JME 3710
September 2, 2010
Homework #1
1. (10 pts) In a general case of conduction in one dimension, temperature and conductivity might
both be variable, i.e. T = T (x) and k = k(x), respectively, whereby we would write the Fourier
conduction equation as
JME 3710
November 10, 2010
Homework #10 Solutions
1. (10 pts) A simple concentrictube heat exchanger uses hot oil to heat cold water. Mass ow
rates on both sides are 0.05 kg/s. The design temperature change on the cold side is Ti |c =
300 K To |c = 370 K
JME 3710
November 10, 2010
Homework #10
1. (10 pts) A simple concentrictube heat exchanger uses hot oil to heat cold water. Mass ow
rates on both sides are 0.05 kg/s. The design temperature change on the cold side is Ti |c =
300 K To |c = 370 K and the oi
JME 3710
November 13, 2010
Homework #11
1. (10 pts) Irradiation of a particular surface results
from 2 contributions: one in which all rays are
parallel (being oriented at an angle = 45o ) and
one that is diuse, having a total intensity of Id =
100 W/(m2
JME 3710
November 13, 2010
Homework #11 Solutions
1. (10 pts) Irradiation of a particular surface results
from 2 contributions: one in which all rays are
parallel (being oriented at an angle = 45o ) and
one that is diuse, having a total intensity of Id =
JME 3710
November 19, 2010
Homework #12
0.3 m
1. (10 pts) Two surfaces are at right angles to one another, as shown in Fig. 1. Each surface has a depth
into the paper of D = 0.5 m and the planar dimensions shown in the gure. Calculate the view factor
F12
JME 3710
November 19, 2010
Homework #12 Solutions
0.3 m
1. (10 pts) Two surfaces are at right angles to one another, as shown in Fig. 1. Each surface has a depth
into the paper of D = 0.5 m and the planar dimensions shown in the gure. Calculate the view f
JME 3710
September 10, 2010
Homework #2
1. (10 pts) Onedimensional steadystate heat conduction occurs in the conguration shown in
Fig. 1. The slab has a thickness of d and a constant thermal conductivity of k. If the temperature distribution is T (x) = a0
JME 3710
December 3, 2010
Homework #13 Solutions
1. (10 pts) Temperature measurement of a uid ow using a thermocouple (TC) generally has to
be corrected for radiation eects if such cannot be neglected, e.g. for hot gases. For example,
absent radiation, th
JME 3710
September 2, 2010
Homework #1 Solutions
1. (10 pts) In a general case of conduction in one dimension, temperature and conductivity might
both be variable, i.e. T = T (x) and k = k(x), respectively, whereby we would write the Fourier
conduction eq
JME 3710
September 17, 2010
Homework #3
1. (10 pts) A particular device is heavily insulated (shaded portion) and dumps heat to the surroundings via an exposed planar
surface on top of area a b per a convection coecient of h and
a temperature dierence of
JME 3710
September 10, 2010
Homework #2 Solutions
1. (10 pts) Onedimensional steadystate heat conduction occurs in the conguration shown in
Fig. 1. The slab has a thickness of d and a constant thermal conductivity of k. If the temperature distribution is
JME 3710
September 17, 2010
Homework #3 Solutions
1. (10 pts) A particular device is heavily insulated (shaded portion) and dumps heat to the surroundings via an exposed planar
surface on top of area a b per a convection coecient of h and
a temperature di
JME 3710
September 24, 2010
Homework #4
x
1. (10 pts) A long plate of thickness 2L = 0.44m is made
of a material having the following properties: =
7800 kg/m3 , k = 55 W/(m K), and cP= 550 J/(kg K).
This plate is placed in a furnace having T = 1000 K
and
JME 3710
October 8, 2010
Homework #6
1. (10 pts) Air ows with a freestream velocity of u = 5 m/s along
a at plate of length L = 1 m and width w = 0.5 m. (Air properties are in Table 1.) A clever measurement method shows the total
shearbased drag force act
JME 3710
October 1, 2010
Homework #5
1. (10 pts) The dimensionless temperature distribution of a particular unsteady heat conduction
problem is given by the standard 1term approximate solution
2
= C1 e1 t cos(1 x ) ,
where x and t are the dimensionless
JME 3710
October 7, 2010
Homework #6 Solutions
1. (10 pts) Air ows with a freestream velocity of u = 5 m/s along
a at plate of length L = 1 m and width w = 0.5 m. (Air properties are in Table 1.) A clever measurement method shows the total
shearbased drag
JME 3710
September 24, 2010
Homework #4 Solutions
x
1. (10 pts) A long plate of thickness 2L = 0.44m is made
of a material having the following properties: =
7800 kg/m3 , k = 55 W/(m K), and c = 550 J/(kg K).
This plate is placed in a furnace having T = 1
JME 3710
October 1, 2010
Homework #5 Solutions
1. (10 pts) The dimensionless temperature distribution of a particular unsteady heat conduction
problem is given by the standard 1term approximate solution
2
= C1 e1 t cos(1 x ) ,
where x and t are the dime
JME 3710
October 21, 2010
Homework #8
1. (10 pts) Free convection can be important in certain cases of horizontal plates, which may be congured in either hotside up
(HSU) or hotside down (HSD) orientations. Under certain conditions, the McAdams correlatio
JME 3710
October 16, 2010
Homework #7 Solutions
1. (10 pts) The socalled slug ow model is simply
an idealized, uniform velocity prole u0 in a pipe
(Fig. 1). For a laminar ow having a uniform surface heat ux, the fullydeveloped temperature distribution is
JME 3710
October 16, 2010
Homework #7
1. (10 pts) The socalled slug ow model is simply
an idealized, uniform velocity prole u0 in a pipe
(Fig. 1). For a laminar ow having a uniform surface heat ux, the fullydeveloped temperature distribution is
r
2
u0 dTm
JME 3710
October 28, 2010
Homework #9
1. (10 pts) Sometimes a heat exchanger will have hot and cold sides of roughly equal thermal
capacities, i.e. (mcp )|h (mcp )|c and these exchangers are said to have balanced ow. Show
that for a simple counterow heat
JME 3710
October 20, 2010
Homework #8 Solutions
1. (10 pts) Free convection can be important in certain cases of horizontal plates, which may be congured in either hotside up
(HSU) or hotside down (HSD) orientations. Under certain conditions, the McAdams
JME 3710
October 28, 2010
Homework #9 Solutions
1. (10 pts) Sometimes a heat exchanger will have hot and cold sides of roughly equal thermal
capacities, i.e. (mcp )|h (mcp )|c and these exchangers are said to have balanced ow. Show
that for a simple count
E w s x T e e x T `h U w e `h b T u s T b x T T U `h b b g e x U ` b g s cfw_ d e x E U e wh
2(VQt7V7r(|7riVitF(Vtri@FQ~(i7@i87Q7rU
xT s u g s W o mG q P P
Viipr#yiF7 iF7tQv(VX |f r)iiVFcCrptQnQfd
s T b e x d h d e R U b e U U E W G q P P P D Uh T ` eh
bb d
XhV
hi UY
oq
u
g f wv
u
Xi
b
f
bd b
XXd
g t w y f t y w d w f f w f w g f w f y n w g r t v w
h8hXpch&ch8A8cfw_s88hAhc
hi f s Y ci UY cfw_h8ck8(8hXch&hhc8(8h8(hX(hh
oq
w r y w w r t v w y f t y w d w f t g w y w r w g f w f f t f r w
W UX
F
AYv8lnj8(8
F p U fe b he f h k | Q
ydGn(RiR(hA6 wA(m
V pe r
p m U r de r V V p e r p U f d p m U e g F Xe f p H h fe
8WAWTAWcuidGc8WYiu8gWi#
p d p V r h p f h f p d b U f d p S p U d re b
uWR8WAqiR(iW8WGcRqudci(f
UGnuRT8WiqiW(W8W8Yt8 H
f V fU p f
V V V
) B7j9 6 gpj
V V
) j9
k f f wf i w u uf p w f f x f i k v g x f kf i i
BhhXj(phh!ho9h@(o(h9y(uq
bbV
c c
gf f k k d e y u x f x f v k f f wf i w u uf x f v g s mf i gf ff g s w y
y(BgBsc9h9hBhhXjthh9ho|njhh(c
)
gy bb g
#BQX#By
gf
W m r t f t d f m t f g x m r g i r x r d i g y W g x
!hce!8!qh8hXqcyl%c!qX8h!qc8'8qhp'9Ae'yc8~0!8hA'hf
s x f t d f r t f r f f t x f ts i g f x f s x f t d f f f x g f x
!h8hXpc~cfw_'!q'hwphXcfw_z!td08hs!88h2!h8hXqcylUde8h!8hs!'
f s x f t d f r t f r