Assignment one for 3rd year Automotive Engineering Department (Mark = 15%) 1) An industrial chiller is designed to operate with an internal air temperature of -19βwhen the external air temperature is 27β and the internal and external heat transfer coefficients are 14 W/ π2 K and 9 W/ π2 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/π2 . 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/ π2 K. The outer surface of the pipe loses heat by convection to air at 18°C and the heat transfer coefficient is 190 W/π2 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.β, and heat is generated in the body rate of πΜ = 2x106 π€ π3 . The left surface of the body is insulated, and the bottom surface is maintained at a uniform temperature of 90 β. The entire top surface is subjected to convection to ambient air at π∞ = 25 β with a convection coefficient of h = 80 π€ π2 β and the right surface is subjected to heat flux at a uniform rate πΜ π = 5000 w/ π2 . The nodal network of the problem consists of 15 equally spaced nodes βπ₯ = βπ¦=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 ( π9 = 98 β &π5 = 108 β) Fig.1 Temperature distribution in the L-shaped plane Prepared by Hailemariam Mulugeta Submission date 29/10/2014 E.C