In: Mechanical Engineering

A Styrofoam(k = 0.035 W/m-°C) box has outer dimensions of 250 mm x 450 mm x 600 mm and is 3 cm thick. Initially, the box is filled with 40kg of ice at 0°C, and the inner surface temperature of the ice chest can always be taken to be 0°C. The heat transfer coefficient between the outer surface of box and surrounding air at 35°C is 20 W/m2 -°C. (a) Determine how long it will take for the ice in the box to melt completely. Assume that the heat transfer from the 450 mm x 600 mm bottom of the box is negligible.

FIreclay brick (ρ=2050 kg/m3, cp=960 J/kg-K, k=1.1 W/m-K) with
dimensions 0.06 m x 0.09 m x 0.20 m is removed from a kiln at 1600K
and cooled in air at 40C with h = 30 W/m2-K. What is the
temperature at the corner of the brick after 50 minutes of cooling?
Give your answer in degrees C.

A circumferential fin (k= 55 W/m C) of thickness 3 mm and length
3 cm is attached to a pipe of diameter 3 cm. The fin is exposed to
a convection environment at 23 C with h=25 W/m2 oC. The fin base
temperature is 223 C. Calculate the heat lost (qf) by the fin.

The inner and outer panes of a double-glazed window of
dimensions 2 m x 2 m and 0.6 cm thick, the temperature is 18 ° C
and 6 ° C, respectively. If the 1 cm gap between the two panes is
filled with still air, determine the rate of heat transfer through
the conduction air layer in kW and the temperatures at the
air-glass interfaces. K air = 0.026 ? / ?.? and K
glass = 0.85 ? / ?.k

A box has dimensions of 1.8 m length (y-direction), 1.8 m width
(x- direction), and 3.6 m height (z-direction). With the head of a
vector at the front, bottom, left-hand corner of the box , and the
tail of the vector at the back, top, right-hand corner of the box
(at the origin); give the vector in Cartesian form,
magnitude/direction angles representation, and the unit vector.

Water flows at 112°C through a steel pipe (k=90 W/m °C) which
has a 6 cm inside diameter and 8cm outside diameter. Such that, hi
=346 W/m2 °C and ho =6.0 W/m2 °C. Surrounding air temperature is
20°C. To reduce heat loss to the surroundings the pipe is covered
with an insulation insulation having the thickness of 4.0 mm and
k=0,5W/m°C . Calculate;
a. The heat loss by convection per unit length from
the bare pipe (before insulation).
b....

A conducting rectangular loop of mass, M, resistance R, and
dimensions w x l falls from rest into a magnetic field B. During
the time interval before the top edge of the loop reaches the
field, the loop approaches a terminal speed vt . Show
that vt=MgR/B2w2

A rectangular swimming pool has dimensions of 25 m x 9 m and a
depth of 1.8 m and is full to the brim with water. Determine a) the
absolute pressure at the bottom of the pool, b) the total force on
the bottom of the pool, and c) the absolute pressure at point P, a
point on the side of the pool just near the bottom. (Worth 2
pts)

Suppose A=(7B^n)/(CD), where A has dimensions [T]/[L]^3, B has
dimensions [T], C has dimensions [T][M]^2, and D has dimensions
[L]^3/[M]^2. Using dimensional analysis, find the value of the
exponent n.

1. A thick metal plate (alpha = 3.5 x 10-6
m2/s and k = 0.7 W/m-K), initially at a uniform
temperature of 100oC, is suddenly exposed to a
convection environment of water at 20oC, giving a very
large convection coefficient.
a. Sketch the surface heat flux, q", as a function of time
b. Using an explicit numerical scheme with a time step of 60 s,
calculate the time required for the temperature to change 80 mm
from the surface.

The steel beam has the cross section shown. The beam length is L = 6.9 m, and the cross-sectional dimensions are d = 345 mm, bf = 185 mm, tf = 15 mm, and tw = 10 mm. Calculate the largest intensity of distributed load w0 that can be supported by this beam if the allowable bending stress is 185 MPa.

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