ME 436, February 3, 2016 Quiz 3 Name: RV‘FN/Qf KQ/j
This quiz is closed notes, open book. You may use calculators. Total time is 20 minutes. Note
that bonus questions are optional.
Grade:
1) A biofuel reactor features a 150 cm thick ceramic plane wall (k
Chapter 3 Part 2:
Conduction with Energy Generation
ME 436 Chapter 3,
Slide 1
Conduction with Energy Generation
Assume (Ts,1 and Ts,2 given):
Energy equation:q
!
Ts,1
T , 2 h2
Integrate once:
T ,1 h1
Integrate again:
Ts,2
-L
L
x
ME 436 Chap
Name: Lab Sec#
MEV436, Feb. 7, 2014 Quiz 3
T his quiz is closed notes, open book. You may use calculators. Total time is 0 minutes.
L 1 1
._ ._ _ _. 2 2
Rt,cond " 7c: Rt,conv a Rt,rad hTA hr 500:9 + Tsur) (Ts + Tsar)
q l : ATtoml
tata Rtotal
1) (2 p
CONVECTION: EXTERNAL FLOW
EMPIRICAL METHOD
EXTERNAL FLOW
We focus now on the
problem of computing heat
and mass transfer rates to or
from a surface in external
flow
In such a flow boundary
layers develop freely,
without constraints imposed
by adjacent sur
TRANSIENT CONDUCTION
THE LUMPED CAPACITANCE METHOD
THE LUMPED CAPACITANCE METHOD
Many heat transfer problems are time
dependent
Such transient problems typically arise
when the boundary conditions of a
system are changed
The changes continue to occur unti
TRANSIENT CONDUCTION
SPATIAL EFFECTS
SPATIAL EFFECTS
Situations frequently arise for which the Biot number is not small, and we
must cope with the fact that temperature gradients within the medium
are no longer negligible
Use of the lumped capacitance met
WHAT IS HEAT TRANSFER?
HEAT TRANSFER MODES AND RATES
WHAT IS HEAT TRANSFER?
Heat transfer (or heat) is thermal
energy in transit due to a spatial
temperature difference
Whenever a temperature difference
exists in a medium or between
media, heat transfer m
HEAT EQUATION
1. cylindrical coordinates
T ( r, , z )
z
1 T
kr
r r r
1 T T
k
+ k
+ 2
r z z
T
q
q
c
+
=
p
g
t
d dT
=0
k
dz dz
d
(qz ) = 0
dz
plane wall!
CONDUCTION
1
1D, SS CONDUCTION
HOLLOW CYLINDER
RADIAL SYSTEMS
Cylindrical and spherical systems
CONDUCTION WITH THERMAL
ENERGY GENERATION
PLANE WALL AND RADIAL SYSTEMS
CONDUCTION WITH ENERGY GENERATION
We now want to consider the
additional effect on the
temperature distribution of
processes that may be occurring
within the medium
In particular, we
PROBLEM 3.126
KNOWN: Dimensions and thermal conductivity of a gas turbine blade. Temperature and convection
coefficient of gas stream. Temperature of blade base and maximum allowable blade temperature.
FIND: (a) Whether blade operating conditions are acce
Parameter
w
L
Number of fins x
Number of fins y
N
b1
b2
h
eta_o
A_t
A_f
A_b
q_t
eta_f
q_f
M
m
P
A_c
k
T_b
T_infinity
Theta_b
sinh(mL)
h/mk
cosh(mL)
epsilon_f
Volume
q'_f
Checks
A
B
Design A
Design B
Aluminum
Aluminum
0.003
0.001
0.03
0.007
6
14
9
17
54
23
PROBLEM 3.84
KNOWN: Composite wall with outer surfaces exposed to convection process.
FIND: (a) Volumetric heat generation and thermal conductivity for material B required for special
conditions, (b) Plot of temperature distribution, (c) T1 and T2, as wel
PROBLEM 3.112
KNOWN: Dimensions of a plate insulated on its bottom and thermally joined to heat sinks at its
ends. Net heat flux at top surface.
FIND: (a) Differential equation which determines temperature distribution in plate, (b) Temperature
distributi
m = ( hP kA c )
1/ 2
(
PROBLEM 3.122 (Cont.)
= 15 W m K ( 0.025 m ) 60 W m K 4.909 10
2
4
m
2
)
1/ 2
= 6.324 m
1
Consider the following design changes aimed at reducing To 100C. (1) Increasing length of the fin
portions: with Lo = 400 and 600 mm, To is 10
PROBLEM 4.45
KNOWN: Heat generation and thermal boundary conditions of bus bar. Finite-difference grid.
FIND: Finite-difference equations for selected nodes.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant
PROBLEM 4.47
KNOWN: Nodal point on boundary between two materials.
FIND: Finite-difference equation for steady-state conditions.
SCHEMATIC:
ASSUMPTIONS: (1) Steady-state conditions, (2) Two-dimensional conduction, (3) Constant
properties, (4) No internal
PROBLEM 4.55
KNOWN: Steady-state temperatures (K) at three nodes of a long rectangular bar.
FIND: (a) Temperatures at remaining nodes and (b) heat transfer per unit length from the bar using
nodal temperatures; compare with result calculated using knowled
PROBLEM 3.84 (Cont.)
T ( L B ) = T1 =
&
qB
2k B
T ( + L B ) = T2 =
&
qB
2k B
( L B )2 C1L B + C2
where T1 = 261C
(4)
( + L B )2 + C1L B + C2
where T2 = 211C
(5)
where q1 = 107,273 W/m2
(6)
&
q
q ( L B ) = q1 = k B B ( L B ) + C1
x
kB
&
Using IHT to s
Parameter
Pin Diameter (m)
Pin Length (m)
Number of fins x
Number of fins y
Number of fins total
Length of base x (m)
Length of base y (m)
L/d Ratio
Volume of Fins
Mass of fins
h
eta_o
A_t
A_f
A_b
q_t
eta_f
q_f
M
m
P
A_c
k
T_b
T_infinity
Theta_b
sinh(mL)
ME 436 Take Home Quiz 4: Cooling System Design Problem
Scenario:Asheatloadscontinuetoescalateinelectronic
equipment,designersseekoutmorepowerfulheatsinks
to cool their electronic devices. In many instances,
designers are turning to pin fin heat sinks, whi
1D, SS CONDUCTION
EXTENDED SURFACES
EXTENDED SURFACES
The term extended surface is commonly
used to depict an important special
case involving heat transfer by
conduction within a solid and heat
transfer by convection (and/or
radiation) from the boundarie
1D, SS CONDUCTION
THE PLANE WALL
THE PLANE WALL
Despite their inherent simplicity, onedimensional, steady-state models may be
used to accurately represent numerous
engineering systems
The term one-dimensional refers to the
fact that only one coordinate is
CONDUCTION
FOURIERS LAW
FOURIERS LAW
Conduction is the transport of energy in
a medium due to a temperature
gradient, and the physical mechanism
is one of random atomic or molecular
activity
Conduction heat transfer is governed
by Fouriers law:
q = kT
Fou
ME 436
Heat Transfer
Lecture 4
Heat Diffusion Equation
1D Steady State Conduction
Boundary and Initial Conditions
Lecture 4 Learning Objectives
Apply an energy balance to find 1D
temperature distribution
Categorize boundary/initial conditions based
heat
ME 436
Heat Transfer
Lecture 6
Conduction with Energy Generation
Lecture 6 Learning Objectives
Formulate the heat diffusion equation to
incorporate steady state energy generation.
Apply boundary conditions to your solution to
the heat diffusion equation
ME 436
Heat Transfer
Lecture 2
Introduction to Heat Transfer and
Energy Balances
Lecture 2 Objectives
Describe the principle modes of heat transfer:
conduction, convection and radiation
Perform basic heat transfer calculations for
different mechanisms
ME 436
Heat Transfer
Lecture 15
Natural (Free) Convection
Lecture 15 Learning Objectives
Define natural convection on the basis of a
temperature driven change in density.
Recognize the Grashof and Rayleigh numbers as
the principle dimensionless quantiti
IOWA STATE UNIVERSITY
ME 436 Heat Transfer
Homework 8 Heat Exchangers
Assigned 11/2, Due 11/11 at 5 PM on Blackboard
Problem 1 (4 points)
ConHugeCo has asked you to evaluate a counterflow oil cooler used as part of an industrial
process to ascertain if it
CONVECTION
BOUNDARY LAYERS
CONVECTION
The term convection describes energy
transfer between a surface and a fluid
moving over the surface
Convection includes energy transfer by
both the bulk fluid motion (advection)
and the random motion of fluid
molecule
ME 436
Heat Transfer
Lecture 18
Introduction to Radiation Heat
Transfer
Lecture 18 Learning Objectives
Define emission as the heat transferred from a
surface and irradiation as the heat transfer to a
surface.
Relate the radiation heat transfer to the ra
ME 436
Heat Transfer
Lecture 9
Convective Heat Transfer
Introduction to Boundary Layers
Lecture 9 Learning Objectives
Recognize that the heat transfer coefficient is
a position dependent quantity.
Define the evolution of convective flow over a
plate on
IOWA STATE UNIVERSITY
ME 436 Heat Transfer
Homework 7 Free Convection
Assigned 10/26. Duo 1 [/2 at 5 PM on Blackboard
Problem 1 (5 points)
A semiconductor manufacturing facility currently runs a process where thin. 100 mm silicon
plates exit an oven in a
ME 436
Heat Transfer
Lecture 8
Transient Heat Conduction
Lumped Capacitance and the SemiInfinite Solid
Lecture 8 Learning Objectives
Assess heat transfer systems using the Biot
number.
Differentiate between the lumped capacitance
and semi-infinite solid