To determine the effect of the temperature dependence of the thermal conductivity on the temperature distribution in a solid, consider a material for which this dependence may be represented as k = ko + aT where ko is a positive constant and a is a coefficient that may be positive or negative. Sketch the steady-state…
Assume steady-state, one-dimensional heat conduction through the symmetric shape shown. Assuming that there is no internal heat generation, derive an expression for the thermal conductivity k(x) for these conditions: A(x) = (1 – x), T(x) = 300(1 – 2x – x3), and q = 6000 W, where A is in square meters, T in kelvins,…
Consider the conditions of problem 1.22. However, now the plate is in a vacuum with a surrounding temperature of 25 C. What is the emissivity of the plate? What is the rate at which radiation is emitted by the surface? All sample problem and notes are based off the following textbook: Fundamentals of Heat and…
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…
Radioactive wastes are packed in a long, thin-walled cylindrical container. The wastes generate thermal energy nonuniformly according to the relation q = qo [1 – (r/ro)2], where q is the local rate of energy generation per unit volume, qo is a constant, and ro is the radius of the container. Steady-state conditions are maintained by…
A square isothermal chip is of width w = 5 mm on a side and is mounted in a substrate such that its side and back surfaces are well insulated, while the front surface is exposed to the flow of a coolant at T infinity = I5 degree C. From reliability considerations, the chip temperature…
Chips of width L = 15 mm on a side are mounted to a substrate that is installed in an enclosure whose walls and air are maintained at a temperature of Tsur =T=25C. The chips have an emissivity of ε = 0.60 and a max allowable temperature of Ts = 85 C. (a) If heat…
A transmission case measures W = 0.30 m on a side and receives a power input of Pi= 150 hp from the engine. If the transmission efficiency is η=0.93 and air flow over the case corresponds T =30 degree C and h=200 W/m2-K. What is the surface temperature of the transmission? All sample problems and notes…
The free convection heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observations of the change in plate temperature with time as it cools. Assuming the plate is isothermal and radiation exchange with its surroundings is negligible, evaluate the convection coefficient at the instant of time when…
An electric resistance heater is embedded in a long cylinder of diameter 30mm. When water with a temperature of 25degree C and velocity of 1 m/s flows crosswise over the cylinder, the power per unit length required to maintain the surface at a uniform temperature of 90degreeC is 28kW/m. When air is also at 25…