Question

= To cool a summer home without using a vapor-compression refrigeration cycle, air is routed through a plastic pipe (k = 0.15 W/m-K, Di -0.15 m, Do-0.17 m) with a smooth interior surface that is submerged in an adjoining body of water. The water temperature is nominally at Too = 17°C, and a convection coefficient of ho- 1500 W/m2K is maintained at the outer surface of the pipe. Air from the home enters the pipe at a temperature of Tm, 1 - 29°C and a volumetric flow rate of v'-0.05 mº/s, where a pipe length L = 20 mis needed to provide a discharge temperature of Tmo. Air Ti Tm Plastic pipe * D D Water, T (a) What is the air outlet temperature, Tm,o? What is the fan power requirement? (b) The convection coefficient associated with airflow in the pipe may be increased twofold by inserting ac Jason from WileyPLUS length of the pipe to disrupt flow conditions near the inner surface. If such a heat transfer enhancement se WileyPLUS Scheduled Mainten the attendant value of Tm,o? Use of the insert would not come without a corresponding increase in the fi As Wiley continues to fine tune What is the power requirement if the friction factor is increased by 50%? Physical Properties Mathematical Functions

please show work

Answer 1

Solutions Given bata, Ka=0.15 w/mk. Dr = 0.15m Do = 0-1#m. ho=1500 w/mrk. volumetric flow rate; te=0.05 mbls. pipe rength's Liom. I calculate mean velocity at air using a Vi-Area of cross-section & Mean velocuity 0.05 = 1.082XV. -> 0.05-4XC0.15)?xv. v=2.829umis Mean velocity. calculate moss flow rate! nape Av=P put density fi= 1.155 kg (m3. 1-155 0.05-0.05795 kg (1. Dynamic viscosity; M= 18-36x108 calculate Reynold's Housing relation? um UxQo5p 95 TX0-15 x 183-6x107 Res 26 699.195. De moim

since; Rezuooo. So, the flow is morbulent Assuming fully developed flow throughout the pipe , calculate internal coefficient of heat transfer wing relation hika 0.023 Re ..&pr 0.3. Di 2 12.535 w/m²K.. calculate inside thermal Resistance using Equation (Reni l hix T DiL 12.535X11X0.158 10 (Rehdi = 0.01693 kw مس 13 Now, Total heat transfer Resistance is gevens Rth= (Ret) t en (Doldi) атруL hoxTDOL -0.016934 enco.it/0.15) 21TX0.15X10 MOOXX OXO (Rth total = 0.03034 KW

3 we know ; (Rehtotal = JX AS surface area. -> JAS = 0.02 0.03034 32.9651WK Specific heat = cp=1007J/kgK -0.05755 kgis asing Relation, Too-Tmio - e - TAS Too Tmi -32.9651 17-Tm, 17-29 e 17 TMO - 0.56685 > e -12 17-Tm,o=-6.8077. f = 0.316 Rely Tm, = 23.8077°C 23.80774 tals outlet Temperature calculate friction paeth ihing relations 0.316 0.02472. 26699.195)"4 pressure drop in the pipe is given by relations AP-fei uzm, i 2D; 0.02472x1.55* (2 82942 a X0-15 140

AP= 7.6189 pal pressure drop in the pipe calculate fan power as below! power APX & = 7.6189 +0.05 power 0.380950 fan power Requirement step 1 = 2 829umis- step 2 = 0.016 93 kw step3 = 0.03034 kw. stepu = 23.8077°C. Step 5=7.6isapa. Step 6 = 0.38 095w. .O please like. It helps a lot for me