 100 \mathrm{W} + 25 \mathrm{W} = 125 \mathrm{W}. \]
02

Apply Energy Balance for Temperature Rise

Using an energy balance, the temperature rise can be expressed as:\[ \dot{m}c_{p}(T_{e}-T_{i}) = P_{total}, \]where \(\dot{m}\) is the mass flow rate. Solving for \(\dot{m}\):\[ \dot{m} = \frac{P_{total}}{c_{p} imes (T_{e}-T_{i})} = \frac{125}{1007 \times 15} \mathrm{\ kg/s} = 0.0083 \mathrm{kg/s}. \]
03

Convert Mass Flow Rate to Volumetric Flow Rate

Convert the mass flow rate \(\dot{m}\) to a volumetric flow rate \(\dot{V}\) by using the air density:\[ \dot{V} = \frac{\dot{m}}{\rho} = \frac{0.0083 \mathrm{\ kg/s}}{1.161 \mathrm{\ kg/m}^{3}} = 0.00715 \mathrm{m}^{3}/\mathrm{s}. \] Thus, the minimum allowable volumetric flow rate is \(0.00715 \mathrm{m}^{3}/\mathrm{s}\).
04

Determine Optimum PCB Location for Component

The component with the highest power density should be placed in the location with the best cooling conditions to minimize thermal failure risk. Place it closer to the air inlet, where the air is coolest.
05

Evaluate Surface Temperature

To find the PCB surface temperature, calculate the heat transfer to the air using:\[ q = \frac{P_{component}}{A}, \]where \(A\) is the surface area in \(m^{2}\). Using the convection equation: \[ q = h(T_s - T_{in}), \] where \(T_s\) is the surface temperature,\[ T_s = T_{in} + \frac{P_{component}/A}{h} = 20 + \frac{10,000}{200} = 70^\circ \mathrm{C}. \] Thus, the surface temperature is 70掳C.

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Key Concepts

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

Thermal Management
Thermal management is all about controlling the temperature of electronic components to ensure they operate efficiently and do not overheat. In electronics, maintaining the right temperature is crucial since excess heat can lead to component failure or reduced performance. Devices like computers, which contain multiple components, must efficiently dissipate heat generated during operation.
  • The basic strategy involves using cooling methods, such as fans or heat sinks, to divert heat away from sensitive areas.
  • One must ensure that the entire system, including both PCBs and external environments, is effectively managed to keep temperature rises within acceptable limits.
  • Efficient thermal management combines the selection of suitable materials and design structures that enhance heat dissipation.
Keeping these strategies in check ensures the longevity and reliability of electronic assemblies.
Forced Convection
Forced convection is a method used to increase heat transfer by using external forces, like fans or pumps, to move fluid over a surface. In computer systems, air is often forcibly circulated to remove heat from hot components, such as CPUs or PCBs.
  • The forced flow of air between PCBs significantly increases the rate of heat transfer compared to natural convection.
  • This method is particularly effective as it allows for precise control over the cooling process by adjusting the air speed and direction.
  • In our exercise, the use of a fan consumes additional power, demonstrating a practical aspect of energy consumption in thermal management systems.
By ensuring proper forced convection, systems can maintain efficiency and protect components from thermal stress.
Volumetric Flow Rate
Volumetric flow rate is crucial in defining how much air passes through a system in a given amount of time. It's an essential factor in forced convection because it determines the air's capacity to remove heat.
  • Higher flow rates typically result in better cooling as more air can absorb heat, but this must be balanced with power consumption by the fan.
  • In the exercise, calculating the minimum allowable volumetric flow rate ensures that the air can sufficiently cool down the PCBs while maintaining efficiency.
  • Volumetric flow is represented using the symbol \(\dot{V}\), usually in cubic meters per second (m鲁/s).
Understanding and calculating the correct volumetric flow rate ensures efficient cooling and prevents overheating of systems.
PCB Cooling
PCB cooling is a vital process for the proper functioning of printed circuit boards in electronic devices. As PCBs host numerous electronic components, effective cooling strategies are necessary to avoid overheating.
  • Cooling techniques can include air cooling, using fans or vents, and liquid cooling for higher efficiency needs.
  • Placements of components play a significant role; critical components are often placed near cooler air inlets.
  • In the example, the placement of the component most susceptible to thermal failure was strategically chosen to minimize the risk.
Proper PCB cooling increases reliability and performance, safeguarding against excessive temperature conditions.
Energy Balance
Energy balance is the practice of ensuring that the input energy (from all sources) is equal to the energy dissipated or used within a system. It relies on the principle of conservation of energy.
  • This concept is crucial in calculating temperature rise, as shown in the exercise.
  • For a steady state, the energy added by the components and fan must equate to the energy carried away by the airflow.
  • The balance helps in predicting outcomes like the temperature rise, enabling better design of cooling solutions like airflow management.
Maintaining energy balance allows for designing efficient systems without thermal inefficiencies, leading to better working conditions for electronic devices.

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Most popular questions from this chapter

A vacuum system, as used in sputiering electrically conducting thin films on microcircuits, is comprised of a buseplate maintained by an electrical heater at \(300 \mathrm{~K}\) and a shroud within the enclosure maintained at \(77 \mathrm{~K}\) by a liquid-nitrogen coolant loop. The circular baseplate, insulated on the lower side, is \(0.3 \mathrm{~m}\) in diameter and has an emissivity of \(0.25\). (a) How much clectrical power must be provided to the baseplate heater? (b) At what rate must liquid nitrogen be supplied to the shiroud if its heat of vaporization is \(125 \mathrm{~kJ} / \mathrm{kg}\) ? (c) To reduce the liquid-nitrogen consumption, it is proposed to bond a thin sheet of aluminura foil \((\varepsilon=0.09)\) to the baseplate. Will this have the desfred effect?

A square isothermal chip is of width \(w=5 \mathrm{~mm}\) on a side and is mounted in a substrate such that its side and bock surfaces are well insulated, while the front surface is exposed to the flow of a coolant at \(T_{w}=15^{\circ} \mathrm{C}\). From reliatility considerations, the chip temperature must not cxceed \(T=85^{\circ} \mathrm{C}\). Coclart \(\longrightarrow T_{m} h\) If the coolant is air and the corresponding convection coefficient is \(h=200 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), what is the maximum allowable chip power? If the coolant is a dielectric liequid for which \(h=3000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}^{\mathrm{K}}\), what is the maximam allowable power?

Liquid oxygen, which has a boiling point of \(90 \mathrm{~K}\) and a latent heat of vaporization of \(214 \mathrm{~kJ} / \mathrm{kg}\), is stored in a spherical container whose outer surface is of \(500-\mathrm{mm}\) diameter and at a temperature of \(-107 \mathrm{C}\). The container is housed in a laboratery whose air and walls are at \(25^{\circ} \mathrm{C}\) (a) If the surface cmissivity is \(0.20\) and the heat transfer coefficient associated with free consection at the outer surface of the container is 10 \(\mathrm{W} / \mathrm{m}^{2}+\mathrm{K}\), what is the rate, in \(\mathrm{kg} / \mathrm{s}\), at which oxygen vapor must be vented from the system? (b) Moisture in the ambient air will result in frost formation on the container, causing the surface emissivity to increase. Assuming the surface temperature and convection coefficient to remain at \(-10^{\circ} \mathrm{C}\) and \(10 \mathrm{~W} / \mathrm{m}^{2}-\mathrm{K}\), respectively, compute the oxygen evaporation rate \((\mathrm{kg} / \mathrm{s})\) as a function of surface cmissivity over the range \(0.2 \leq \varepsilon \leq 0.94\).

A furnace for processing semiconductor materials is formed by a silicon carbide chamber that is zone heated on the top section and cooled on the lower section. With the elevator in the lowest position, a robot arm inserts the silicon wafer on the mounting pins. In a production operation, the wafer is rapidly moved toward the hot zone to achieve the temperature-time history required for the process recipe. In this position the top and boltom surfaces of the wafer exchange radiation with the hot and cool rones, respectively, of the chamber. The zone temperatures are \(T_{\mathrm{a}}=1500 \mathrm{~K}\) and \(T_{c}=\) \(330 \mathrm{~K}\), and the emissivity and thickness of the wafer are \(e=0.65\) and \(d=0.78 \mathrm{~mm}\), respectively. With the ambient gas at \(T_{w}=700 \mathrm{~K}\), convection coefficients at the upper and lower surfaces of the wafer are 8 and \(4 \mathrm{~W} / \mathrm{m}^{2}-\mathrm{K}\). respectively. The silicon wafer has a den. sity of \(2700 \mathrm{~kg} / \mathrm{m}^{3}\) and a specific heat of \(875 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\). (a) For an initial condition corresponding fo a wafer tempersture of \(T_{w i}=300 \mathrm{~K}\) and the position of the wafer shawn schematically. determine the corresponding time rate of change of the wafer tempereture, \(\left(d T_{w} / d r\right)_{0}\). (b) Determine the steady state temperature reached by the wafer if it remains in this position. How significant is convection heat transfer for this situation? Sketch how you would expect the wafer temperature to vary as a function of vertical distance.

Under conditions for which the same room temperature is maintained by a heating or cooling system, it is not uncommon for a person to feel chilled in the winter but comfortable in the summer. Provide a plausible explanation for this situation (with supporting calculations) by considering a room whose air temperature is maintained at \(20^{\circ} \mathrm{C}\) throughout the year, while the walls of the room are nominally at \(27^{\circ} \mathrm{C}\) and \(14^{\circ} \mathrm{C}\) in the summer and winter, respectively. The exposed surface of a person in the room may be assumed to be at a temperature of \(32^{\circ} \mathrm{C}\) throughout the year and to have an emissivity of \(0.90\). The coefficient associated with heat transfer by natural convection between the person and the room air is approximately \(2 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\).
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