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ME 259Heat TransferLecture Slides I

Dept. of Mechanical Engineering,

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Introduction

Reading: Incropera & DeWitt

Chapter 1

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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

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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

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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

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Heat Quantities

Quantity Text Notation SI Unit English Unit

heat Q Joule (J) Btu(heat transfer)

heat rate q Watt (W) Btu/hr(heat transfer rate)(heat energy rate)(rate of heat flow)

heat flux q” W/m2 Btu/hr-ft2(heat rate per unit area)

heat rate per unit length q’ W/m Btu/hr-ft

volumetric heat generation q W/m3 Btu/hr-ft3(rate of heat production perunit volume)

Conversions: 1 Btu = 1054 J1 kcal = 4184 J

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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)

sysEWQ

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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

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Heat Transfer Modes - Conduction

Rate equation (Fourier & Biot, 1820) is known as Fourier’s law; for 1-D conduction,

where 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

or dx

dTkq

dx

dTkAq xx

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Heat Transfer Modes - Conduction

Steady-state heat conduction through a plane wall:

L

TTkq

L

TT

dx

dTdx

dTk

dx

dTkq

x

x

2112 ,

constant thenconstant, if

constant

L

T1 T2

x

q (T1>T2)

k

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Heat Transfer Modes - Conduction

Example: What thickness of plate glass would yield the same heat flux as 3.5 of glass-fiber insulation with the same S-S temperature difference (T1-T2) ?

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Heat Transfer Modes - Conduction

Insulation “R-value”:

where 1 W/m-K = 0.578 Btu/hr-ft-°F

F-ft-hrBtu

ft value"-R"

k

L

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Heat Transfer Modes - Convection

Rate equation (Newton, 1700) is known as Newton’s law of “cooling”:

where 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)

)(or )( TThAqTThq sss

Fluid flow, TAs

Ts (>T)q

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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

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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

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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,

where E = emissive power (W/m2) = Stefan-Boltzmann constant

= 5.67x10-8 W/m2-K4

= emissivity (0< <1) of surface Ts = surface temperature in absolute

units (K)

4sb TE

4sTE

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Heat Transfer Modes - Radiation

Radiation incident upon an object may be reflected, transmitted, or absorbed:

whereG = irradiation (incident radiation) = reflectivity (fraction of G that is reflected) = transmissivity (fraction of G that is transmitted = absorptivity (fraction of G that is absorbed) = emissivity (fraction of black body emission)

E and the interaction of G with each participating object determines the net heat transfer between objects

G G

G

G

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Heat Transfer Modes - Radiation

Heat transfer between a small object and larger surroundings (As<<Asur):

where = emissivity of small object As = surface area of small object

Ts = surface temperature of small

object (K) Tsur = temperature of surroundings (K)

)(or )(" 4444sursssurs TTAqTTq

q

Ts

Tsur

, As

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Conservation of Energy – Control Volume

Control volume energy balance:

– from thermodynamics:

– Incropera & DeWitt text notation:

dt

dEgzvPum

gzvPumWQ

cv

eeeeeee

iiiiiii

2/

2/

2

2

V

V

stgoutin EEEE

W

Q

mass in

mass out

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Conservation of Energy – Control Volume

Energy rates:

– where:

CV within storage energy of rate

CV within generation energy of rate

CV exiting rates work andheat all

CV entering rates work andheat all

st

g

out

in

E

E

E

E

exist conditions state-steady if

substances ibleincompress

and gases ideal for

0

st

vst

E

dt

dTVcE

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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:

0 outin EE

Ein

Eout

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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)

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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

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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.)