2. Electrical components often failure due to thermal overload. It follows that thermal analysis of electrical components is critical to their longevity. Consider a silicon chip which is sitting atop a ceramic substrate with 35 mm2 of exposed surface area. Operating at steady state, the chip can pull up to 120 mW of power. The chip surface is cooled by convection from flowing air at 20°C. The heat transfer from the chip to the air is given by Q = hA(T, – T,) where h is the thermal convection coefficient, A is the exposed surface area, and Tb and Tr are absolute temperatures of the body and coolant fluid, respectively. h of the flowing air is found to be 250 W/(m2-K). Assuming heat transfer to the substrate is negligible compared to convection, determine: a. the heat transfer occurring at steady state (W) b. the temperature at the outer surface of the chip (C)

2. Electrical components often failure due to thermal overload. It follows that thermal analysis of electrical components is critical to their longevity. Consider a silicon chip which is sitting atop a ceramic substrate with 35 mm2 of exposed surface area. Operating at steady state, the chip can pull up to 120 mW of power. The chip surface is cooled by convection from flowing air at 20°C. The heat transfer from the chip to the air is given by Q = hA(T, – T,) where h is the thermal convection coefficient, A is the exposed surface area, and Tb and Tr are absolute temperatures of the body and coolant fluid, respectively. h of the flowing air is found to be 250 W/(m2-K). Assuming heat transfer to the substrate is negligible compared to convection, determine: a. the heat transfer occurring at steady state (W) b. the temperature at the outer surface of the chip (C)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

2. Electrical components often failure due to thermal overload. It follows that thermal analysis of
electrical components is critical to their longevity. Consider a silicon chip which is sitting atop a
ceramic substrate with 35 mm2 of exposed surface area. Operating at steady state, the chip can
pull up to 120 mW of power. The chip surface is cooled by convection from flowing air at 20°C.
The heat transfer from the chip to the air is given by
Q = hA(T, – T)
where h is the thermal convection coefficient, A is the exposed surface area, and Tb and Tr are
absolute temperatures of the body and coolant fluid, respectively. h of the flowing air is found
to be 250 W/(m2-K). Assuming heat transfer to the substrate is negligible compared to
convection, determine:
the heat transfer occurring at steady state (W)
the temperature at the outer surface of the chip ("C)
a.
b.

Expert Solution

Step 1

a) In steady state condition

Q_in = Q_out = 0.12 W

b) T_b = 33.71 deg C

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A solar collector and storage tank, shown in Figure (a) below, is to be optimized to achieve minimum first cost. During the day the temperature of water in the storage vessel is elevated from 25 °C (the minimum useful temperature) to tmax, as shown in Figure (b). The collector receives 260 W/m² of solar energy, but there is heat loss from the collector to ambient air by convection. The convection coefficient is 2 W/(m²*K), and the average temperature difference during the 10-hour day is (25 + tmax)/2 minus the ambient temperature of 10 °C. The energy above the minimum useful temperature of 25 °C that is to be stored in the vessel during the day is 200,000 kJ. The density of water is 1000 kg/m³, and its specific heat is 4.19 kJ/(kg*K). The cost of the solar collector in dollars is 20A, where A is the area in square meters, and the cost of the storage vessel in dollars is 101.5V, where V is the volume in cubic meters. Storage tank Collector (a) Temperature, °C tmax conforte 25°C, lowest…