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Session 1465

Integr ating Var ious Mathematical Tools with a Senior Mechanical Engineer ing Labor ator y Exper iment

A.B. Donaldson

Depar tment of Mechanical Engineer ing New Mexico State Univer sity

Abstract

A senior mechanical engineering laboratory utilizes a simple experiment to provide application of several mathematical tools, including: fitting of experimental data using multi-variable linear regression, integration of non-linear, ordinary differential equations, solution of the heat diffusion equation by finite difference methods, and probability and statistics. All of the required mathematical tools are available in Excel® as functions, or can be solved by using a spreadsheet. The experiment involves heating a fine, resistive wire (nichrome) by DC current from room temperature up through break (due to melting). In the first lab meeting, heat transfer analysis of the problem is applied to predict break time, considering the expected modes of heat transfer. These results are submitted to the laboratory instructor. In the second meeting, students make break-time measurements for 30, presumably identical experiments. The computed results are then compared to the experimental results, and the model is refined, if warranted, to rationalize the comparison.

I. Introduction

The senior Mechanical Engineering laboratory “Experimental Methods II” is focused on demonstration of the principles of the thermal and fluid sciences and includes group interactions with both written and oral presentation of results. Companion lectures which correspond to each exercise, reviews both the technical principles and mathematical tools to be used in that exercise. Of the six required exercises, the first four begin with a group analysis of a physical problem by application of theoretical principles and the prediction of outcome, followed by experimental measurement to verify the model which was applied. Of these, one deals with the prediction of break-time for a resistive wire that is heated by passage of sufficient current to result in electrical continuity break (melting followed by liquid beading, due to surface tension).

Metallic electrical conductors passing current may be encountered in various applications, including but not limited to fuses, hot wire ignition of pyrotechnics and explosives, illumination, and heating elements, and trip wires for strand burner timing. Models based on the conservation of energy, coupled to heat transfer and thermodynamic principles, can be analyzed by application of various mathematical tools.

Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright© 2004, American Society for Engineering Education

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Donaldson, A. (2004, June), Integrating Various Mathematical Tools With A Senior Mechanical Engineering Laboratory Experiment Paper presented at 2004 Annual Conference, Salt Lake City, Utah. 10.18260/1-2--12719