Question

# a) A 12 mm diameter mild steel sphere (k = 42.5 W/m K) is exposed to...

a) A 12 mm diameter mild steel sphere (k = 42.5 W/m K) is exposed to cooling airflow at 27 0C resulting in the convective coefficient, h = 114 W/ m2 K. The relevant properties of mild steel are given as follows: Density , /7850 2 mkg  Specific heat K kgJc p / 475 and thermal diffusivity hr m /043.0 2  Determine: (i) Time required to cool the sphere (lumped parameter system) from 540 0C to 950C. [7 marks] (ii) Instantaneous heat transfer rate 2 minutes after the start of cooling [5 marks] (iii) Total energy transferred from the sphere during the first 2 minutes [5 marks] (b) Sun may be approximated as black body. It emits radiation having maximum intensity at λmax = 0.5 micron. Calculate: (i) The surface temperature of sun using Wien’s displacement law [2 marks] (ii) The radiation heat flux at sun’s surface using Stefan-Boltzmann Law. The Stefan-Boltzmann constant, σ = 5.67 x 10-8 W/m2 K4. [3 marks] (c) One side of a 15 cm thickness layer of insulation (k = 0.75 W/m 0C) has a temperature of 200 0C while the other loses heat to an ambient at 27 0C at the rate of 600 W/m2. Take A = 1.0 m2. Calculate: (i) The air-film heat transfer coefficient (h) [2 marks] (ii) The skin temperature (say, T”) of the insulation [2 marks] (d) What are the concept of ‘Black body’ and ‘Gray body’ Radiation??

(b) The concept is to apply " Weins Displacement Law " which calculates the temperature corresponding to maximum wavelength.Once the temperature is known at Sun's s surface ,the heat flux can be calculated by using ' Stefan's law ' using Stefan-Boltzman constant.