## Transient conduction in a solid material occurs every time we use an oven to cook food. The oven is heated to a high temperature, and the temperature of the food changes over time.

### engineering

##### Description

Educational Objectives

1. Become familiar with theoretical models of a spherical object that is cooled by convection

2. Measure temperature change with time of multiple heated objects, and use the models to estimate convection coefficients

3. Design and conduct your own experiment, and report out results in a presentation format.

Background

Transient conduction in a solid material occurs every time we use an oven to cook food. The oven is heated to a high temperature, and the temperature of the food changes over time. In the oven, the heat transfer mechanisms can be radiation heat transfer from the walls to the food, natural convection from the heated air currents in the oven, or for “convection” ovens, there may even be a fan in the oven that forces hot air around. Similarly, transient conduction occurs when the food cools off after the cooking process is over. In this at-home experiment, you will apply two theoretical models for the cooling process of a spherical shaped object to experimental data that your group collects. From the model, you should be able to estimate the convection coefficient that occurred during the cooling process.

Lumped Capacitance Model

For a hot object subjected to convection heat transfer at its surface with a cool air temperature, if the cooling process occurs slowly enough, the temperature distribution in the solid body may be spatially uniform due to conduction that occurs within the body. This is known as the lumped capacitance approximation (see Bergman et al., Ch. 5.1-5.2), and is generally reasonable if the Biot number (Bi) is less than 0.1: