1. Sphere 1 with a diameter of 0.1 m is completely enclosed by another sphere 2 of diameter 0.4 m. The view factor F12 is
2. One-dimensional steady state heat conduction takes place through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is
3. A thin vertical flat plate of height L, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings, and the properties of the surrounding fluid, are constant. The relationship between the average Nusselt and Rayleigh numbers is given as Nu = K Ra1/4 , where K is a constant. The length scales for Nusselt and Rayleigh numbers are the height of the plate. The height of the plate is increased to 16L keeping all other factors constant.
If the average heat transfer coefficient for the first plate is h1 and that for the second plate is h2, the value of the ratio h1/h2 is ______________.
4. Consider two concentric circular cylinders of different materials M and N in contact with each other at r=b, as shown below. The interface at r=b is frictionless. The composite cylinder system is subjected to internal pressure P. Let (urM,urespectively, uθM) and (σrrM,σθθM material ) denote the radial and tangential displacement and stress components, respectively, in material M. Similarly, (urN,uθN) and (σrrN,σθθN ) the radial and tangential displacement and stress components, respectively, in material denote N. The boundary conditions that need to be and satisfied at the frictionless interface between the two cylinders are:
(A) urM = urN and σrrM = σrrN only
(B) urM = urN and σrrM = σrrN and uθM = uθN and σθθM = σθθN
(C) uθM = uθN and σθθM = σθθN only
(D) σrrM = σrrN and σθθM = σθθN only
5. Three sets of parallel plates LM, NR and PQ are given in Figures 1, 2 and 3. The view factor FIJ is defined as the fraction of radiation leaving plate I that is intercepted by plate J. Assume that the values of FLM and FNR are 0.8 and 0.4, respectively. The value of FPQ (round off to one decimal place) is ______.
6. Hot and cold fluids enter a parallel flow double tube heat exchanger at 100 °C and 15 °C, respectively. The heat capacity rates of hot and cold fluids are Ch = 2000 W/K and Cc = 1200 W/K, respectively. If the outlet temperature of the cold fluid is 45 °C, the log mean temperature difference (LMTD) of the heat exchanger is _________ K (round off to two decimal places).