## I3 Heat Transfer

Heat transfer is the branch of engineering science that deals with the prediction of energy transport caused

The ratio k/pC is also a material property called thermal diffusivity u. Appendix II gives thermophysical properties of many common engineering materials.

For steady, one-dimensional conduction with no heat generation,

D T dx2

This will give T = ax + b, a simple linear relationship between temperature and distance. Then the application of Fourier's law gives

a simple expression for heat transfer across the Ax distance. If we apply this concept to insulation for example, we get the concept of the R value. R is just the resistance to conduction heat transfer per inch of insulation thickness (i.e., R = 1/k).

Multilayered, One-Dimensional Systems. In practical applications, there are many systems that can be treated as one-dimensional, but they are composed of layers of materials with different conductivities. For example, building walls and pipes with outer insulation fit this category. This leads to the concept of overall heat-transfer coefficient, U. This concept is based on the definition of a convective heat-transfer coefficient,

This is a simplified way of handling convection at a boundary between solid and fluid regions. The heat-transfer coefficient h represents the influence of flow conditions, geometry, and thermophysical properties on the heat transfer at a solid-fluid boundary. Further discussion of the concept of the h factor will be presented later.

Figure I.4 represents a typical one-dimensional, multilayered application. We define an overall heat-transfer coefficient U as

Q = UA (Ti - To) We find that the expression for U must be

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