The energy transferred from the anterior chamber of the eye through the cornea varies considerably depending on whether a contact lens is worn. Treat the eye as a spherical system and assume the system to be at steady state. The convection coefficient h o is unchanged with and without the contact lens in place. The cornea and the lens cover one-third of the spherical surface area. Values of the parameters representing this situation are as follows: r 1 = 10.2 mm r 2 = 12.7 mm r 3 = 16.5 mm T ∞ , o = 21 ° C T ∞ , i = 37 ° C k 2 = 0.80 W/m ⋅ K k 1 = 0.35 W/m ⋅ K h o = 6 W/m 2 ⋅ K h i = 12 W/m 2 ⋅ K Construct the thermal circuits. labeling all potentials and flows for the systems excluding the contact lens and including the contact lens. Write resistance elements in terms of appropriateparameters. Determine the heat loss from the anterior chamber with and without the contact lens in place. Discuss the implication of your results.
The energy transferred from the anterior chamber of the eye through the cornea varies considerably depending on whether a contact lens is worn. Treat the eye as a spherical system and assume the system to be at steady state. The convection coefficient h o is unchanged with and without the contact lens in place. The cornea and the lens cover one-third of the spherical surface area. Values of the parameters representing this situation are as follows: r 1 = 10.2 mm r 2 = 12.7 mm r 3 = 16.5 mm T ∞ , o = 21 ° C T ∞ , i = 37 ° C k 2 = 0.80 W/m ⋅ K k 1 = 0.35 W/m ⋅ K h o = 6 W/m 2 ⋅ K h i = 12 W/m 2 ⋅ K Construct the thermal circuits. labeling all potentials and flows for the systems excluding the contact lens and including the contact lens. Write resistance elements in terms of appropriateparameters. Determine the heat loss from the anterior chamber with and without the contact lens in place. Discuss the implication of your results.
The energy transferred from the anterior chamber of the eye through the cornea varies considerably depending on whether a contact lens is worn. Treat the eye as a spherical system and assume the system to be at steady state. The convection coefficient
h
o
is unchanged with and without the contact lens in place. The cornea and the lens cover one-third of the spherical surface area.
Values of the parameters representing this situation are as follows:
r
1
=
10.2
mm
r
2
=
12.7
mm
r
3
=
16.5
mm
T
∞
,
o
=
21
°
C
T
∞
,
i
=
37
°
C
k
2
=
0.80
W/m
⋅
K
k
1
=
0.35
W/m
⋅
K
h
o
=
6
W/m
2
⋅
K
h
i
=
12
W/m
2
⋅
K
Construct the thermal circuits. labeling all potentials and flows for the systems excluding the contact lens and including the contact lens. Write resistance elements in terms of appropriateparameters.
Determine the heat loss from the anterior chamber with and without the contact lens in place.
The initial temperature distribution of a 5 cm long stick is given by the
following function. The circumference of the rod in question is completely
insulated, but both ends are kept at a temperature of 0 °C. Obtain the heat
conduction along the rod as a function of time and position ? (x =
1.752 cm²/s for the bar in question)
100
A) T(x1) = 1 Sin ().e(-1,752 (³¹)+(sin().e (-1,752 (²) ₁ +
1
3π
TC3
.....)
100
t + ··· .......
13) T(x,t) = 200 Sin ().e(-1,752 (²t) + (sin (3). e (-1,752 (7) ²) t
B)
3/3
t + …............)
C) T(x.t) = 200 Sin ().e(-1,752 (²t) (sin().e(-1,752 (7) ²) t
–
D) T(x,t) = 200 Sin ().e(-1,752 (²)-(sin().e (-1,752 (²7) ²) t
E) T(x.t)=(Sin().e(-1,752 (²t)-(sin().e(-1,752 (²) t+
t + ··· .........)
t +....
t + ··· .........)
…..)
You are asked to estimate the maximum human body temperature if the metabolic
heat produced in your body could escape only by tissue conduction and later on the surface by
convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in
radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when
the temperature only depends on the radial coordinater from the centerline. The governing
dT
+q""=0
dr
equation is written as
1 d
k-
r dr
r = 0,
dT
dr
=0
dT
r=ro -k -=h(T-T)
dr
(k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the
skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat
generation rate in the body (W/m³) and is defined as heat generated per unit volume per second.
The 1-D (radial) temperature distribution can be derived as:
T(r) =
q"¹'r² qr qr.
+
4k 2h
+
4k
+T
, where k is thermal conductivity of tissue
air
(A) q" can be calculated…
A thermometer has a time constant of 10 s and behaves as a first-order system. It is initially at a temperature 30°C and then suddenly subjected to a surrounding temperature of 150°C. Calculate the 90 percent rise time and the time to attain 99 percent of the steady-state temperature. Repeat these calculations for a time constant of 5 s and compare the results with that of the previous case
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