A cylindrical pipe is made up of two materials. The inner material A, which has thermal conductivity of ka, has inner radius ra and outer radius re. On the other hand, the outer material B, which has themal conductivity of k, has inner radius r. and outer radius rp. Contact resistance between the two materials is known to be hc. The temperature at the inner radius of material A (at ra) is Ta. while the temperature at the outer radius of material B (at r3) is T3. Find an expression for the temperature at the inner radius of material B (at rc) in terms of the given variables.

Parts A-C solve carefully and label them ( use image below)

A square steel bar of side length w = 0.21 m has a thermal conductivity of k = 15.6 J/(s⋅m⋅°C) and is L = 2.7 m long. One end is placed near a blowtorch so that the temperature is T1 = 95° C while the other end rests on a block of ice so that the temperature is a constant T2. a. input an expression for the heat transferred to the cold end of the bar as a function of time using A=w^2 as the cross-sectional area of the bar.  b. how much energy in joules was conducted in 1 hour, assuming t2=0*C c. input an expression for the mass of the water melted in one hour using Q1 from above and Lf in the latent heat of fusion.  mw=

For steady state heat conduction in a composite wall (As = 5 m², LA=1 cm and LB =2 cm) as shown in below figure. Calculate the total thermal resistance and the rate of heat transfer from the wall also find the temperatures Ts1, Ts2 and Tc To,z=200°C h₂=10W/m².K KA=0.1 W/m-K T5,1 HL-L₂ 17 Tc Too,2 = 40°C h₂-20W/m².K k=Q04 W/m-K