Assignment one for 3rd year Automotive Engineering Department (Mark = 15%)
1) An industrial chiller is designed to operate with an internal air temperature of -19℃when the
external air temperature is 27℃ and the internal and external heat transfer coefficients are 14 W/
𝑚2 K and 9 W/ 𝑚2 K, respectively. The walls of the chiller are composite construction, comprising
of an inner layer of plastic (k = 1 W/m K, and thickness of 3 mm), and an outer layer of stainless
steel (k = 16 W/m K, and thickness of 1 mm). Sandwiched between these two layers is a layer of
insulation material with k = 0.07 W/m K. The determine the width/thickness/ of the insulation that
is required to reduce the convective heat loss to 15 W/𝑚2 .
2) Water at 90 °C is pumped through 120 m of stainless-steel pipe , k = 16 W/m K of inner and
outer radii 46 mm and 52 mm respectively. The heat transfer coefficient due to water is 2100
W/ 𝑚2 K. The outer surface of the pipe loses heat by convection to air at 18°C and the heat
transfer coefficient is 190 W/𝑚2 K. Calculate
a) the heat flow through the pipe .
b) the heat flow through the pipe when a layer of insulation, k = 0.1 W/m K and 50 mm radial
thickness is wrapped around the pipe .
c) Put your recommendation based on your result
d) Find Temperature distribution at (r =48 mm,50mm,51mm for case a and @ r= 60
mm,70mm,90 for case b).
3) Consider steady heat transfer in an L-shaped solid body whose cross section is given (Fig.1).
Heat transfer in the direction normal to the plane is negligible, and thus heat transfer in the body
is two-dimensional. The thermal conductivity of the body is k = 15 W/m.℃, and heat is generated
in the body rate of 𝑔̇ = 2x106
𝑤
𝑚3
. The left surface of the body is insulated, and the bottom surface
is maintained at a uniform temperature of 90 ℃. The entire top surface is subjected to convection
to ambient air at 𝑇∞ = 25 ℃ with a convection coefficient of h = 80
𝑤
𝑚2 ℃
and the right surface is
subjected to heat flux at a uniform rate 𝑞̇ 𝑅 = 5000 w/ 𝑚2 . The nodal network of the problem
consists of 15 equally spaced nodes ∆𝑥 = ∆𝑦=1.2 cm, as shown in the figure.
a) Obtain the finite difference equation at the remaining nine nodes.
b) the nodal temperature by solving them.
(Assume the nodal temperature ( 𝑇9 = 98 ℃ &𝑇5 = 108 ℃)
Fig.1 Temperature distribution in the L-shaped plane
Prepared by Hailemariam Mulugeta
Submission date 29/10/2014 E.C