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DEPARTMENT OF MECHANICAL ENGINEERING V -semester Heat transfer UNIT NO. 01 INTRODUCTION TO BASIC MODES OF HEAT TRANSFER

CHAPTER 1:- SYLLABUS Introduction to Heat Transfer Modes of Heat Transfer Laws of Heat Transfer General Heat Conduction Equation in Cartesian, Cylindrical and Spherical Coordinate. One dimensional steady state heat Conduction Equation. Thermal resistance Critical thickness of insulation. DTEL 3

LECTURE 01:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 01:- INTRODUCTION TO HEAT TRANSFER Conduction, Convection, and Radiation DTEL 4

LECTURE 01:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 01:- INTRODUCTION TO HEAT TRANSFER Heat Energy Energy is what makes things happen. All materials are made of tiny particles called molecules. Molecules are always moving. Molecules in motion The movement creates heat. The amount of heat depends on how fast the molecules move. As the molecules move faster, they take up more space and make the object expand. DTEL 5

LECTURE 01:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 01:- INTRODUCTION TO HEAT TRANSFER Heat Transfer Heat can be transferred from one object to another in 3 different ways: Conduction Convection Radiation DTEL 6

LECTURE 01:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 01:- INTRODUCTION TO HEAT TRANSFER Conduction Heat traveling through solids. Two objects must touch or have direct contact. As molecules heat up they move faster and expand. When you touch one hot surface to another, the hot molecules bump into the other molecules which makes them start to move faster. An object gets hotter from the movement of the molecules. All solid objects conduct heat, some are better conductor than others. Metals are good conductors. DTEL 7

LECTURE 01:- INTRODUCTION TO HEAT TRANSFER Examples of Conduction MODES OF HEAT TRANSFER LECTURE 01:- INTRODUCTION TO HEAT TRANSFER Examples of Conduction DTEL 8

LECTURE 02:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 02:- INTRODUCTION TO HEAT TRANSFER Convection Heat traveling through liquids or gases As molecules heat up, the heat makes the molecules move more rapidly and expand. Creates currents in liquids or gases – hot air rises and cold air sinks. Uneven heating of our ocean creates ocean currents. Uneven heating of our atmosphere produces huge convection wind currents. Scientists use global and local wind patterns to predict weather. DTEL 9

LECTURE 02:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 02:- INTRODUCTION TO HEAT TRANSFER Examples of Convection DTEL 10

LECTURE 02:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 02:- INTRODUCTION TO HEAT TRANSFER Radiation Release of invisible heat energy waves from the sun or fire. No movement of molecules to transfer heat. Feel warm without touch – heat radiates. Radiators got their name from this type of heat. When the radiant energy from the sun hits the earth, the earth soaks up the energy and changes it into heat. DTEL 11

LECTURE 02:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 02:- INTRODUCTION TO HEAT TRANSFER Examples of Radiation DTEL 12

LECTURE 02:- INTRODUCTION TO HEAT TRANSFER MODES OF HEAT TRANSFER LECTURE 02:- INTRODUCTION TO HEAT TRANSFER Balance Whenever a hot object is placed near a cold object, the hot object will transfer heat to the cold object until they reach a state of balance. Balance happens when the temperatures of both objects are the same. The fast moving molecules mix with the slow moving molecules until they are all mixed and balanced. DTEL 13

LECTURE 03:- INTRODUCTION TO HEAT TRANSFER LAWS OF HEAT TRANSFER LECTURE 03:- INTRODUCTION TO HEAT TRANSFER Fourier’s Law A rate equation that allows determination of the conduction heat flux from knowledge of the temperature distribution in a medium Its most general (vector) form for multidimensional conduction is: Implications: Heat transfer is in the direction of decreasing temperature (basis for minus sign). Fourier’s Law serves to define the thermal conductivity of the medium Direction of heat transfer is perpendicular to lines of constant temperature (isotherms). Heat flux vector may be resolved into orthogonal components. DTEL 14

LECTURE 03:- INTRODUCTION TO HEAT TRANSFER LAWS OF HEAT TRANSFER LECTURE 03:- INTRODUCTION TO HEAT TRANSFER Cartesian Coordinates: Cylindrical Coordinates: Spherical Coordinates: DTEL 15

LECTURE 03:- INTRODUCTION TO HEAT TRANSFER LAWS OF HEAT TRANSFER LECTURE 03:- INTRODUCTION TO HEAT TRANSFER In angular coordinates , the temperature gradient is still based on temperature change over a length scale and hence has units of C/m and not C/deg. Heat rate for one-dimensional, radial conduction in a cylinder or sphere: Cylinder or, Sphere DTEL 16

LECTURE 03:- INTRODUCTION TO HEAT TRANSFER LAWS OF HEAT TRANSFER LECTURE 03:- INTRODUCTION TO HEAT TRANSFER Stefan-Boltzmann formula Surface area (m2) HEAT REAT (watts) Q = E s A T4 Absolute temperature (K) Stefan-Boltzmann constant 5.67 x 10-8 watts/m2K4) DTEL 17

LECTURE 04:- INTRODUCTION TO HEAT TRANSFER Thermophysical Properties LECTURE 04:- INTRODUCTION TO HEAT TRANSFER Thermophysical Properties Thermal Conductivity K: A measure of a material’s ability to transfer thermal energy by conduction. Thermal Diffusivity a : A measure of a material’s ability to respond to changes in its thermal environment. DTEL 18

LECTURE 04:- INTRODUCTION TO HEAT TRANSFER Thermophysical Properties LECTURE 04:- INTRODUCTION TO HEAT TRANSFER Thermal response of a plane wall to convection heat transfer. DTEL 19

LECTURE 05:- INTRODUCTION TO HEAT TRANSFER HEAT CONDUCTION EQUATION LECTURE 05:- INTRODUCTION TO HEAT TRANSFER GENERAL HEAT CONDUCTION EQUATION In the last section we considered one-dimensional heat conduction and assumed heat conduction in other directions to be negligible. Most heat transfer problems encountered in practice can be approximated as being one-dimensional, and we mostly deal with such problems in this text. However, this is not always the case, and sometimes we need to consider heat transfer in other directions as well. In such cases heat conduction is said to be multidimensional, and in this section we develop the governing differential equation in such systems in rectangular, cylindrical, and spherical coordinate systems. DTEL 20

LECTURE 05:- INTRODUCTION TO HEAT TRANSFER HEAT CONDUCTION EQUATION LECTURE 05:- INTRODUCTION TO HEAT TRANSFER Rectangular Coordinates DTEL 21

LECTURE 05:- INTRODUCTION TO HEAT TRANSFER HEAT CONDUCTION EQUATION LECTURE 05:- INTRODUCTION TO HEAT TRANSFER DTEL 22

LECTURE 05:- INTRODUCTION TO HEAT TRANSFER HEAT CONDUCTION EQUATION LECTURE 05:- INTRODUCTION TO HEAT TRANSFER DTEL 23

LECTURE 06:- INTRODUCTION TO HEAT TRANSFER HEAT CONDUCTION EQUATION LECTURE 06:- INTRODUCTION TO HEAT TRANSFER Cylindrical Coordinates Relations between the coordinates of a point in rectangular and cylindrical coordinate systems: DTEL 24

LECTURE 07:- INTRODUCTION TO HEAT TRANSFER HEAT CONDUCTION EQUATION LECTURE 07:- INTRODUCTION TO HEAT TRANSFER Spherical Coordinates Relations between the coordinates of a point in rectangular and spherical coordinate systems: DTEL 25

LECTURE 08:- INTRODUCTION TO HEAT TRANSFER BOUNDARY CONDITION LECTURE 08:- INTRODUCTION TO HEAT TRANSFER The description of a heat transfer problem in a medium is not complete without a full description of the thermal conditions at the bounding surfaces of the medium. Boundary conditions: The mathematical expressions of the thermal conditions at the boundaries. The temperature at any point on the wall at a specified time depends on the condition of the geometry at the beginning of the heat conduction process. Such a condition, which is usually specified at time t = 0, is called the initial condition, which is a mathematical expression for the temperature distribution of the medium initially. DTEL 26

LECTURE 08:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 08:- INTRODUCTION TO HEAT TRANSFER Boundary Conditions Specified Temperature Boundary Condition Specified Heat Flux Boundary Condition Convection Boundary Condition Radiation Boundary Condition Interface Boundary Conditions Generalized Boundary Conditions DTEL 27

1- Dimensional Heat Conduction ONE DIMENSIONAL HEAT CONDITION LECTURE 09:- INTRODUCTION TO HEAT TRANSFER 1- Dimensional Heat Conduction The Plane Wall : .. .. . . … . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . . …. . . . . . .. .. .. . . . . .. . .. . . . . .. . . . . . . . . k T∞,2 Ts,1 Ts,2 x=0 x=L Hot fluid Cold fluid Const. K; solution is: DTEL 28

LECTURE 09:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 09:- INTRODUCTION TO HEAT TRANSFER Thermal resistance (electrical analogy) OHM’s LAW :Flow of Electricity V=IR elect Voltage Drop = Current flow×Resistance DTEL 29

LECTURE 09:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 09:- INTRODUCTION TO HEAT TRANSFER Thermal Analogy to Ohm’s Law : Temp Drop=Heat Flow×Resistance DTEL 30

LECTURE 09:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 09:- INTRODUCTION TO HEAT TRANSFER 1 D Heat Conduction through a Plane Wall .. .. . . … . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . . . . . …. . . . . . .. .. .. . . . . .. . .. . . . . .. . . . . . . . . k T∞,2 Ts,1 Ts,2 x=0 x=L Hot fluid Cold fluid T∞,1 T∞,1 Ts,1 Ts,2 T∞,2 qx A h 2 1 A k L A h 1 (Thermal Resistance ) DTEL 31

LECTURE 09:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 09:- INTRODUCTION TO HEAT TRANSFER Resistance expressions DTEL 32

LECTURE 10:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 10:- INTRODUCTION TO HEAT TRANSFER Composite Walls : A B C T∞,1 T∞,2 h1 h2 K A K B K C L A L B L C q x T∞,1 T∞,2 A h 1 2 Overall heat transfer coefficient DTEL 33

LECTURE 10:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 10:- INTRODUCTION TO HEAT TRANSFER Overall Heat transfer Coefficient Contact Resistance : A B TA TB DTEL 34

LECTURE 10:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 10:- INTRODUCTION TO HEAT TRANSFER Series-Parallel : A B D C T1 T2 K c K D K A K B AB+AC=AA=AD LB=LC DTEL 35

LECTURE 10:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 10:- INTRODUCTION TO HEAT TRANSFER Series-Parallel (contd…) T1 T2 Assumptions : Face between B and C is insulated. (2) Uniform temperature at any face normal to X. DTEL 36

LECTURE 11:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 11:- INTRODUCTION TO HEAT TRANSFER Critical Insulation Thickness : r0 ri T∞ Ti h Insulation Thickness : r o-r i Objective : decrease q , increases Vary r0 ; as r0 increases ,first term increases, second term decreases. DTEL 37

Critical Insulation Thickness (contd…) BOUNDRY CONDITION LECTURE 11:- INTRODUCTION TO HEAT TRANSFER Critical Insulation Thickness (contd…) Maximum – Minimum problem Set at Max or Min. ? Take : DTEL 38

LECTURE 11:- INTRODUCTION TO HEAT TRANSFER BOUNDRY CONDITION LECTURE 11:- INTRODUCTION TO HEAT TRANSFER Critical Insulation Thickness (contd…) Minimum q at r0 =(k/h)=r c r (critical radius) good for steam pipes etc. good for electrical cables R c r=k/h r0 R t o t DTEL 39

THANK YOU DTEL 40