1 INTRODUCTION TO HEAT TRANSFER
Cengel Chapter 1, or Welty et al. p 201-214 or Incropera et al. p 1-12 Learning objectives, tasks, readings, Learn ChemE Videos
1. Explain the differences between: a. Conduction
b. Convection
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c. Radiation
d. Driving forces, resistances, constants (k, h, )
2. Use the following equations to calculate heat transfer rates and explain the meanings of the terms in each equation:
a. Fourier’s Law (conduction)
b. Newton’s Law of Cooling (convection)
c. Boltzman Equation (radiation)
d. Learn ChemE – “Heat Transfer Basics”
e. Multi-modal (Learn ChemE – “Potato Example”)
3. Begin filling in the table of symbols, definitions and units By the end of this week you should be able to:
Determine which modes of heat transfer will be relevant for a given problem, and which are negligible
Find, reference and use appropriate values of thermal conductivity and emissivity (along with other standard thermal properties of common fluids – e.g. density, heat capacity, etc)
Set out a solution to a problem based on the method described (end of lecture notes), including diagrams, assumptions, data, analysis, calculations (with appropriate significant figures), and critical review of the answer
WHAT IS HEAT TRANSFER?
THERMODYNAMICS
Energy (heat) can be transferred between system and surrounds.
Heat goes from hot to cold regions. Temperature difference = driving force
Deals only with End states (eg at equilibrium).
Tells nothing about modes or rates of Heat Transfer.
HEAT TRANSFER
____________________________________________________ ____________________________________________________ ____________________________________________________ ____________________________________________________
You have a 330 mL can of drink, which has density 1000 kg m-3 and specific heat 4.2 kJ kg-1 K-1. The can has been sitting in your car on a hot day, and is now at 35 oC. You would like to cool it down to 5 oC.
a. how much ice at 0 oC (latent heat of 334 kJ kg-1) is required to cool the can to 5 oC?
b. how much water (density 1000 kgm-3, specific heat 4.2 kJ kg-1 K-1) at1oCisrequiredtocoolthecanto 5oC?
c. how much air (density 1.3 kgm-3, specific heat 1.0 kJ kg-1 K-1) at 1 oC is required to cool the drink to 5 oC?
d. what would you do to cool the drink fastest and why?
HEAT TRANSFER SYMBOLS AND UNITS
Actions for students:
complete the units column in the table of symbols, and indicate which variables are vectors; and
update table of symbols as course progresses.
TABLE OF HEAT TRANSFER SYMBOLS AND UNITS (note – textbooks vary widely!!!)
Definition
heat transfer heat transfer temperature resistance to heat transfer Definition
oC or K or oF
W/mK W/m2 K
Study guide
Textbook (Incropera)
q A T R q”
heat transfer flux
Study guide
Textbook (Incropera)
thermal conductivity heat transfer coefficient
Stefan-Boltzmann constant, 5.669 x 10-8
Emissivity (0 ≤ ε ≤ 1) radiative property of a surface
1.1 RATE EQUATIONS FOR PHYSICAL PROCESS
Rate Driving Force Resistance
________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ _______________________________________________________
1.2 THE GENERAL FORM OF HEAT TRANSFER EQUATIONS
The general form of the rate equation:
Equation H-1
q = heat transfer rate (W)
A = heat transfer area (m2)
T = temperature (oC or K)
R = resistance to heat transfer
Commonly expressed as heat flux:
q qA f ( T )
Where: q” = heat flux (W/m2)
E q u a t i o n H – 2
Modes of heat transfer
Conduction: In a stationary medium, energy is transferred due to
interactions between particles. In gases:
In liquids:
In solids:
Convection: Energy transfer between a surface and the adjacent fluid. Convection arises from the combined effects of conduction and fluid flow.
Radiation: Electromagnetic energy emitted at the molecular or atomic level, which transmits through space and is absorbed, transmitted or reflected by receiving molecules.
CONDUCTION
Rate of heat transfer: Fourier’s Law
For 1-dimensional steady-state conduction, rate of heat transfer from T2 to T1:
Fourier’s Law: Equation H-3 Where:
12 q kA (T T )
Negative sign: denotes heat flow in x direction down thermal gradient ( T ).
k = thermal conductivity (W/mK)
Consider the rate equation for physical processes:
Rate Driving Force Resistance
For 1-d, steady state conduction, define in words, symbols and units: Rate:
Driving force:
Resistance:
Which will have higher conductivity?
Steel or brick?________________
Wood or rock?_______________
Banana or air?______________
1.3 EXAMPLE – WHAT IS THE RATE OF CONDUCTION THROUGH A CONCRETE WALL?
What is the rate of heat conducted through a concrete wall of width 20 cm, if the outside surface temperature is 35 oC, and the inside surface is kept at 22 oC, through air conditioning?
CONVECTION
Convection involves heat transferred from a surface to a fluid. Examples: ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________
Rate of heat transferred from surface at TS to surrounding fluid, bulk temperature T∞
q hA Ts T H-4
h = heat transfer coefficient (W/m2K)
TS isthesurfacetemperature,oCorK
T∞ is the bulk fluid temperature, oC or K
h is dependent on:
Fluid velocity;
System geometry,
Nature of convection
Fluid properties.
Values for h are usually derived from empirical dimensionless correlations.
Modes of Convection
1. Forced Convection: fluid flow is driven by external force
Gases: h = 25 – 250 Wm-2K-1
Liquids: h = 50 – 20,000 Wm-2K-1
2. Natural Convection:
Flow induced by buoyancy forces due to temperature (or concentration) generated density differences.
o Gases: h = 2 – 25 Wm-2K-1
o Liquids: h = 50 – 1,000 Wm-2K-1
3. Boiling & Condensation Convection:
Phase change induced flow creates latent heat transfer and fluid mixing.
o Gases & Liquids: h = 2,500 – 100,000 Wm-2K-1 e.g.
RADIATION FROM SURFACE TO/FROM SURROUNDS
Examples: ________________________________________________________ ________________________________________________________ ________________________________________________________ ________________________________________________________
Rate of heat emitted from a surface at temperature TS
q AT 4 S
Equation H-5
σ = Stefan-Boltzmann constant = 5.669 x 10-8 (W/m2K4) TS = absolute temperature (K) of emitting surface
ε = emissivity (0 ≤ ε ≤ 1) radiative property of a surface Radiation energy, E, striking a surface will be:
Absorbed, α, or
Reflected, ρ, or
Transmitted τ.
Equation H-6
Absorptivity, α, Reflectivity, ρ , Transmissivity, τ and Emissivity, ε:
Are optical properties;
Depend on __________________ and _______________
Radiation differs from conduction and convection in that it
Does not require the presence of matter
_______________________________________
Rate of heat transferred between 2 bodies due to radiation depends on:
_______________________________________ _______________________________________ _______________________________________ _______________________________________
COMBINED MODES
Many real situations involve heat transfer by more than 1 mode:
Solve by an energy balance using appropriate equations.
1.4 SUMMARY: CONDUCTION, CONVECTION AND RADIATION
1-D STEADY STATE CONDUCTION IN A SOLID
q kA T x
q = rate of heat conduction from T1 →T2 (units: W) A = cross-sectional area (units: m2)
k = thermal conductivity (units: )
CONVECTION FROM A SURFACE TO A FLUID
qhAT T S
q = rate of heat transferred between surface and surrounding fluid (units: )
h = heat transfer coefficient (W/m2K)
TS = surface temperature (units: ) T∞ = ambient fluid temperature (units:
RADIATION FROM A SURFACE TO SURROUNDS
q ATS4
ε = surface emissivity (units: ) σ = Stefan-Bolzman constant = 5.67 x 10-8 Wm-2K-4 Ts = surface temperature (units: )
A = surface area (units: )
HOW TO SET OUT SOLUTIONS TO PROBLEMS: GUIDELINES/MARKING CRITERIA
Your solutions should to satisfy the following criteria:
1. Diagram. Draw a useful diagram of the physical system. Symbols, dimensions, materials, flows of energy and other relevant properties should be defined on the diagram.
2. Define the problem. State what you will determine, e.g. heat loss from furnace to surrounding air.
3. Assumptions. List and justify assumptions and simplifications.
4. Data. Clearly state data needed for calculations, including units and reference
5. Analysis. Define appropriate equations, define all symbols.
6. Calculation. After completely developing the analysis in symbols, substitute
numerical values and calculate results. Clearly show and explain working. Final
answer should be stated clearly, with correct units and significant figures.
7. Interpretation
a. CHECK – how confident am I of the answer? e.g.
Under what circumstances is it valid?
Is the answer likely to be an under- or over-estimated?
Can I check for sense against general knowledge, or knowledge of the problem?
b. ANALYSE – what does it tell me about the system? e.g.
What is controlling heat loss?
c. APPLY – what actions should be taken because of what I learn from these calculations? e.g. How can heat loss be reduced?
The guidelines above will make it easier for you to solve new problems, and to check your work and correct errors.
Following the guidelines will also make it easier for others to understand your work, which is important for professional engineers. And the added bonus is that lecturers and tutors will find it easier to follow your work, and so better able to help you during the tutorial, and to award part marks during assessment when you have made an error.
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