effect of temperature on thermal conductivity of metals

 Effect of Temperature on Thermal Conductivity of Heat Transfer 

Today we are going to learn the review of heat transfer thermal conductivity effect of thermal conductivity on solids liquids and gases electrical analogy and thermal

Heat energy is the energy transfer across the boundary of a system because of the temperature difference and heat transfer is the transfer of heat from one substance to another substance provided that there must be temperature difference generally heat flows from heat reservoir to heat sink.

We have studied three modes of heat could heat transfer that is Conduction, Convection, and Radiation 

so we have learned conduction is the transfer of heat from one part of a substance to another part of the same without appreciable displacement of molecule and conduction takes place in two ways is by lattice vibration and by transfer of free electrons lattice vibration means there is a different molecular structure in solids liquids and gases as we supply heat energy the molecule vibrates with respect to its mean position when one molecule vibrates or collide with another heat transfer takes place that is known as by lattice vibration.

 In the case of liquids and gases generally, heat is transferred by lattice vibration through conduction process but in the case of metals in the case of solids generally, heat transfer takes place by free electrons every solids-free electrons are there when heat energy is supplied to that solid it's free electrons get energized and it carries heat energy from one part of the metal to another part of metal convection is the transfer of heat within a fluid by mixing one portion of the fluid with other or with an appreciable displacement of the molecule.

We are seeing why wind flows when the wind is heated it loses its density it goes up?

It is replaced by new cold air again it is heated it goes up in this way light wind it flows up it is replaced by a new cold air and wind flows similarly when water is heated the water which is in contact with heat it becomes light it goes up it is replaced by new cold water again it is heated it goes up and in.

This way convection current starts generally convection is of two types free convection that is natural convection which does not require any mechanical means here the transfer of molecule takes place automatically for example when forced convection enforce convection we require mechanical means like blower pump etc motor etc.

Radiation is the transfer of heat through space or matter or by other than conduction or convection radiation does not require any medium radiation is thought of electromagnetic wave means heat is carried in the form of electric electromagnetic wave that is contacted in an earlier lecture we have seen for yourself it conduction the statement of Fourier law of heat conduction walls the rate of flow of heat through a simple homogeneous solid is directly proportional to the area of section at right angles to the direction of feed flow and to the change of temperature with respect to the length of the path of heat flow let us take an example when a metal draws when a metal rod is heated with help of candle a flame of candle what will happen the heat will flow from open-end towards hand and here the heat transfer takes place with the help of free electrons.

The conduction equation by Fourier law is given as Q in the direction X, Q X is equal to (-DT) upon (DX) where,

QX is the heat transferred across

X-direction

K represents thermal conductivity of that material a is the area right angles to the direction of heat transfer DT upon DX is the temperature gradient.

 Newton's law of cooling the rate of heat loss of a body per unit area is directly proportional to the difference in temperature between the body and its surrounding let's example let me have earlier seen when water is heated with help of burner here the cold water it loses its density it becomes less dense and that hot water rises it is shown with help of a red arrow it is replaced by cold water which is denser again it is heated again it goes up so in this way it forms convection current and that convection rate of the equation is given with help of Newton's law of cooling Q is equal to H a TW (-T) infinity where Q is the heat transfer through convection H is the convective heat transfer coefficient a is the area through which heat transfer takes place.

kW is the temperature of water in this case or temperature of that surface and D infinity is the surrounding temperature thermal conductivity the amount of heat conducted through unit area and unit thickness in unit time when the temperature difference between the phases causing heat flow is unit difference that is known as thermal conductivity its expression can be rearranged from four years law K is equal to Q upon a DX upon DT its SI unit is fat per meter degree centigrade or vat per meter Kelvin so thermal conductivity generally depends on material structure whether it is a solid porous or any structure moisture content in that material or gas density of material and operating temperature and pressure the Y thermal conductivity is important do you know thermal conductivity decides the amount of heat transfer through conduction more the thermal conductivity more is the heat transfer capability so one table is shown here first material is silver which is having highest thermal conductivity its value is 410 van per meter Kelvin second copper 385 aluminum 225 ad per meter Kelvin so these materials has high thermal conductivity means it has high capability to transfer heat if you consider few bottom material and is glass wool sawdust water free on its thermal conductivity is zero point zero three zero point zero seven zero point zero zero eight three as the thermal conductivity is less its heat conduction properties are less means those materials are act as insulator so thermal conductivity of any material it may be metal it may be fluid it is due to flow of free electrons and lattice vibrations that we are already seen in case of metal generally thermal conductivity is due to flow of free electrons in case of fluids that is liquids and gases thermal conductivity is generally dependent on lattice vibration so we will see first effect of temperature on thermal conductivity of metals so first we will see solids generally thermal conductivity of most metal decreases with increase in temperature and there are two exceptional cases aluminium and uranium one graph is shown here thermal conductivity versus temperature almost in all metals starting from copper gold platinum iron carbon steel and stainless steel thermal conductivity decreases with increasing temperature why does it happen can you guess this is because in metals generally heat transfer takes place by free electrons as we have already studied due to increase in temperature the violently vibrating particle obstruct the path of this free electron that's why thermal conductivity of most of the metal decreases with increasing temperature because of obstruction of free electron that's why we can write in case of metal thermal conductivity is inversely proportional to temperature thermal conductivity in case of pure metal is the highest and it decreases with increasing impurity more the impurity added in pure metal its thermal conductivity goes on decreases in general the relationship between thermal conductivity and temperature can be expressed as K is equal to k0 into bracket 1 plus 80 plus BT square plus C T cube where K is thermal conductivity of any solid or you can consider metal here k naught is thermal conductivity of that solid at zero degree centigrade T is the temperature at which we have to find out

thermal conductivity ABC these are the arbitrary constants now we will consider effect of temperature on thermal conductivity on nonmetals in case of nonmetals the conduction is solely due to lattice vibration means if you supply heat energy as the temperature increases particles vibrate violently with higher frequency that's why as the temperature increases its thermal conductivity also increases again when graph is shown thermal conductivity versus temperature and three to four nonmetals are shown that is Raider bricks concrete bricks which are generally used for building construction third one is fire bricks that's why in summer season as the temperature of this material increases its thermal conductivity also increases that why in summer we feel warmer and warmer because it's heat carrying capacity increases in case of mineral wool also thermal conductivity increases as temperature increases this is because the number of collisions per unit time increases with increase in temperature

we will consider in case of liquids for most of the liquids thermal conductivity is inversely proportional to temperature except water why does it happen because in case of liquids thermal conductivity is dependent on its density so as temperature increases density decreases

and in most of the liquids the value of thermal conductivity decreases with increasing temperature so there is an inverse relation of temperature and thermal conductivity in the case of liquids here there is exceptional that is water but remaining all liquids on including alcohol thermal conductivity decreases with increase in temperature also thermal conductivity is found to be a function of temperature as well as pressure effect of temperature on gases in case of cases generally heat transfer takes place by lattice vibration in gases molecule collide with other

molecule now as the temperature of the gas increases the collisions number of collisions increases yes thermal conductivity of gases is directly

proportional to temperature so one graph is shown different gases are shown and almost all gases starting from water vapor oxygen-carbon dioxide air and nitrogen and argon thermal conductivity increases as temperature increases because as temperature increases it results in violent vibration of the molecule also in case of gases thermal conductivity is found to be a function of temperature pressure and humidity remember in different season humidity of air is also different it will affect on thermal conductivity now coming to electrical analogy when two physical systems are described by similar equations and have similar boundary conditions

these are said to be analogous the heat transfer process is analogous with electricity in an electrical register as the flow of electrical current in the electrical resistance is directly proportional to potential difference this is Ohm's law similarly we can write heat flow that is heat transfer rate is directly proportional to temperature difference DT the heat of flow calculations through the composite structure can be easily worked using a technique that is known as an electrical analogy.