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modes_of_heat_transfer

modes_of_heat_transfer - MODES OF HEAT TRANSFER I Heat is...

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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 so-called “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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