MECH3260 Chap.7 Heat Transfer Exam Toolkit
Heat Transfer Exam Toolkit
Weeks 7 to 12 of MECH3260 cover Heat Transfer, which is examined on the Final Exam only and not on the Mid-semester Test. The Final Exam is closed book, and the Heat Transfer equation and data sheet is supplied with it, along with any tables and charts a question needs.
That changes what preparation means: the marks are not in recalling formulas but in recognising which supplied formula a described situation calls for and substituting into it in consistent units. This chapter is built around that skill.
It walks the equation sheet section by section, giving each group its physical meaning and the question shape it answers, across conduction and thermal resistance networks, fins and extended surfaces, transient conduction and the lumped-capacitance limit, heat exchangers, the dimensionless groups that govern convection, and radiation exchange.
What this chapter covers
- 01
Fourier's law of conduction and the resistance-network method (plane wall, cylinder, convection film, critical radius of insulation)
- 02
Fin heat rate, fin efficiency eta_f = tanh(mL*)/mL*, and overall surface efficiency eta_o
- 03
Transient conduction via lumped capacitance, validity checked with the Biot number Bi = hLc/k
- 04
Heat exchangers: LMTD method, Q = UA * LMTD, and overall U built from series resistances
- 05
Dimensionless groups Nu, Pr, Re, Gr, Ra that correlate convective heat transfer
- 06
Radiation: blackbody emissive power E = epsilon sigma T^4, net exchange, radiosity
Recognising which equation-sheet formula a stem wants (three-card drill)
- +2Pipe with radii and length, asked for heat loss per unit length: cylindrical conduction resistance R = ln(r2/r1)/2*pi*k*L.
- +2Metal sphere cooling in a stirred bath: lumped capacitance, but check Bi = hLc/k < 0.1 first.
- +2Parallel plates at different temperatures in vacuum: net radiative exchange Q_net = epsilon*sigma*A*(Ts^4 - Tsur^4), temperatures in kelvin.
Key terms
- Thermal resistance
- The temperature difference divided by the heat rate, defined so that resistances in series add just as they do in an electrical circuit. It is the organising idea behind almost every conduction question on the exam.
- Critical radius
- The insulation thickness on a pipe below which adding more insulation increases heat loss rather than reducing it, because the extra outer surface area for convection outweighs the extra conduction resistance.
- Fin efficiency
- The actual fin heat rate compared with the rate the fin would give if all of it sat at the base temperature. It is always at most one and falls as a fin is made longer or thinner, since more of it approaches the fluid temperature.
- Overall surface efficiency
- The blend of fin efficiency with the bare area between fins, weighted by how much of the total surface each contributes. This is the number that enters a heat-exchanger resistance network, since finned surfaces are usually one side of an exchanger.
- Biot number
- The ratio of a solid's internal conduction resistance to its surface convection resistance. Below about a tenth the interior is nearly uniform in temperature and the lumped-capacitance treatment applies.
- Time constant
- The product of density, specific heat and volume divided by the product of convection coefficient and area. It sets how quickly a lumped body approaches the fluid temperature, and the response is exponential in time divided by it.
- Log mean temperature difference
- The averaging of the two end temperature differences that makes the simple heat rate expression exact for a heat exchanger. It is the standard route when both inlet and outlet temperatures are known.
- Effectiveness
- The actual heat transfer divided by the largest transfer thermodynamically possible for the given inlet temperatures. It pairs with the number of transfer units, and this route is the one to use when outlet temperatures are unknown.
Heat Transfer Exam Toolkit FAQ
Do I need to memorise the Heat Transfer equations for the Final Exam?
No. The exam is closed book, but the Heat Transfer equation and data sheet is provided, together with any tables and charts a question requires. The sheet's own closing note adds that transient-conduction equations and convection correlations from the tables and charts document will also be supplied if a question needs them.
What is being tested is recognition and correct substitution, not recall, so preparation should be spent on knowing what each group of equations is for.
How do I choose between the log mean temperature difference method and the effectiveness method?
By what the question tells you. If all four terminal temperatures are known, or three are known and the fourth follows from an energy balance, the log mean route is direct. If the outlet temperatures are the unknowns, the log mean route needs iteration and the effectiveness and number-of-transfer-units route does not. Recognising which situation you are in before you start is worth more time than any algebra later.
When is it safe to treat a cooling object as a single lumped temperature?
When the Biot number, formed with the characteristic length equal to volume divided by surface area, is below roughly a tenth. That says the resistance to conduction inside the body is small compared with the resistance to convection at its surface, so the interior stays nearly uniform while the whole thing cools.
Above that threshold the temperature varies with position and the exponential decay expression no longer describes the object.
Why does adding insulation sometimes make a pipe lose more heat?
Because insulating a curved surface does two things at once. It adds conduction resistance, which reduces the loss, but it also enlarges the outer surface exposed to the surrounding air, which increases the convective loss. Below the critical radius the second effect wins.
It only bites on small-diameter pipes and wires, which is exactly where a question will set it up, so treat any thin cylinder plus insulation problem as a prompt to check the critical radius first.
Exam move
Work from the equation sheet itself rather than from a summary of it, because that sheet is what you will have in the room. Go through it group by group and write beside each block the kind of question it answers and the one clue in a question stem that points to it, so that in the exam you are matching a situation to a location on a page you already know.
Practise the resistance-network drawing separately from the arithmetic, since almost every conduction question is won or lost on getting the chain of resistances and their geometries right. Then rehearse the two heat-exchanger routes as a decision rather than as two methods, choosing between them from what the question leaves unknown.
Keep a standing unit check for radiation, where absolute temperature is required and a Celsius value produces an answer that is wrong by orders of magnitude. Finally, pair this chapter with your own lecture notes and tutorial problems from this half of the unit, since those carry the worked applications and the correlation charts your tutor emphasised.
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