Answer to Question #180739 in Material Science Engineering for Jessica

Question

A well-designed drill bit minimizes the risk of burning your fingers when you remove the bit from the drill. To achieve that goal, an important design objective is to minimize the heat flow along its length while simultaneously making sure the drill bit doesn’t mechanically fail during operation. Assume the maximum temperature generated at the drill bit tip is attained quickly and remains constant so that the temperature gradient, Δ𝑇, along the shaft is constant with time. The length, L, of the shaft is fixed but its radius, R, is variable.

a.Derive the material index for this application. Assume the heat, q, flow is:

𝑞=(𝜆Δ𝑇𝜋𝑅^2)/𝐿 where 𝜆 is the thermal conductivity,and the failure torque is:𝑇f=(𝜋𝑅^3𝜎y)/4 Start the problem by listing the objective, constraints and free variables

Answer 1

Components have functions: to carry loads safely, to transmit heat, to store energy, to insulate, and so forth. Each function has an associated material index. Materials with high values of the appropriate index maximize that aspect of the performance of the component.

Heat sinks, maximum thermal flux, thermal expansion prescribed α/𝜆