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 must not exceed T = 85 degrees C.
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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,…
An array of 10 silicon chips, each of length L=10 mm on a side, is insulated on one surface and cooled on the opposite surface by atmospheric air in parallel flow with T∞=24°C and u∞=40m/s. When in use, the same electrical power is dissipated in each chip, maintaining a uniform heat flux over the entire cooled surface….
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…
Background The purpose of this design project is to design a cooling system for a power plant, which includes designing a heat exchanger and a piping system from the river to the condenser to cool the superheated steam from the Rankine cycle. The Rankine cycle produces 1.4MW of power from the steam turbine. The average…
A blood warmer is to be used during the transfusion of blood to a patient. This device is to heat blood taken from the Blood Bank at 10°C to 37°C at a flow rate of 200 mL/min. The blood passes through tubing of length 2 m, with a rectangular cross-section of 6.4 mm x 1.6…
Consider the geometry of Problem 2.14 for the case where the thermal conductivity varies with temperature as k = ko + aT. where ko = 10W/m-K, a =-10-3 W/m-K2, and T is in kelvins. The gradient at surface B is partial differential T/partial differential x = 30 K/m. What is partial differential T/partial differential y at…