Transfer of Heat
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| Discuss Transfer of Heat TRANSFER OF HEAT
The flow of heat from one body to another or from one place to another is called the transference of heat. Basically, there are three modes of transfer of heat conduction, convection and radiation.
THERMAL CONDUCTION
This is the slowest mode of heat transmission, where the energy is transferred from the hotter end to the cooler end of the body, due to the collisions of molecules or atoms. In the case of metals, free electrons also conduct heat by travelling from warmer to the cooler end. Thus, the conductivity in metals is high as compared to those materials in which there are no free electrons.
NOTE: conduction is possible only due to the vibration and collision of the molecules or by free electrons.
THERMAL CONDUCTIVITY
Thermal conductivity is defined as the measure of the ability of a substance to conduct heat. Quantitatively it can be defined as the quantity of heat conducted per unit time per unit area per unit temperature gradient. If H be the quantity of heat conducted from one part of a substance to the other part in a time t and the difference in temperatures is DT, then
|
H = -KA DT t /l |
Where K is the coefficient of thermal conductivity. Its unit is Wm-1K-1. ( the negative sign is due to T2 - T1 and since T1 > T2)
TEMPERATURE GRADIENT
Temperature gradient is defined as the rate of change of temperature with distance in the direction of heat flow. Mathematically it is given as -d q /dx.
STEADY STATE HEAT FLOW
When heat is given to one surface of the body, it travels through the body and comes out of the other surface. In the beginning, when the two surfaces of the body are at two different temperatures, the heat supplied to one end does not completely come out of the other end. A part of the heat supplied is absorbed by the material for its own heating, so that the material may have a particular temperature gradient. Finally, a state comes when the temperature gradient is established and no part of the body takes heat takes heat for its own heating. So whatever heat is given to the body at one end, comes out of the other end completely.
This thermal state of the body is called its steady state, and the heat flow in this case is called steady state heat flow.
THERMAL RESISTANCE
Thermal resistance is defined as a measure of the opposition to the heat flow offered by the substance. It is given by
|
R = -DT/H |
DT/H = l/KA
Or,
| R = l/KA |
COMBINATION OF THERMAL RESISTANCES
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SERIES COMBINATION
The resulting resistance in the case of series combination of conducting substances, as shown in the figure, is given by
| R = R1 + R2 |
|
K = (l1+ l2)/ [ (l1/K1) + (l2/K2) ] |
NOTE: if the cross section is variable as shown in the diagram then we take into account the effective area, i.e. the common area.
PARALLEL COMBINATION
In the case of parallel combination the resulting resistance is given by
|
R = 1/R1 + 1/R2 |
|
K = [K1 A1+ K2/A2 ]/ [A1 +A2] |
NOTE: in this case all the lines on the common surface will be isothermal lines, and the temperature is same throughout any vertical plane.
CONVECTION
In convection the heat is transferred from one place to another by the actual motion of the heated material. If the heated material in the case of convection is forced to move then the convection is termed as forced convection. If the material is able to move freely then it is termed as a natural of free convection.