Question

3) Insulating a Cold Fluid Line This is a steady-state problem, and latent heat eonsiderations do not matter As show in Fig. (a), an uninsulated hose of outer radius r1 cm is used to transfer a liquid refrigerant at a 273 K Tice r 1 cm uniform temperature T 265 K. Since the hose is uninsulated, the outer surface is also at 265 K. Because the outer surface of the hose is below the melting point of water, a layer of ice (kce = 2 W/m - K) will begin to form on the hose. This ice layer will continue to grow until the system reaches steady state (which is the state considered in this analysis). The outer surface of the ice experiences convection heat trans fer with air at To = 300 K with a convection coefficient of h 5 W/m2 - W h 5 'm2K TR 265 K dice? Ter =300K W kice2- т - К (a) a) What is the temperature of the outer surface of the ice layer when the system has reached steady state? (Hint: what allows the ice to condense in the first place?) b) Estimate the thickness of the ice, dices that forms on the surface of the hose Calculate the rate of heat transfer per unitl length of the hose. c) 1 cm Te TR dfoam ? kfoam (b) Now ignore the icc formation around the hose, in accordance with Fig. (b) d) Suppose we use foam to insulate the hose. We can choose from two foams with thermal conductivities k 0.05 W/m - K and k2 = 0.1 W/m - K. respectively. The maximum total radius max =r + dfoam = cm due to geometric constraints What thickness of foam 1 should we use to minimize heat transfer to the hose? I П. What thickness of foam 2 should we use to minimize heat transfer to the hose? Which optimi performance ic. minimizes heat trans fer to the refrigerant)? III isulation, foam 1 or foam 2, gives the best des ired

Answer 1

Solution-) ice = 273k h-5wlk 3ook By fu continuity (re stcady state); (b) Tre= 273k Tice Tin Ta-The Th25 Kie 2 almk hAo 273 25 300-273 O.O1 5x2T 2T (2) 135.1.) get we hunos cs Scanned with CamScanner

diu = 0. 031C m hA, (T-Tie) 5 x 2T /0-041) (Jo0-273) X = 35. 286 Cmtialadi, d) K O.05 O.01 m - 1cm So, we'l Use to mimimis hat transfer foam Qcm 0.02m foom Again, we Use (ii) Foam 1 Scanned with CamScanner