Question

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 the given geometry and indicated nodal positions, labeling them 1 through 6 with node 1 located at the insulated wall.

(b) Using the energy balance, or finite volume method, derive the finite difference equations for each of the nodes,

(c) Solving the simultaneous algebraic equations, determine the steady-state temperature distribution.

(d) Determine the temperature predicted by an exact analytical solution at each of the finite-volume centers (node).

Answer #1

71 mm thick horizontal plate made of an opaque material of
thermal conductivity k= 25 W/m-K. At the bottom, water flows at a
temperature of T∞,w = 25C, whereas air flows at the top of the
plate at T∞,a = 710 C having convection coefficient of ha= 71
W/m2-K. Assuming a diffused top of the plate that receives an
irradiated flux of 7100W/m2, of which 30% is reflected back. The
top and bottom surface temperatures are maintained at 43 C...

Consider a cube of density, specific heat, and thermal
conductivity of 2700 kg/m3, 0.896 kJ/kg-K, and 204 W/m-K,
respectively. The cube is 5 cm in length, and is initially at a
temperature of 20 oC. For t>0, two of the boundary surfaces are
insulated, two are subjected to uniform heating at a rate of 10,000
W/m2, and two dissipate heat by convection to an ambient
temperature of 20 oC, with a heat transfer coefficient of 50
W/m2-K.
Assuming lumped capacitance...

A long 10 cm × 20 cm rectangular cross section steel bar ݇ k=
63.9 W/mK and alpha=18.8*10^-6 m^2 /s was heated to an initial
temperature of 450°C. The steel bar is allowed to cool in a room
with a temperature of 25°C and convection heat transfer coefficient
of 25 W/m^2 K. The bottom surface of the bar is insulated while the
other surfaces are exposed to convection. With a uniform nodal
spacing of 5 cm, determine the duration required...

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...

Air has a thermal conductivity of 3 x 10-4 J cm-1 s-1 K-1.
Consider a window with double panes
of glass where the temperature of the inside pane is 25 oC and the
temperature of the outside
pane is -5 oC. The size of the window is 40 cm x 60 cm, and the
panes are 8 mm apart. What is
the heat flow in watts through the window? You can ignore
convection.

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...

Assume that we are working with an aluminum alloy (k = 180
W/moC) triangular fin with a length, L = 5 cm, base thickness, b =
1 cm, a very large width, w = 1 m. The base of the fin is
maintained at a temperature of T0 = 200oC (at the left boundary
node). The fin is losing heat to the surrounding air/medium at T? =
25oC with a heat transfer coefficient of h = 15 W/m2oC. Using the...

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