(SEM V) THEORY EXAMINATION 2023-24 HEAT AND MASS TRANSFER

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}θi​θ​=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.