Question

1. Consider 1D conduction along connected bars (no heat loss, steady state), with the length and temperature profile given in the figure. a) Google the thermal conductivity of bulk Si. b) Find out the thermal conductivity of the unknown material and the thermal contact resistance between two bars (per unit cross-section area). A320 K Temperature (K) Silicon - 310 K 308 K 300 K Unknown material 50 mm 100 mm x Silicon Unknown material

Answer 1

Ape +3lok Temp(K) 2.3K Book silicon Unknown loommn 5umm golution is given for an Untnown material, (as Here Temp-thicknen plot ements a cie. Silicon & The Thermal conductivity of from Law of Conduction Bulk Si= 150 wenk. (6) we know, Q = -K A(2) Here; Q is heat flow & K is thermal conductivity, . In Question it is given that there is No Heat loon and it's a steady state condition: so; the He at flow through both be the Elemento will be same. Qsilicon = Qualnown. X2 - - Kashion X. ( T2 - T)) = -Kunknon A- (T3-T) [ Unit Corner => 7150 (310-320) = 7 K (26.-203) LX2=X;=50mm] - 150 x (A») = 48) K ..^= iso x lo = 187.5 (mm) . K for on know material in 187.5 (We). M

both surfa Now, Thermal Contact it Resistane between Resistance we know, Q= KA (dB) Ihly di Resistance KA Q = kaina Q = 150x IX (320-310) 0.05 Q = 30,000 lei i Rethermal - thermal Contact et 310-308 30,000 = Thermal Contact Resistante - 30,000 = 6.667 x 105 11 30,000 (m.)