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Heat transfer Final Exam, Papers of Heat and Mass Transfer

Heat transfer Final exam Summer

Typology: Papers

2020/2021

Uploaded on 09/14/2023

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ME 3333 Heat Transfer
Midterm Exam
Summer 2020
(Duration: 24 Hours)
Notes:
1. Open textbook, open notes. Calculator allowed.
2. No communication between students allowed.
3. There are totally 7 problems. Please write your answers of
problem 2-7 on blank sheets.
pf3
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Download Heat transfer Final Exam and more Papers Heat and Mass Transfer in PDF only on Docsity!

ME 3333 Heat Transfer

Midterm Exam

Summer 20 20

(Duration: 24 Hours)

Notes:

1. Open textbook, open notes. Calculator allowed.

2. No communication between students allowed.

3. There are totally 7 problems. Please write your answers of

problem 2- 7 on blank sheets.

  1. (5 pts) TRUE/FALSE (1 point each, please circle your answer,

there is no penalty for guessing)

  1. If the Biot number is large for a solid sphere immersed in a fluid, then

conduction within the sphere is extremely fast relative to convection

on the surface, and temperature distribution in the sphere is uniform.

TRUE FALSE

  1. To solve for the transient temperature distribution in 1-D planar wall

(solid), two boundary conditions (spatial) and one initial condition (in

time) must be known.

TRUE FALSE

  1. When using the lumped capacitance approach to determine the change

in temperature of an object over time, the total change in thermal

energy in the object can be calculated as: mc(T(t)-T(0)) ; where c is

the specific heat, m is the objects mass, T(t) is the object’s

temperature at the t , and T(0) is the initial temperature.

TRUE FALSE

  1. In 1D steady state heat conduction, a boundary condition with

adiabatic or insulated surface means the surface temperature must be

equal to zero.

TRUE FALSE

  1. In 1D heat transfer problems, the surface energy balance at the control

surface holds for both steady-state and unsteady-state conditions.

TRUE FALSE

  1. (15 pts) A 0.5 m x 1 m double paned window is made of two

silica glass panes 1 cm thick, with air in between. Under steady

conditions, linear (constant gradient) temperature profiles are

found in both silica panes, as well as the air.

a) If the room (and the inner surface of the inner glass pane) is

at a temperature of 25

o

C , while outdoors it is - 25

o

C with a

convection coefficient of 18 W m

- 2

K

- 1

, what is the rate of

heat loss through the window?

b) What is the rate of heat loss if the room temperature is

decreased to 20

o

C?

c) Finally, what is the rate of heat loss for a room temperature

of 25

o

C , but with one of the panes (and the air) removed?

  1. ( 10 pts) The steady-state temperature distribution in a 1-D wall

with a thickness of L=10 cm (considered as characteristic

length) is given as T(x)=-3000x

2

+100x+500 (“T” in Kelvins and

“x” in meters). On both sides, the wall is losing heat by

convection to a liquid at 300 K. Determine the Biot number on

each side of the wall. Note that the thermal and/or material

properties of the wall are not known.

  1. ( 20 pts) Heat is generated uniformly in a 1 m long nuclear fuel

rod, which has a radius of 5 cm. The rod is cooled by the

surrounding water at T ∞

= 20 °C. Due to the directionality of the

flow, convection heat transfer coefficients on each side of the

rod are different. To simplify the problem, we can assume that,

uniformly h 1

=50 W/m

2

× K on the right-hand side of the dashed

rectangle and it is h 2

=25 W/m

2

× K on the left-hand side.

Determine the maximum allowable heat generation rate within

the rod for the centerline temperature to not exceed 3000 K at

steady-state. The thermal conductivity of the rod is k= 1 W/m

×

K.

  1. ( 20 pts) A sphere with 30 mm in diameter initially at 800 K is

quenched in a large bath having a constant temperature of 320

K with a convection heat transfer of 75 W/m

2

×

K. The

thermophysical properties of the sphere material are: ρ=

kg/m

3

, c=1600 J/kg × K, and k=1.7 W/m × K. (Use characteristic

length Lc=V/A to determine applicability of lumped method; Use

radius of the sphere for one term approximation)

a) Calculate the time required for the surface of the sphere to

reach 415 K.

b) Determine the heat flux (W/m

2

) at the outer surface of the

sphere at the time determined in part a).

c) Determine the energy (J) that has been lost by the sphere

during the process of cooling to the surface temperature of

415 K.