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MECH 3040: Heat Transfer Spring 2013

Design Project: Due Last day of classes

You are expected to do this project entirely on your own. See me if you have questions.

Project description

A manufacturer of CPU chips is soliciting designsfor heat sinks. Their chip has a 6 cm 6 cm sur-face area, and the design operating temperatureof the chip is 50 C. The heat sink is to be madefrom a rectangular block of aluminum, with abase matching that of the chip and a height ofH =5 cm. Rectangular channels are machined inthe aluminum, as illustrated in the figure.

The tops of the channels are covered with a thinaluminum plate. Each channel therefore providesa closed flow passage. Air is forced through thechannels by means of a fan and a duct. The specsof the fan can be found at www.jameco.com.Your task is to find a design which will max-imize the rate of heat transfer from the chip.This design will specify 1) the number of chan-nels NC and 2) the channel width w. The thick-ness of the wall separating one channel from theother, denoted as t, will depend on NC and w viaW = (NC + 1)t + NCw, where W = 6 cm. Theminimum allowable wall thickness is 0.5 mm.

The project will combine extended surfaceheat transfer and internal flow analysis. The ba-

sic tasks in performing a design analysis, for testvalues ofNC and t, will be

1. Determine the pressure drop across the flowchannels and the resulting volumetric flowrate and mass averaged velocity. The specsfor the fan given in the link provide a) themaximum flow rate provided by the fan and2) the stagnation pressure (the pressure in-crease when there is no net flow); thesetwo quantities can be used, when combinedwith pipe flow analysis, to predict the flowrate for a given channel configuration.

2. Determine the perimeteraveraged heattransfer coefficient for the channel. Theheat transfer conditions can be modeled asconstant surface temperature; this is an ap-proximation, as the side walls will behaveas extended surfaces and the temperature

will drop from the bottom (base) to the topof the wall. Relations in Ch. 8 for rectan-gular channels will be useful. Developingflow conditions should be addressed: theflow length may not be adequately long forconditions to become fully developed (andthis may be a benefit as far as the designobjectives are concerned).

3. Use fin efficiency relations, combined withthe heat transfer coefficient determinedabove, to obtain an overall heat transfer co-efficient which characterizes the heat trans-fer from the chip surface to the fluid.

4. Use the overall heat transfer coefficient inthe energy equation to obtain the fluid out-let temperature and the net heat transferrate.

We will discuss the project in class, I am sure.

http://www.jameco.com/1/1/3406-afb0612vhd-dc-brushless-tubeaxial-fan-bearing-type-ball.html