(Solved): The inner and outer surfaces of a 20cm thick wall are at 20C and 40C, respectively. The out ...
The inner and outer surfaces of a 20cm thick wall are at 20?C and 40?C, respectively. The outer surface of the wall exchanges heat by radiation with surrounding surfaces at 35?C, and convection with ambient air also at the same temperature with a convective heat transfer coefficient of 10 W/m2. Solar radiation is incident on the surface at a rate of 150W/m2. If both the emissivity and the solar absorptivity of the outer surface are 0.8 , determine the effective thermal conductivity of the wall. Qcond ?+Qradloss ?+Qconv ?=Qsun ?Qcond ?=Qsun ??Qradloss ??Qconv ?1?kWT(Tint ??Text ?)?=Qsun????(Text4??Tamb4?)?h(Text ??Tamb?)? Here you can solve easily. Variations of this exercise can include, among others: - Calculate the equilibrium outside wall temperature if the incident radiation is changed (unlikely, the equation can get tricky to solve) - Calculate how much of the incident radiation would need to be blocked for a different outside wall temperature.
Useful Equations Cp?=(?T?H?)p?q=?kdXdT?Q=qA=?kAdXdT?Rcond ?Rconv ??=kAL?=hA1??r1??r2?1?=rT?1?=r1?1?+r2?1?TSR=E?L??f?k?(?x??(kx??x?T?)+?y??(ky??y?T?)+?z??(kz??z?T?))+qg?=?Cp??t?T?(?r2?2T?+r1??r?T?+r21???2?2T?+?z2?2T?)+kqg??=?1??t?T?Q=hA(T1??T2?)Ri=R?2Gr?Gr=?vg??L3?Pr=?v?Re=vvx?Nu=kh??LMTD=ln?T2??T1???T1???T2??Udesign ?=Rcond ?+Rcon ?1?Eb??=exp(?TC2??)?1C1???5?Ureal ?=Udesign ?1?+Rf???C1?=3.742108W?m4/m2;Eb?=??1??2??Eb??d?C2?=1.4387104?mK.?Eb?=?T4?=Eb?E??=5.6710?8W/m2K42898?mK=?max?TEb?max?=1.28710?5T5qnet?=?(T14??T24?)Q0?Qa??+Q0?Qr??+Q0?Qt??=1?