A spherical vessel has an inner radius r 1 and an outer radius r 2 . The inner surface ( r = r 1 ) of the vessel is subjected to a uniform heat flux q 1 . The outer surface ( r = r 2 ) is exposed to convection and radiation heat transfer in a surrounding temperature of T ∞ . The emissivity and the convection heat transfer coefficient on the outer surface are ε and h , respectively. Express the boundary conditions and the differential equation of this heat conduction problem during steady operation.
A spherical vessel has an inner radius r 1 and an outer radius r 2 . The inner surface ( r = r 1 ) of the vessel is subjected to a uniform heat flux q 1 . The outer surface ( r = r 2 ) is exposed to convection and radiation heat transfer in a surrounding temperature of T ∞ . The emissivity and the convection heat transfer coefficient on the outer surface are ε and h , respectively. Express the boundary conditions and the differential equation of this heat conduction problem during steady operation.
Solution Summary: The author describes the boundary conditions for the heat conduction during the steady operation and the differential equation for heat transfer through the outer surface.
A spherical vessel has an inner radius r1 and an outer radius r2. The inner surface
(
r
=
r
1
)
of the vessel is subjected to a uniform heat flux q1. The outer surface
(
r
=
r
2
)
is exposed to convection and radiation heat transfer in a surrounding temperature of
T
∞
. The emissivity and the convection heat transfer coefficient on the outer surface are
ε
and h, respectively. Express the boundary conditions and the differential equation of this heat conduction problem during steady operation.
The furnace wall shown in the figure is made of a material with a thermal conductivity of 5 W / m ° C, the radiant emission coefficient of the outer surface of the wall is 0.95, Stefan Boltzman constant is 5.67x104 W / m ^ 2 (K ^ 4), ambient temperature and air temperature 297 K is. The heat transfer coefficient between the outer surface of the wall and the air is h = 20 W / m (K ^ 2). Wall inner surface temperature 573 K, outer surface temperature 308 K Since the value is kept constant a) Find the layer thickness of the wall? b) Find the layer thickness of the wall if the moving fluid medium on the outer surface of the wall is corroded?
The interior surface of a 25 cm thick wall has a temperature of 27 \deg C as shown in the figure. The outer surface is exposed to a solar radiation of 150 W/m^2 and exchanges heat by radiation and convection with the surroundings and the air that are at the same temperature of 40 \deg C. The coefficient of heat transfer by convection is 8 W/m^2* K, consider both the absorptivity (\alpha ) and emissivity (\epsi equal to 0.8. Assuming transfer of 1D heat and at steady state, determine the surface temperature outside and the heat flow by conduction in the wall in three conditions different: a) If the wall is made of brick (k=0.72 W/m*K) b) If the wall is made of wood (k=0.17 W/m*K) c) If the wall is made of rigid foam (polyurethane) (k=0.026 W/m*KMake a diagram of the corresponding thermal resistance circuit and a diagram of the variation of temperatures from the interior wall to the air abroad.
10 hot rods (L = 5 m and d = 2 cm) are buried in the ground parallel to each other each rod is 10 cm apart and at a depth 3 m from the ground surface. The thermal conductivity of the soil is 0.6 W/m K. If the surface temperature of the rods and the ground are 600 K and 30 °C, respectively. Draw the figure and determine the rate of heat transfer from the fuel rods to the atmosphere through the soil
Chapter 2 Solutions
Heat and Mass Transfer: Fundamentals and Applications
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