Department of Materials Science and Engineering
MSE202A Assignment sheet 5 ( Problems on convection and radiation)
DISCUSSION on Friday 17th February, 2023
Problem 1 Consider flow of heat in a solid to be approximated as a semi infinite planner geometry.
Given that surface temperature is 598 K and ambient temperature is 298K, Estimate the
instantaneous heat flux at t=40s and time average heat flux over a period of 120o seconds.
Thermal conductivitu and thermal diffusivity of the solid are respectively 30 and 5x10 -6 ( in SI
unit)
Problem 2 A sphere of aluminium is melting in a molten steel bath. The governing equation is:
T
R ( t )
Ks
- h c (Tbath - TM,i ) = ρs ΔH
r
t
Estimate the complete melting time on the basis of the basis of an initial diameter based Reynolds
number and the following given data. The following are the applicable data set: initial sphere
diameter=0.05m, melting point of aluminium =770 C, Bulk temperature =1600 C. Assume that
Ranz-Marshall correlation is applicable , free stream liquid velocity is =0.05m/s, Prandtl number
of the fluid is 2 and kinematic viscosity of steel is 10-6 m/s. Assume that there is no shell formation
, negligible temperature gradient in Al sphere and latent heat of melting 271954 J/kg.
Problem 3:Consider a horizontal platinum wire of length 0.1m and diameter 0.0005m which is
heated by the passage of an electric current. The platinum wire which is of cylindrical shape is
submerged in a fluid (air) with an ambient temperature of 25 oC and free stream velocity of
100m/s in the direction of the length of the wire. The resistance of the wire is 0.06 ohm and its
surface temperature remains constant throughout at 300 oC. On the basis of the following
properties of air, estimate the magnitude of the current flowing through the platinum conductor.
Density=0.812 kg/m3 , thermal conductivity =0.0354 W/m.K, Kinematic viscosity=3.02x10 m2/s,
Pr=0.71 and applicable convective heat transfer correlation: NuD=0.683 (ReD )0.466 (Pr)0.33
Problem 4 Estimate the steady rate of heat loss from the BOF converter mouth assumed to be
behaving like a black body at 1500 deg C to the surrounding atmosphere at 300 K.
Problem 5: Estimate the radiative exchange between two grey bodies ( 2 dimensional steel and
refractory plates having 0.2mx0.2m area each ) separated by a distance of 0.2 m ( view factor is
0.2). Emissivity of steel is 0.8 and that of refractory is 0.5. Surface temperature of steel is 1200K
and that of refractory 600 K.
Problem 6 A flat steel plate is cooling in stagnant air. The surface temperature is 1400K and the
ambient temperature is 300K. If emissivity of steel is 0.8, calculate the relative radiative to
convective heat flux, given that the following free convection correlation is applicable:
NuL=0.3(GrL)1/4. Assume a 1 m plate length and apply properties of air from net/literature at
300k ( or, 25 deg.C).