Course: B.Tech (Mechanical Engineering)
Semester: V
Subject Code: KME501
Subject Title: Heat and Mass Transfer
Maximum Marks: 100
Duration: 3 Hours
Paper Structure:
Section A: Short answer questions — 20 marks
Section B: Descriptive questions — 30 marks
Section C: Numerical/Analytical/Long questions — 50 marks
SECTION A — Short Answer Questions (10 × 2 = 20 Marks)
All questions are compulsory.
Main topics tested:
Effect of temperature on thermal conductivity of metals and its SI unit.
Concept of thermal resistance.
Unsteady state heat conduction — definition and significance.
Effectiveness and efficiency of fins.
Difference between natural and forced convection.
Sketch of velocity boundary layer over a flat plate.
Rules for radiation shape factor determination.
Black body and gray body concepts.
Fouling factor in heat exchangers.
Modes of mass transfer — diffusion, convection, evaporation.
This section mainly checks theoretical understanding of conduction, convection, radiation, and basic heat exchanger principles
SECTION B — Descriptive Questions (3 × 10 = 30 Marks)
Attempt any three questions.
Derivation of General Heat Conduction Equation for Cartesian coordinates.
Lumped Parameter Analysis:
Assumptions used.
Derivation of the transient heat conduction relation:
- θθi=e−Bi⋅Fo\frac{\theta}{\theta_i} = e^{-Bi \cdot Fo}θiθ=e−Bi⋅Fo
Reynolds and Colburn Analogy: Derivation of Nusselt Number for turbulent flow over a flat plate.
Reciprocity Theorem for shape factor — statement and proof.
Explanation of:
Fick’s Law of Diffusion
Film-wise and Drop-wise Condensation
SECTION C — Numerical and Analytical Questions (5 × 10 = 50 Marks)
Attempt one part from each of Q3–Q7.
Q3. Heat Conduction (Conduction Problems)
(a) Derive expression for critical radius of insulation for a cylinder and determine effectiveness for a 10 mm cable with rubber insulation (given h=8.5W/m2°Ch = 8.5 W/m^2°Ch=8.5W/m2°C, k=0.155W/m°Ck = 0.155 W/m°Ck=0.155W/m°C).
(b) Derive steady-state heat transfer rate for a hollow cylinder and solve given numerical with stainless steel and asbestos insulation
Q4. Fins and Heat Dissipation
(a) Derive the temperature distribution for a fin insulated at the tip.
(b) Design calculation for aluminium square fins on a semiconductor device (given k=200W/m°Ck = 200 W/m°Ck=200W/m°C, h=15W/m2°Ch = 15 W/m^2°Ch=15W/m2°C, surface temperature = 80°C, ambient = 40°C).
Q5. Convection and Dimensionless Numbers
(a) Explain the following:
Nusselt Number Grashoff Number
Prandtl Number Stanton Number
(b) Problem: Calculate heat transfer coefficient and heat transfer rate from a vertical plate (2 m × 2 m) with given air properties and constants C=0.15C = 0.15C=0.15, n=1/3n = 1/3n=1/3.
Q6. Radiation Heat Transfer
(a) Numerical on radiation shield — determine % reduction in heat transfer when a shield (ε = 0.1) is placed between two plates (ε₁ = 0.5, ε₂ = 0.7, T₁ = 1000 K, T₂ = 500 K).
(b) Theoretical explanation:
Kirchhoff’s Law
Stefan-Boltzmann Law
Absorptivity, Reflectivity, Transmissivity
Q7. Heat Exchanger and Boiling Phenomena
(a) Derive NTU-method effectiveness expression for a parallel flow heat exchanger.
(b)
Draw boiling curve and label regimes of pool boiling.
Numerical: Counterflow heat exchanger cooling 50,000 kg/hr of fluid from 65°C → 40°C using 40,000 kg/hr of water (10°C inlet).
Given: U=580W/m2KU = 580 W/m^2KU=580W/m2K, Cp(liquid)=3700J/kgKC_p (liquid) = 3700 J/kgKCp(liquid)=3700J/kgK, Cp(water)=4180J/kgKC_p (water) = 4180 J/kgKCp(water)=4180J/kgK.
Find required surface area.
Key Concepts Covered
Modes of heat transfer (conduction, convection, radiation) Critical insulation and fin analysis
Heat exchangers and NTU method Dimensionless parameters and empirical correlations
Radiation heat transfer and shielding Lumped system and transient conduction
Diffusion and condensation phenomena
FAQs
Q1. What is thermal conductivity’s SI unit?
→ W/m·K
Q2. What is the critical radius of insulation?
→ The radius at which adding insulation increases heat loss rather than reducing it.
Q3. Define fouling factor.
→ A measure of resistance due to deposit formation in heat exchangers.
Q4. What is the role of Nusselt Number?
→ It represents the ratio of convective to conductive heat transfer across a boundary.
Q5. What is Kirchhoff’s Law?
→ It states that for a body in thermal equilibrium, absorptivity = emissivity at a given wavelength and temperature.
