HeatTransport - previous index Heat Transport: Conduction,...

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previous index Heat Transport: Conduction, Convection, Radiation Michael Fowler Conduction If different parts of an isolated solid are at different temperatures, heat will flow from the hot places to the cold ones until eventually all is at the same temperature. By “isolated” here we mean that the solid is not able to exchange heat with the outside world. Experimentally, it is found that for most substances the rate of heat flow at any point is proportional to the temperature gradient—how fast the temperature is changing with position. To give an example, consider heat flowing down a thin rod, heated at one end, and assume the rod is wrapped in insulation so all the heat flows down the rod, none escapes from the surface. The natural unit of heat flow down the rod is how many joules per second pass a fixed point in the rod. It is found that: dQ dT dt dx where Q is in joules, T in degrees Kelvin, x is meters down the rod. The heat flow rate is then in joules per second, or watts. It is evident from this equation that if heat is supplied at a steady rate to one end of the rod, and drains from the other end, the temperature distribution will ultimately settle down to = constant, a linear drop along the rod from one end to the other. / dT dx It is also found experimentally that a rod of double the cross-section carries twice the heat current at the same temperature difference. (This is also true for electric current, but remember it is not true for water in a pipe—the “caloric” fluid evidently doesn’t act like a viscous liquid.) This makes it possible to define a coefficient of thermal conductivity κ for a particular material by dQ A dt = for heat flow across an area A (in square meters) for a given temperature gradient .
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HeatTransport - previous index Heat Transport: Conduction,...

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