Indian Institute of Technology, Kanpur

Department of Materials Science and Engineering

MSE 651: Transport Phenomena

Academic Year: 2025-2026

Semester: I

Assignment 5

Total Marks: 60

Marks for individual questions are given in parentheses.

Question 1

(a) In radiation, the named laws are important. What are the physical contents of the laws associated with the following scientists: Stefan and Boltzmann, Planck, Kirchhoff, and Wien?

(b) How are the Stefan-Boltzmann law and the Wien displacement law related to the Planck black-body spectral distribution law?

Marks: (2 × 4 + 4 = 12 marks)

Question 2

(a) Calculate the total emissive power of a black body (Eb) at 1200 K.

Given: The value of the proportionality constant in the Stefan-Boltzmann Law, σ = 5.673 × 10⁻⁸ W m⁻² K⁻⁴.

(b) Calculate the fraction of the total thermal emission from the black body in the wavelength range 0–500 µm (f0–500µm) at 1200 K.

Given: The values of the constants in Planck’s distribution for calculating the spectral emissive power of a black body (Eb,λ) are C1 = 3.742 × 10⁸ W µm⁻⁴ m⁻² and C2 = 1.439 × 10⁴ µm K.

Marks: (4 + 7 = 11 marks)

Question 3

An opaque horizontal plate, which is insulated on its backside, receives total irradiation at the rate of 3000 W/m², of which 500 W/m² is reflected. The plate is at a temperature of 200°C and has a total hemispherical emissive power (E) of 500 W/m².

Air at 25°C flows over the plate and the average convective heat transfer coefficient over the entire plate is 20 W/m²·K.

Calculate the following:

(a) The total hemispherical emissivity and the total hemispherical absorptivity.

(b) The total hemispherical radiosity of the plate.

Marks: ([2 + 2] + 2 + 3 = 9 marks)

Question 4

Calculate view factors for all surfaces shown in the figure. Use charts for view factors uploaded in the portal if necessary, but the use of charts should be kept to a minimum.

Make use of the summation rule and reciprocity rule to minimize the use of charts.

Marks: 8 marks

Question 5

A well-insulated electrically heated cylindrical crucible has a diameter of 12 cm and depth of 20 cm and is open to the atmosphere at its upper end.

If the inner walls of the crucible behave as black bodies, calculate the power required to maintain the bottom surface (surface 1) at 1400°C and the vertical side walls (surface 2) at 1200°C.

The ambient temperature outside the crucible is 25°C.

Question 6

The figure shows the cross section of a long duct in which the inner wall conditions are:

T1 = 600 K and emissivity ε1 = 0.5

T2 = 800 K and emissivity ε2 = 0.6

T3 = 1000 K and emissivity ε3 = 0.7

Calculate the radiosities of the inner surfaces of the duct and the net heat flux at the walls.

Use the charts uploaded in the portal for calculating the view factors.

MSE 651: Transport Phenomena | IITK | Assignment 5 | PDF