(SEM V) THEORY EXAMINATION 2024-25 HEAT & MASS TRANSFER

Subject Code: BME501

Subject Name: Heat & Mass Transfer

Course: B.Tech (Semester V)

Maximum Marks: 70

Duration: 3 Hours

Exam Year: 2024–25

Sections: A, B, and C

SECTION A – Short Answer Questions (2 × 7 = 14 Marks)

Attempt all questions briefly.

a. Define heat transfer and explain its importance in engineering applications.
b. List the factors affecting thermal conductivity.
c. Explain how extended surfaces (fins) enhance heat transfer.
d. Differentiate between steady-state and transient heat conduction.
e. State the relation between fluid friction and heat transfer in forced convection.
f. State Planck’s law and its significance.
g. Explain the significance of fouling factors in heat exchangers.
 

SECTION B – Medium-Length Questions (7 × 3 = 21 Marks)

Attempt any three of the following.

Use the concept of critical radius of insulation to determine whether adding insulation increases or decreases heat loss.

Summarize temperature measurement errors due to thermometer wells.

Apply the empirical relation to calculate the heat transfer coefficient for natural convection over a vertical plate.

Determine heat transfer rate between two non-black surfaces in an enclosure using the radiation network method.

Describe the LMTD method and compare dropwise and filmwise condensation.
 

SECTION C – Long / Analytical Questions (7 × 5 = 35 Marks)

Attempt one part from each question.

Q3. Conduction

a. Compare heat conduction equations in rectangular, cylindrical, and spherical coordinates.
OR
b. A plane wall 150 mm thick, area 4.5 m², thermal conductivity 9.35 W/m°C.

Surface temperatures: 150°C and 45°C.

Find:
(i) Heat flow through wall
(ii) Temperature gradient along thickness.

Q4. Transient Conduction

a. Identify key assumptions in the lumped capacitance method.
OR
b. A copper slab (50 cm × 50 cm × 6.25 mm) initially at 300°C is suddenly exposed to 36°C air.

Given: ρ=9000 kg/m3, c=0.38 kJ/kg°C, k=370 W/m°C, h=90 W/m2°Cρ = 9000 \, kg/m^3, \, c = 0.38 \, kJ/kg°C, \, k = 370 \, W/m°C, \, h = 90 \, W/m^2°Cρ=9000kg/m3,c=0.38kJ/kg°C,k=370W/m°C,h=90W/m2°C.

Find time to reach 108°C.

Q5. Convection

a. Differentiate between laminar and turbulent flow heat transfer in natural convection.
OR
b. Explain momentum–heat transfer analogy for turbulent flow over a flat plate.

Q6. Radiation

a. Compare emissive properties of black and gray bodies with examples and explain how surface geometry affects shape factors.
OR
b. A small sphere (OD = 60 mm, T1=300°CT_1 = 300°CT1​=300°C) is placed concentrically inside a large sphere (ID = 360 mm, T2=15°CT_2 = 15°CT2​=15°C).

Assuming black body behavior, determine:
(i) Fraction of emission from large sphere incident on small one.
(ii) Net heat interchange between them.

Q7. Heat Exchangers

a. Differentiate between NTU and LMTD methods — highlight applicability and advantages.
OR
b. In a counter-current heat exchanger:

Fluid A: 1 kg/s, Tin=420°C, cp=1 kJ/kg⋅KT_{in} = 420°C, \, c_p = 1 \, kJ/kg·KTin​=420°C,cp​=1kJ/kg⋅K.

Fluid B: 1 kg/s, Tin=20°C, cp=4 kJ/kg⋅KT_{in} = 20°C, \, c_p = 4 \, kJ/kg·KTin​=20°C,cp​=4kJ/kg⋅K.

Effectiveness = 75%.

Find:
(i) Heat transfer rate
(ii) Exit temperature of fluid B.

Key Topics to Study

Conduction: Fourier’s law, steady vs transient, 1D heat flow equations

Convection: Laminar/turbulent heat transfer, boundary layer theory

Radiation: Blackbody laws, shape factors, emissivity

Heat Exchangers: LMTD and NTU methods, effectiveness, fouling

Mass Transfer: Diffusion, analogies between heat, mass, and momentum

Numericals: Critical radius, heat transfer coefficient, radiation networks

Preparation Tips

Revise formulas and units:

q=−kAdTdxq = -kA \frac{dT}{dx}q=−kAdxdT​, Nu=hLkNu = \frac{hL}{k}Nu=khL​, ε=qσT4ε = \frac{q}{σT^4}ε=σT4q​, Q=UAΔTmQ = U A ΔT_mQ=UAΔTm​.

Practice numericals on plane wall, lumped system, and heat exchangers.

Draw clear sketches for radiation enclosure and convection boundaries.

Remember assumptions for analytical methods (steady state, 1D, constant properties).

Review real-world applications — fins, cooling systems, condensers.