Page 1 PROBLEM 3.1 KNOWN: One-dimensional, plane wall ...

PROBLEM 3.3KNOWN: Desired inner surface temperature of rear window with prescribed inside and outside airconditions.FIND: (a) Heater power per unit area required to maintain the desired temperature, and (b) Compute andplot the electrical power requirement as a function of T ∞ ,o for the range -30 ≤ T ∞ ,o ≤ 0°C with h o of 2,20, 65 and 100 W/m 2 ⋅K. Comment on heater operation needs for low h o . If h ~ V n , where V is thevehicle speed and n is a positive exponent, how does the vehicle speed affect the need for heateroperation?SCHEMATIC:ASSUMPTIONS: (1) Steady-state conditions, (2) One-dimensional heat transfer, (3) Uniform heaterflux, q′′ h , (4) Constant properties, (5) Negligible radiation effects, (6) Negligible film resistance.PROPERTIES: Table A-3, Glass (300 K): k = 1.4 W/m⋅K.ANALYSIS: (a) From an energy balance at the inner surface and the thermal circuit, it follows that for aunit surface area,T∞,i −Ts,i Ts,i −T∞,o+ q′′h =1h Lk+1hio( )$ $Ts,i T ,o T ,i T 15 C − −10 C$ $− ∞ ∞ − s,i25 C −15 Cq′′ h = − = −Lk+1h 0.004 m 1 1o 1hi+1.4 W m ⋅ K 2 265 W m ⋅ K 10 W m ⋅ K′′2 2= ( − ) =