WAHYUDIICP FISIKA 2011THERMAL CONDUCTIONIn heat transfer, conduction (or heat conduction) is a mode of transfer of energy withinand between bodies of matter, due to a temperature gradient. Conduction means collisional anddiffusivetransfer of kineticenergythroughparticles of ponderablematter (as distinct fromphotons). Conduction takes place in all forms of ponderable matter, such as solids, liquids, gasesand plasmas. Heat spontaneously tends to flow from a body at a higher temperature to a body at alower temperature. In the absence of eternal driving flues, temperature differences, over time,approach thermal equilibrium.In conduction, the heat flows through the body itself, as opposed to its transfer by the bulkmotionof thematter asinconvection, andbythermal radiation. Insolids, it isduetothecombination of vibrations of the molecules in a lattice or phonons with the energy transported byfreeelectrons. Ingasesandliquids, conductionisduetothecollisionsanddiffusionofthemolecules during their random motion. !hotons in general do not collide with one another andthermal transport by electromagnetic radiation is not regarded as conduction of heat. In solids, itis not simple toseparate transfer byphotons fromtransfer byponderable matter, but thedistinction can be more easily made in liquids, and is routinely made in gases. In the engineeringsciences,heat transfer includestheprocessesofthermalradiation,convection,andsometimesmass transfer. "suallymore thanone of these processes occurs ina givensituation. #heconventional symbol for the material property, thermal conductivity, is.$namicroscopicscale, conductionoccursasrapidlymovingorvibratingatomsandmoleculesinteract with neighboring particles, transferring some of their kinetic energy. Heat istransferred by conduction when ad%acent atoms vibrate against one another, or as electrons movefrom one atom to another. Conduction is the most significant means of heat transfer within a solidor between solid ob%ects in thermal contact. Conduction is greater in solids because the networkofrelativelyclosefiedspatialrelationshipsbetweenatomshelpstotransferenergybetweenthem by vibration.&luids (and especially gases) are less conductive. #his is due to the large distance betweenatoms in a gas' fewer collisions between atoms means less conduction. Conductivity of gasesincreases with temperature. Conductivity increases with increasing pressure from vacuum up to acritical point that the density of the gas is such that molecules of the gas may be epected tocollide with each other before they transfer heat from one surface to another. (fter this pointconductivityincreases onlyslightlywith increasing pressure and density.#hermal contactWAHYUDIICP FISIKA 2011conductance is the study of heat conduction between solid bodies in contact. ( temperature dropis often observed at the interface between the two surfaces in contact. #his phenomenon is said tobe a result of a thermal contact resistance eisting between the contacting surfaces.Interfacialthermal resistanceis a measure of an interface)s resistance tothermal flow. #his thermalresistance differs fromcontact resistance, as it eists evenat atomicallyperfect interfaces."nderstandingthe thermal resistance at the interface betweentwomaterials is of primarysignificance in the study of its thermal properties. Interfaces often contribute significantly to theobserved properties of the materials.#he inter*molecular transfer of energy could be primarily by elastic impact as in fluids orby free electron diffusion as in metals or phonon vibration as in insulators. In insulators the heatflu is carried almost entirely by phonon vibrations. +etals (e.g. copper, platinum, gold,etc.) areusually good conductorsof thermal energy. #his is due to the way that metals are chemicallybonded' metallic bonds (as opposed to covalent or ionic bonds) have free*moving electrons whichare able to transfer thermal energy rapidly through the metal. #he ,electron fluid, of a conductivemetallic solid conducts most of the heat flu through the solid. !honon flu is still present, butcarries less of the energy. -lectrons also conduct electric current through conductive solids, andthethermalandelectrical conductivitiesof mostmetalshaveabout thesameratio. (goodelectrical conductor, such as copper, also conducts heat well. #hermoelectricity is caused by theinteraction of heat flu and electrical current. Heat conduction within a solid is directly analogousto diffusion of particles within a fluid, in the situation where there are no fluid currents.#oquantifytheeasewithwhichaparticularmediumconducts, engineersemploythethermalconductivity, also known astheconductivity constant orconductioncoefficient,k. Inthermal conductivitykis defined as ,the quantity of heat, ., transmitted in time (t) through athickness (/), in a direction normal to a surface of area ((), due to a temperature difference (0#)1...2., #hermal conductivity is a materialpropertythat is primarily dependent on the medium)sphase, temperature, density, and molecular bonding. #hermal effusivity is a quantity derived fromconductivity which is a measure of its ability to echange thermal energy with its surroundings.3teadystateconductionistheformofconductionthat happenswhenthetemperaturedifference(s) driving the conduction are constant, so that (after an equilibration time), the spatialdistributionoftemperatures(temperaturefield)intheconductingob%ectdoesnotchangeanyfurther. #hus, all partial derivatives of temperature with respect to spacemay either be 4ero orhavenon4erovalues, but all derivativesoftemperatureat anypointwithrespect totimeareWAHYUDIICP FISIKA 2011uniformly 4ero. In steady state conduction, the amount of heat entering any region of an ob%ect isequal toamount ofheat comingout(ifthiswerenotso, thetemperaturewouldberisingorfalling, as thermal energy was tapped or trapped in a region).For example, a bar may be cold at one end and hot at the other, but after a state of steadystate conduction is reached, the spatial gradient of temperatures along the bar does not changeany further, as time proceeds. Instead, the temperature at any given section of the rod remainsconstant,andthistemperature varies linearly in space,along the direction ofheattransfer. Insteady state conduction, all the laws of direct current electrical conduction can be applied to ,heatcurrents,. In such cases, it is possible to take ,thermal resistances, as the analog to electricalresistances. In such cases, temperature plays the role of voltage, and heat transferred per unit time(heat power) is the analog of electrical current. 3teady state systems can be modelled by networksof such thermal resistances in series and in parallel, in eact analogy to electrical networks ofresistors. 3ee purely resistive thermal circuits for an eample of such a network.#he law of heat conduction, also known as &ourier)s law, states that the time rate of heattransfer through a material is proportional to the negative gradient in the temperature and to thearea, at right angles to that gradient, through which the heat is flowing. 5e can state this law intwo equivalent forms' the integral form, in which we look at the amount of energy flowing into orout of a body as a whole, and the differential form, in which we look at the flow rates or flues ofenergy locally. #he form of &ourier)s /aw of thermal conduction shows that the localheat fludensity, q, is equal to the product of thermal conductivity, k, and the negative local temperaturegradient, -T. #he heat flu density is the amount of energy that flows through a unit area per unittime.q= -k Twhere (including the 3I units)q is the local heat flu, 56m78k is the material)s conductivity, 56m796:79,-T is the temperature gradient, :6m79.#he thermal conductivity, k, is often treated as a constant, though this is not always true. 5hilethe thermalconductivityofamaterial generally varieswith temperature,thevariation canbesmall over a significant range of temperatures for some commonmaterials. Inanisotropicmaterials, the thermal conductivity typically varies with orientation; in this case k is representedby a second*order tensor. In nonuniform materials, k varies with spatial location.WAHYUDIICP FISIKA 2011ONDU!I THERMAL