Chemical Engineering 6453 Heat Transfer Prof. Geoff Silcox Spring 2005 Homework Assignment 5 Due Wednesday, 16 February, by 17:00.

Problem 1 Consider the MATLAB code, plate.m and associated files, that is linked to the schedule under 9 February. Validate that code by (a) making sure that it produces a symmetrical temperature field when the BC’s and source term are symmetrical and by (b) performing an energy balance on the plate to ensure that the energy from the source is lost to the edges.

Problem 2 The following problem is copied, with small changes from Glen E. Myers text, Analytical Methods in Conduction Heat Transfer, AMCHT Publications, Madison, WI (1998), ISBN 0-9666065-0-7, p. 378. Please reply to the following memo. To: H. T. Expert From: P. D. Hot Subject: Evaluation of Heat Meter Is the heat meter, described by the attached flyer, suitable for measuring heat-transfer rates of about 10,000 W/m2 from an ambient at 400 K to an isothermal wall at 300 K? The following questions have arisen. 1. Is the temperature rise of the sensing plate less than 20 percent of the

temperature difference between the wall and the ambient so that the wall might still be assumed isothermal?

2. Can the thickness of the sensing plate be altered to make the device more suitable for our needs if it is found to have too large a temperature difference across it?

3. Is the meter reading really proportional to the total heat flux entering the sensing plate as implied by the Beehive Engineering Company?

4. Can this device be used, as is, to make accurate heat-flux measurements in flow fields where the average heat-transfer coefficient for the sensing disk is unknown? If not, can you suggest any modifications that would allow the device to be used in such an application?

Beehive Engineering Company Salt Lake City, Utah

Our engineering department has recently developed an improved heat meter for measuring local heat-transfer rates. It is finding wide acceptance for measurement of convective heat-transfer rates. The heat-meter sensor consists of a thin, square sensing plate mounted over an evacuated cavity in a heat sink. It is thermally and electrically bonded to the heat sink at the perimeter of the cavity. As heat is transferred to the sensing plate from a convective heat source, it flows along the plate into the sink. Since the plate is thin compared to its width, a temperature difference is generated between the center and edge which is directly proportional to the rate of heat transfer to the sensor. By making the plate from a thermoelectric material such as constantan and attaching wires of a second thermoelectric metal such as copper at the center and edge, a differential thermocouple is generated to allow measuring the temperature difference. The signal is proportional to the heat flux. The device is sketched below. Let our sales staff show you how this device can solve your heat flux measurement challenges.

Outputsignal

Heat sink, T0

1.2 mm

2.5 cm

Center wireEdgewire

Problem 3 Read Lesson 15 of the notes posted on the web (see link at Monday, 14 February). Find the analytical solution to Equation III.A.1.