A plane wall is constructed of a material having a thermal conductivity that varies as the square of the temperature according to the relation k =k0(1+βT^2 ). Derive an expression for the heat transfer in such a wall. Find the heat transfer per unit area through the composite wall Assume one-dimensional heat flow.

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=

A pipe carries hot molten lead from one part of a factory floor to another. The mass flow rate of lead is 0.05 kg/s. While trying to figure out the heat loss from the pipe, you found that over a 2-m length of he pipe the lead temperature drops from 580 C to 557.C. What is the rate at which thermal energy is being lost from the lead carrying pipe in this 2-m section? Use the property table to find out properties of lead as needed.