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Unformatted text preview: MODES OF HEAT TRANSFER
I: Heat is the energy transfer or exchange caused'by a temperature difference. Hence if
there is a temperature difference there shall be a heat'transfer whether the two locations ‘
of the temperature are separated by a solid, liquid, gas or vacuum. The three modes are: Conduction: Operates in solids and stationary liquids and gases (no stirring allowed). Convection: Operates in liquids and gases due to thermal stirring. Radiation: Operates in vacuum. Indeed interposition of matter impedes radiation. CONDUCTION
Transfer of heat occurs layer by layer. Higher temperature (higher kinetic energy) layer
hands over energy to a lower temperature layer thereby causing a heat “current” to “ﬂow”
from high T to low T
We will concentrate on the steady state situation. That 1s, the temperatures don’ t vary with time.
BM 3 LLLﬁ TL) {2 ' iﬂémﬁfbﬁ T2.
(Assume that there is no heat loss from the curved surfaces)
Consider a block of cross section A and length! where the temperatures are T1 (left face)
and T2 (right face).
For example: T1 = 373 K (Steam) T2 = 273 K (Ice) The heat current is equal to amount of heat ﬂow per second
DQ
At We can measure 1:? by keeping track of the amount of ice melting per second (It costs 80cal/ gm at 273K). Expts. will show that:
D_Q_
At D—Q —is proportional to— 1 or[—1—] ——is proportional to area A At 12 Ax
D_Q At —is proportional to (T —T 2) or AT DQ. and of course W 18 governed by the material of the block so the steady state equation for conduction becomes Ebmﬂ
At Ax where k = Thermal Conductivity of the material [MI]1 T“3 0“] Note the minus sign on the right of this equation. It ensures that heat always ﬂows form
high T to low T. Indeed, Typical k values
' kw N 400J/m/sec/°C
kwm, ~0.1J/m/sec/°C ' so our conducting boundary will be made of thin copper of large area while insulating
boundary would need thick wood with a small area. o‘ = 6 x 10'8 W/mz/ K4. Notice, if T goes from 300K to 900, (1?ng increases by a factor of 81! Of course, if the surroundings have temperature TS they also radiate and their
energy must go through the same surface so [E] = A 601‘,4
At m Hence , At The object will increase its T if Ts > T and will cool if Ts < T. Again, all exchange StOpS
if T5 = T.
Further, (Pg) = Ae0(TS4 — T4) (DY?) ”WT, — TXYI + ”(712+ 7Q) So if (Ts — T) << Ts and T, (T, + T) and (T,2 + T2) are essentially constant, yielding.
[29—] a. (2; — T)
At me! which is Newton’s Law of Cooling. That is, for small temperature differences, rate of
cooling, by radiation, is proportional to the temperature difference. The emissivity 6 depends on surface roughness, color etc. Rough, Dark surfaces have
ew 1. Highly polished, shiny surfaces have very low emissivity. They are shiny because
they reﬂect thereby cutting down on the leakage. CONVECTION Occurs only in liquids and gases as it involves
thermal stirring. There are no equations (aren’t we
glad!) but we can roughly understand it as follows:
let us concentrate on a layer of thickness Ay . It is in equilibrium because the sum of the forces is equal
to zero giving Apt: 7/)" gAy. Supposing we add some heat DQ to it. The ﬂuid expands and p drops, the equilibrium is disturbed, upward force becomes larger and the ﬂuid starts moving up. This will cause
the colder ﬂuid on the top to start moving down thereby setting up thermal stirring some
thing like not? WM
\ .DQ “\,
‘  " mummwzmrr Causing a net heat current upwards. Convection is a very efﬁcient process as the warm
ﬂuid carries energy rapidly tothe colder regions while the coolerﬂuid quickly makes its way to the warmer spots.
Simple example of convection is the socalled “WIND CHILL FACTOR” in winter. RADIATION
Radiation is most effective in vacuum. It is most difﬁcult to understand as it involves
knowledge of waves. For now we imagine that when any object is at a ﬁnite temperature
T, radiant heat continuously comes out of its surface because of “leakage” (i.e.
transmission) each time a “wave” hits the surface from the inside. . Radiant
' :3 “we? Energy The Heat Current depends on surface Area A, nature Of surface, emissivity e, the fourth
power of the temperature, in Kelvin T and the universal constant 0' (Stefan—Boltzmann) (g) = A eo'T4
At 0N1 ...
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 Spring '10
 Shawhan
 Physics, Heat

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