ME 345, HEAT TRANSFER
REVIEW FOR THE FIRST EXAM
I. BASIC HEAT TRANSFER: the three types (Ch. 1) **
1) Know what the following concepts are: heat transfer, heat flux, heat generation, conservation of energy for a surface or a control volume; know HOW heat moves (i.e. be able to visualize and draw the heat flows), adiabatic
2) Know these basic equations: Fourier’s law, Newton’s law of cooling, and the basic radiation equation
A) Know how to formulate the basic energy conservation equations and calculate heat transfer and/or temperatures
II. BASICS OF CONDUCTION: (Ch. 2)
1) Know what the following concepts are: thermal properties, including k, cp, , , and how they affect conduction; know the physical meaning of terms in the diffusion equation
2) Be able to recognize appropriate initial condition, or boundary conditions in temperature or flux from a physical situation, be able to calculate heat flux from a temperature distribution (such as T(x))
A) Be able to write the diffusion equation for a particular situation (wall or cylinder or sphere)
B) Given T(x,t) be able to calculate heat transfer, heat flux, rate of change of temperature, rate of energy storage
III. STEADY 1-D CONDUCTION:
1) what steady and 1-d mean physically; when to assume them, what the basic temperature profiles look like for the wall, cylinder and sphere if there is no generation or if there is, and if k is constant or not,
2) Basic idea behind the electrical analogy: how it works;
3) Basic ideas of fins (extended surfaces), how they are used, how to get the boundary conditions for them, the idea of symmetry
A) Be able to get the temperature distribution, heat transfer and heat flux for the energy (diffusion) equation without generation for the wall, cylinder, and sphere (see Table 3.3) Know how to apply other boundary conditions if there are not two temps given!
B) Be able to set up an equivalent circuit using conduction, convective, contact, and radiative resistances, and use it to solve for temperatures anywhere along the circuit as necessary, or for heat transfer
C) Be able to get the temperature distribution, heat transfer and heat flux for the energy (diffusion) equation WITH generation for the wall, cylinder, and sphere (Note: CANNOT use electrical circuit for the problem if it includes generation because q is not uniform in the body!)
D) Be able to formulate a fin problem, and calculate the temperature distribution along it, the total heat transfer from it (see Table 3.4) , and the fin effectiveness f and the fin efficiency f
** You should know how to do items preceded by a numberwithout your sheet. Items preceded by a letter may be done using your review sheet.
ME 345 EXAM GROUND RULES:
Exam has two parts
1)closed book portion first, only pen or pencil allowed. (NO calculators) 25% of exam
2)open sheet portion: handed out as first part is turned in
ALLOWED on second part:
Front of ONE handwritten 8 ½ x11” sheet of paper ONLY!!!.
Calculators.
I will hand out copies of any properties, tables, figures that you will need to do the exam.
There is to be NO sharing of materials, texts, etc.
ME 345 EXAMPLE EXAM # 1
CLOSED BOOK, CLOSED NOTES!! YOU WILL BE GIVEN THE REST OF THE EXAM WHEN YOU TURN THIS IN. I suggest that you take no more than 10-15 minutes for this part. If you want credit for something, write it down!
1) (15%) Briefly answer the following questions:
a) How does the subject of heat transfer differ from the subject of thermodynamics?
b) How does heat energy move in convection?
c) If you have 1-d heat transfer through a wall, what is the boundary condition at x=0 if the surface has convection?
2) (10%) For the conduction (or heat diffusion) energy equation below,
a) write inwords the physical meaning of each term in the equation and
b) state all the assumptions required to derive the equation from the basic conduction or energy conservation equation. (In other words, what assumptions are "included" in this equation?)
ME 345 EXAMPLE EXAM # 1
OPEN BOOK, OPEN NOTES. Be sure to state all of your assumptions, write all units, and BOX YOUR ANSWERS!
3) (25%) The temperature of the outer surface of a cast iron (k = 50 W/mK) furnace is 200C. The walls of the furnace are 6.0mm thick. The inside surface temperature of the walls of the surrounding room is 10C due to heat loss to the outside. You may assume that the emissivity of the outer furnace surface and the walls is 0.90. There is convection between the furnace and the room air, and also between the room air and the walls. You may assume that the temperature of the room air is uniform throughout. The convective heat transfer coefficient between the furnace surface and the air has the same value as that between the air and the outside wall: 10 W/m2K. Assuming 1-d, steady-state, and constant properties:
a) What is the heat flux to the room walls? (Hint: circuit)[answer: 3.2kW/m2]
b) What is the room air temperature? [378K]
c) What is the temperature of the INSIDE surface of the furnace? [200.4C]
4) (20%) To increase the heat dissipation from a heat exchanger tube with 2.5 cm outer diameter, rectangular annular fins of an aluminum alloy (k = 200 W/mK) are soldered to the outer surface. The fins are 0.1 cm thick and have an outer diameter of 5.5cm. If the tube temperature is 100C, the surroundings temperature is 25C, and the convective heat transfer coefficient between the fin and the environment is 65 W/m2K:
a) What is the fin efficiency? (Hint: p.123) [91%]
b) What is the rate of heat loss from one fin? [17.3W]
c) What is the fin effectiveness? [45.1]
(You may assume that contact resistance is negligible.)
5) (30%) In a graphite moderated nuclear reactor, heat is generated uniformly in long uranium rods (diameter = 0.05m) at the rate of 75,000 kW/m3. These rods sit in a pressurized water bath that is kept at 120C. The water cools the rods with a convective heat transfer coefficient of 55 kW/m2K. If the thermal conductivity of uranium is assumed to be constant at 29.5 W/mK:
a) What is the heat FLUX from the surface of the rod? [937.5 kW/m2]
(Hint: energy balance)
b) What is the temperature of the outer surface of the rod? [137C]
c) What is the temperature at the center of the rod? [534C]