A large plane wall, with a thickness L and a thermal conductivity k, has its left surface ( x = 0 ) exposed. to a uniform heat flux q 0 . On the right surface ( x = L ) , convection and radiation heat transfer occur in a surrounding temperature of T ∞ . The emissivity and the convection heat transfer coefficient on the right surface are ε and h respectively. Express the boundary conditions and the differential equation of this heat problem during steady operation.
A large plane wall, with a thickness L and a thermal conductivity k, has its left surface ( x = 0 ) exposed. to a uniform heat flux q 0 . On the right surface ( x = L ) , convection and radiation heat transfer occur in a surrounding temperature of T ∞ . The emissivity and the convection heat transfer coefficient on the right surface are ε and h respectively. Express the boundary conditions and the differential equation of this heat problem during steady operation.
Solution Summary: The author explains the boundary condition and differential equation of heat conduction during steady operation.
A large plane wall, with a thickness L and a thermal conductivity k, has its left surface
(
x
=
0
)
exposed. to a uniform heat flux
q
0
. On the right surface
(
x
=
L
)
, convection and radiation heat transfer occur in a surrounding temperature of
T
∞
. The emissivity and the convection heat transfer coefficient on the right surface are
ε
and h respectively. Express the boundary conditions and the differential equation of this heat 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?
an unsisulated 100 mm diameter steam pipe runs for 25 meters inside a room whose walls and air are at a temperature of 25 C. the superheated steam inside the pipe maintains the temperature at the pipe surface at 150 C. if the natural convection heat transfer coefficient of the air outside the pipe is 10 w/m^2 k and the surface emissivity is 0.8, compute for the total rate of heat transfer from the surface of the pipe in k/W
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.
Chapter 2 Solutions
Heat and Mass Transfer: Fundamentals and Applications
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