ME 259
Heat Transfer
Lecture Slides I
Dr. Gregory A. Kallio
Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology
California State University, Chico
Introduction
Reading: Incropera & DeWitt
Chapter 1
Heat Transfer as a Course
Has a “reputation” for being one of the most challenging courses in ME
Why??
–Physically diverse: thermodynamics, material science, diffusion theory, fluid mechanics, radiation theory
–Higher-level math: vector calculus, ODEs, PDEs, numerical methods
–Physically elusive: heat is invisible; developing intuition takes time
–Appropriate assumptions: required to simplify and solve most problems
However, Heat Transfer is interesting, fun, and readily applicable to the real world
Relevance of Heat Transfer
Electric Power Generation
Alternate Energy Systems
Combustion/Propulsion Systems
Building Design
Heating & Cooling Systems
Domestic Appliances
Materials/Food Processing
Electronics Cooling & Packaging
Cryogenics
Environmental Processes
Space Vehicle Systems
Definition of Heat Transfer
Flow of energy due solely to a temperature difference
–all other forms of energy transfer are categorized as work
–from 2nd Law of Thermodynamics, heat flows in direction of decreasing temperature
–heat energy can be transported through a solid, liquid, gas, or vacuum
Heat Quantities
Relationship Between the Study of Heat Transfer & Thermodynamics
1st Law of Thermodynamics for Closed System:
Thermodynamics – allows calculation of total heat transferred (Q) during a process in which system goes from one equilibrium state to another (i.e., the “big picture”)
Heat Transfer – provides important physical laws that allow calculation of instantaneous heat rate, length of time required for process to occur, and temperature distribution within material at any time (i.e., the “details” required for design)
Heat Transfer Modes
Conduction
–transfer of heat due to random molecular or atomic motion within a material (aka diffusion)
–most important in solids
Convection
–transfer of heat between a solid surface and fluid due to combined mechanisms of a) diffusion at surface; b) bulk fluid flow within boundary layer
Radiation
–transfer of heat due to emission of electromagnetic waves, usually between surfaces separated by a gas or vacuum
Heat Transfer Modes – Conduction
Rate equation (Fourier & Biot, ~1820) is known as Fourier’s law; for 1-D conduction,
uwhere qx = heat rate in x-direction (W)
q”x = heat flux in x-direction (W/m2)
T = temperature (°C or K)
A = area normal to heat flow (m2)
k = thermal conductivity of material
(W/m-K); see Tables A.1-A.7
Heat Transfer Modes – Conduction
Steady-state heat conduction through a plane wall:
Heat Transfer Modes – Conduction
Example: What thickness of plate glass would yield the same heat flux as 3.5² of glass-fiber insulation with the same S-S temperature difference (T1-T2) ?
Heat Transfer Modes – Conduction
Insulation “R-value”:
where 1 W/m-K = 0.578 Btu/hr-ft-°F
Heat Transfer Modes – Convection
Rate equation (Newton, ~1700) is known as Newton’s law of “cooling”:
uwhere q” = heat flux normal to surface
q = heat rate from or to surface As
Ts = surface temperature
T¥ = freestream fluid temperature
As = surface area exposed to fluid
h = convection heat transfer coefficient
(W/m2-K)
Heat Transfer Modes – Convection
The convection heat transfer coefficient (h)
–is not a material property
–is a complicated function of the many parameters that influence convection such as fluid velocity, fluid properties, and surface geometry
–is often determined by experiment rather than theory
–will be given in most HW problems until we reach Chapter 6
Heat Transfer Modes – Convection
Types of Convection
–Forced convection: flow caused by an external source such as a fan, pump, or atmospheric wind
–Free (or natural) convection: flow induced by buoyancy forces such as that from a heated plate
–Phase change convection: flow and latent heat exchange associated with boiling or condensation
Heat Transfer Modes – Radiation
Rate equation is the Stefan-Boltzmann law which gives the energy flux due to thermal radiation that is emitted from a surface; for a black body:
For non-black bodies,
uwhere E = emissive power (W/m2)
s = Stefan-Boltzmann constant
= 5.67×10-8 W/m2-K4
e = emissivity (0< e<1) of surface
Ts = surface temperature in absolute
units (K)
Heat Transfer Modes – Radiation
Radiation incident upon an object may be reflected, transmitted, or absorbed:
where
G = irradiation (incident radiation)
r = reflectivity (fraction of G that is reflected)
t = transmissivity (fraction of G that is transmitted
a = absorptivity (fraction of G that is absorbed)
e = emissivity (fraction of black body emission)
E and the interaction of G with each participating object determines the net heat transfer between objects
Heat Transfer Modes – Radiation
Heat transfer between a small object and larger surroundings (As<<Asur):
uwhere e = emissivity of small object
As = surface area of small object
Ts = surface temperature of small
object (K)
Tsur = temperature of surroundings (K)
Conservation of Energy – Control Volume
Control volume energy balance:
–from thermodynamics:
–Incropera & DeWitt text notation:
Conservation of Energy – Control Volume
Energy rates:
–where:
Conservation of Energy – Control Surface
Surface energy balance:
–since a control surface is a special control volume that contains no volume, energy generation and storage terms are zero; this leaves:
Summary: The Laws Governing Heat Transfer
Fundamental Laws
–Conservation of mass
–Conservation of momentum
–Conservation of energy
Heat Rate Laws
–Fourier’s law of heat conduction
–Newton’s law of convection
–Stefan-Boltzmann law for radiation
Supplementary Laws
–Second law of thermodynamics
–Equations of state:
»ideal gas law
»tabulated thermodynamic properties
»caloric equation (definition of specific heat)
Objectives of a Heat Transfer Calculation
ANALYSIS
–Calculate T(x,y,z,t) or q for a system undergoing a specified process
»e.g., calculate daily heat loss from a house
»e.g., calculate operating temperature of a semiconductor chip with heat sink/fan
DESIGN
–Determine a configuration and operating conditions that yield a specified T(x,y,z,t) or q
»e.g., determine insulation needed to meet a specified daily heat loss from a house
»e.g., determine heat sink and/or fan needed to keep operating temperature of a semiconductor chip below a specified value
Classes of Heat Transfer Problems
Thermal Barriers
–insulation
–radiation shields
Heat Transfer Enhancement (heat exchangers)
–boilers, evaporators, condensers, etc.
–solar collectors
–finned surfaces
Temperature Control
–cooling of electronic components
–heat treating & quenching of metals
–minimizing thermal stress
–heating appliances (toaster, oven, etc.)

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