Lecture 2: Fundamentals. Sourav Saha

Transcription

1 ME 267: Mechanical Engineering Fundamentals Credit hours: 3.00 Lecture 2: Fundamentals Sourav Saha Lecturer Department of Mechanical Engineering, BUET address: Personal website My Google Scholar Page 1

2 Why study heat transfer when there is thermodynamics? Thermodynamics tells us about the quantity of heat transfer from one equilibrium state to another but it doesn t give any indication about how long this transfer process will take. Thermodynamics (equilibrium thermodynamics) is more concerned with the equilibrium states while heat transfer actually tells us about the rate of energy transfer. However, science of heat transfer is based on thermodynamics. 2

3 Some definitions Internal Energy, U, is defined as the sum of all microscopic forms of energy in a system. This includes energy due to various levels of microscopic activities. Specific heat, C, is defined as the heat energy required to increase the temperature of a unit mass of substance by one degree. Common unit is kj/kgk. The sensible heat transfer through any incompressible substance can be modeled as, U Q m C T Here Q is the heat transfer. In rate form we may denote this as Q 3

4 Definition of Heat Transfer Energy can be transferred from and to a given mass by two mechanisms: heat transfer and work transfer. When the transfer of energy from one system to another or from one substance to another is solely due to the temperature difference the energy interaction is called heat transfer. The rate of heat transfer per unit area normal to the direction of heat transfer is called the heat flux, q. Unit is J/m 2 q Q A 4

5 Heat Transfer Mechanisms There are three modes of heat transfer from hot region to cold region: A) Conduction B) Convection C) Radiation. 5

6 Conduction Bangladesh University of Engineering and Technology Conduction is the transfer of thermal energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between particles. Conduction can take place in solid, liquids, gases and even in plasmas. Thermal conductivity When the dimension x tends to zero, This simple law is known as the Fouriers s Law of heat conduction. 6

7 Conduction Bangladesh University of Engineering and Technology Thermal Conductivity, k, is defined as the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference. This is the measure of a material s ability to transfer heat. Unit of thermal conductivity is W/mK. Crystalline solids have a high value of k. Thermal conductivity of gases and insulating materials is much less than that of metals. Why? 7

8 Mechanism of Conduction From the definition of conduction we know this method is nothing but the transfer of energy from energetic molecules to non-energetic ones through vibration. This is the basic mechanism. So the phase of substance which facilitates this transfer process must possess higher thermal conductivity. 8

9 Mechanism of Conduction In gaseous substances, molecules move randomly and collide with each other in the process. These molecules are far from each other and hence the only way to transfer energy is collide and change momentum much like two tennis balls do when they collide with each other. This makes the thermal transport weaker in gases. However, from kinetic theory of gas we know, 1 2 m v k T B So we see velocity is proportional to the square root of thermodynamic (absolute) temperature T. Guess what else is proportional to square root of T?? Thermal conductivity of gases! In a similar manner we can see that k of gases is inversely proportional to the square root of their molar mass, M. 9

10 Mechanism of Conduction In liquids, the molecules are more closely spaced compare to gases. But the distance between those is still larger than that of solids. So, thermal conductivity lies somewhere between gases and solids. Unlike gases, thermal conductivity of liquids decreases with increase in temperature (water being an exception). This behavior of liquids can be explained by Bridgman s equation Fig. 1. Case of water k 2 3 N 2.8 k v. B s V Here, V is the molar volume which is proportional to the temperature and key factor governing the thermal conductivity of fluids. Thermal conductivity of fluids is also inversely proportional to the molar mass. This is information can be derived from the Bridgman s equation too. 10

11 Mechanism of Conduction Conductivity of the solid substances is the highest. Thermal conduction in solids can be attributed to two mechanisms: 1) Lattice Vibration. 2) Transport of free electron. Lattice vibrational waves carry the energy from one part of the substance to another in solid. Metals typically have a relatively high concentration of free conduction electrons, and these can transfer heat as they move through the lattice. Phonon-based conduction also occurs, but the effect is swamped by that of electronic conduction. 11

12 Mechanism of Conduction Thermal conductivity of solids is obtained by adding the lattice vibration and electronic transport components. This is why metals (which have plenty of electrons) are good conductors of heat. Lattice vibrational component of the thermal conductivity depends on how ordered the lattice is. This is why diamond has the highest known thermal conductivity. There are some crystalline solids like diamond and semiconductors like silicon which have high thermal conductivity but relatively poor electrical conductivity. These materials are very popular in electronics industry. Some recent materials are reported to have very high thermal conductivity. For example, experiments found graphene has thermal conductivity in the order of 2500 W/mK. Single wall Carbon nanotubes also have thermal conductivities around 2000 W/mK. [Thermal properties of graphene and nanostructured carbon materials, Alexander A. Balandin,Nature Materials 10, (2011)]. Coupled with their excellent mechanical attributes these are the materials for future. Some other 2D materials like silicene, stanene, germanene, etc are showing great potentials. 12

13 Mechanism of Conduction One would think that alloys, composed of two metals, must have higher thermal conductivities than both of the parent metals. But actually opposite happens. Alloys are reported to have very low thermal conductivities. This happens due to disruption of vibrational transport thorough the lattice of alloys. 13

14 Mechanism of Conduction Thermal conductivity of solid is also dependent on temperature. Moreover, in anisotropic materials this property varies spatially. Temperature dependence of solids causes considerable complexities in calculation. This is why throughout this course we shall assume this to be constant. For the same reason, all materials will be assumed isotropic. Thermal diffusivity is a property frequently used in transient heat conduction and defined as, k c. 14

15 Convection Bangladesh University of Engineering and Technology Convection is the mode of heat transfer between a solid surface and adjacent liquid or gas in motion. It involves combined effect of conduction and liquid motion. Convection = conduction + advection Presence of bulk fluid motion is compulsory for convection. Without it, the heat transfer is just conduction. 15

16 Convection Bangladesh University of Engineering and Technology Convection can be classified in many ways. For the time being, on the basis of governing mechanism, we shall classify it into natural and forced convection. Natural convection: When the driving force of fluid motion is the buoyant force arising due to temperature gradient in the fluid the convection mechanism is natural convection. Forced convection: When bulk fluid motion is created by external means like pump, fan or blower the convection is known as forced convection. 16

17 Convection: Newton s Law of cooling Sir Isaac Newton took a break from discovering calculus and saving the world to find a simple and elegant way (as always) to find heat transfer due to convection Q & h A ( T T ) s s THIS GUY AGAIN!!!!! Here, h is the convective heat transfer coefficient. A s is the surface area over which convection is taking place. T s is the temperature of the heated surface. and T α is the convective fluid s temperature. The study of convection is centered around finding the value of h for different cases involving complex geometries, different fluids, different velocities, etc. 17

18 Radiation Bangladesh University of Engineering and Technology Radiation is the energy emitted by the matter in the form of electromagnetic waves as a result of the changes in electronic configurations of the atoms or molecules. Anything with a finite temperatures emits some thermal radiation. This mode of heat transfer doesn t require any medium to transfer heat. Heat transfer due to radiation is expressed by, 4 4 Q& A ( T T ). s s s u r r Here σ is the Stefan-Boltzman constant = W/m 2 K 4. ε is the emissivity of the surface. A s is the surface area. T s is the temperature of the surface. T surr is the surrounding temperature. 18

19 That s it for today. Some problems on the topic will be covered in next lecture. EID MUBARAK! Enjoy your vacation. 19