Attempt the problem entirely on your own. Set up the schematic, list given values, note necessary assumptions, and identify the required equations.
(Heat loss through a double-pane window), the solution follows these steps Identify Knowns : Glass thickness, air gap width, thermal conductivities ( k sub g l a s s end-sub k sub a i r end-sub ), and indoor/outdoor temperatures. State Assumptions Steady-state conditions. One-dimensional heat transfer. Constant thermal conductivities. Negligible radiation (unless specified). Build Resistance Network : Calculate Calculate Heat Transfer Rate
When practicing with the , focus on these types of problems:
Mixing millimeters, centimeters, and meters. Thermal conductivity is typically given in ; all spatial dimensions ( ) must be converted to meters before calculation. Attempt the problem entirely on your own
The heat transfer from the insulated pipe is given by:
Many mistakes in Chapter 3 stem from failing to convert millimeters to meters or hours to seconds. The manual provides a baseline for tracking unit consistency.
Electric wire (r_1 = 0.0015 , m), (k_ins=0.08), (h=12). State Assumptions Steady-state conditions
When heat passes through multiple layers (e.g., a wall with insulation), the total resistance is the sum of individual resistances in series:
The heat transfer from the not insulated pipe is given by:
( \dotQ = \fracT_in - T_outR_total = \frac22 - (-5)0.17204 = \frac270.17204 \approx 156.9 , W ) Negligible radiation (unless specified)
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The solution manual for this chapter heavily relies on developing the for various geometries. A. The Thermal Resistance Concept Just as electric current ( ) flows through a resistor ( ) due to voltage difference ( ) flows through a material due to temperature difference (
Rtotal=Rconv,1+Rwall,1+Rwall,2+…+Rconv,2cap R sub t o t a l end-sub equals cap R sub c o n v comma 1 end-sub plus cap R sub w a l l comma 1 end-sub plus cap R sub w a l l comma 2 end-sub plus … plus cap R sub c o n v comma 2 end-sub
) . If the wire is smaller than this radius, adding plastic actually helps it "breathe" better. 3. The "Fin" Efficiency Story