Question

The initial temperature distribution across a wall with a thickness of 60 cm is described with the following function:

*T(x) =* *-250x+100**x ^{2}*

where *T* is temperature in
degrees Celsius and *x* is the coordinate in meters.

The wall has a thermal conductivity of
2.5 W cm^{-1} K^{-1}.

(i) On a unit surface area basis, determine the heat flux into the wall on the left face.

(ii) On a unit surface area basis, determine the heat flux out of the wall on the right face.

Answer #1

A rectangular furnace wall is made of fire clay (Height = 3m,
Width = 1.2m, thickness L=0.17m) The temperautre of the inside
surface ( area H x W, Tx, is 1592 K,and of the outside surface
(area = H x W ), Tc is 1364 K
Determine the temperature gradient
Determine the heat transfer rate
Determine the heat transfer flux
Determine thermal resistance

The steady-state temperature distribution inside a solid object
is described by the following expression, where x is the spatial
co-ordinate: T(x) =2x3- 3x2 + x +10
If the thermal conductivity and thickness of the solid are 10
W.m-1.K-1 and 0.8 m respectively, what will
be the form of heat flux expression?
At what point within the solid does the heat flux reach a
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A flat wall is exposed to an environmental temperature of 38
degrees C. The wall is covered with a layer of insulation 2.5 cm
thick whose thermal conductivity is 1.8 W/(m.K), and the
temperature of the wall on the inside of the insulation is 320
degrees C. The wall loses heat to the environment by convection.
Compute the value of the convection heat transfer coefficient that
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that the...

In a warehouse, a cold room that is maintained at
10oC has a wall made of two layers of
materials. The inner layer has a thickness of 2 cm and a thermal
conductivity of 0.1 W/mK. The outer layer, which is 4 cm thick, has
a thermal conductivity of 0.04 W/mK. The temperature of the outside
ambient is 30oC . The convective heat transfer
coefficients on the outside and the inside of the wall are 40
W/m2K and 20 W/m2K...

The wall of an industrial furnace is constructed from a fireclay
brick layer which is covered with another layer of ordinary brick.
The outer surface wall temperature has a steady-state temperature
of 110 °C when the ambient air has a temperature of 20°C. Heat is
lost from the outer surface wall via convection and radiation. The
internal furnace wall has a surface temperature of 500 DegreeC.
Convection heat transfer coefficient between outer wall and air:
5 W/m2K
Stefan-Boltzmann constant σ:...

consider a 0.8 cm thick steel plate with a thermal
conductivity of 50W/m-k.When the inside surface of the plate is
subjected to a uniform heat flux 0f 5*104 w/m2 the oter surface
temperature of the plate is measured to be 110c under steady
operating condition
a)express the differential equation and the boundary
conditions for steady one dimensional heat conduction through the
wall
b)obtain the relation for the variation of temperature
in the plate by solving the differential equation.
c)evaluate the...

To determine the effect of the temperature dependence of the
thermal conductivity on the temperature distribution in a solid,
consider a material for which this dependence may be represented
by: k = k0 + a T, where “k0“ is a positive constant and “a” is a
coefficient that may be positive or negative. Starting with a
steady-state energy balance, derive a relationship for temperature
(T) as a function of distance (x) from the lower temperature wall.
You may assume that...

Consider an R-134a based freezer operating at -30°C. The
surrounding temperature is at 25°C. External size of the freezer is
33.62" wide x 37.37" tall x 20.68" deep. Wall thickness of the
freezer is 1" and made of polystyrene (thermal conductivity=.033
W/mK). Thermal conductivity of the wall is the same as polystyrene.
For simplicity, you may assume the inner and outer convection
coefficients of the freezer are both equal to 10 W/m2/K.
The heat removal rate is: q(convection)=186.22 W
The...

Consider a large uranium plate of thickness 5 cm and thermal
conductivity k = 28 W/m K in which heat is generated uniformly at a
constant rate of q˙ = 6 × 10^5 W/m^3 . One side of the plate is
insulated while the other side is subjected to convection in an
environment at 30◦C with a heat transfer coefficient of h = 60 W/m2
K. Considering six equally spaced nodes with a nodal spacing of 1
cm,
(a) Sketch...

Homework-9
Due:
Q) A fuel plate is fabricated from 0.3 cm thick 1.5% enriched
uranium. The cladding is 0.25 mm 304 stainless steel. The coolant
saturation temperature is 260 oC. The
average thermal neutron flux is 2.5 X
1014
neutrons/cm2 /s. The surface
temperature of the clad is 350 oC.
Assume any missing data to answer the following questions:.
1) Write an expression of the heat generated per unit volume
2 What is the heat flux at the surface of...

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