# Thermal Analysis

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**New for November 2007! **Thermal analysis is important in electronics, because reliability is related *intimately* to temperature. So much that these two often have an illegitimate child, named "Failure"!

Heat flow can be enabled by conduction, convection, and radiation. In electronics we usually rely on conduction and convection, unless we are designing for a space application where heat can only exit the payload via radiation.

### Steady state analysis

Steady-state implies that the equipment has heated up enough so that the temperature along the heat path is no longer varying with time. In the analysis, you need a heat source, and a heat sink. The heat sink is usually considered to operate at a fixed temperature.

### Transient analysis

Transient analysis is a much harder problem to analyze than steady state. Heat flow by conduction is governed by a partial differential equation, which is called Fourier's Law.

dQ/dt=-kdT/dx

where k is the thermal conductivity of the material. Its S. I. units are W/m-K

Fourier's law is an empirical. It states that the rate of heat flow, dQ/dt, through a homogeneous solid is directly proportional to the area, A, of the section at right angles to the direction of heat flow, and to the temperature difference along the path of heat flow, dT/dx. It requires knowledge of initial conditions in order to predict what happens over time. It also depends on the thermal resistance of the material, k. There are few examples of Fourier's equation being solved to a closed form expression, however, partial differential equations are quite solvable using numerical integration techniques, which is what computers were invented for.

The numerical integration of Fourier's Law is easy to understand in transient analysis where heat flows in just one dimension, of you apply conservation of energy, the first law of thermodynamics. For a thin slab of material, the heat into one face plus the heat generated within the slab must be equal to the heat out of the other face, plus the heat stored in the slab (what goes in, must come out). This "heat stored" term is where the heat capacity of teh material comes in.

More to come!

**Author : **Unknown Editor