PROBLEM 3 In the given schematic of heat transfer for a wall, there is heat conduction through the wall and the outer surface of the wall is subject to both convection and radiation. T₁ = 308 K k = 0.3 W/m-K - L = 3 mm → ε = 0.95 111 Air Tsur = 297 K T = 297 K h=2 W/m²-K (Air) (a) Write the energy conservation equation for the system in terms of the three heat transfer modes. (b) Find the surface temperature Ts in °C.

6. a. The heat flux applied to the walls of the biomass combustion furnace is 20 W/m2. The furnace walls have a thickness of 10 mm and a thermal conductivity of 12 W/m.K. If the wall surface temperature is measured to be 50oC on the left and 30oC on the right, prove that conduction heat transfer occurs at a steady state!b. Heating the iron cylinder on the bottom side is done by placing the iron on the hotplate. This iron has a length of 20 cm. The surface temperature of the hotplate is set at 300oC while the top side of the iron is in contact with the still outside air. To reach the desired hotplate temperature, it takes 5 minutes. Then it takes 15 minutes to measure the temperature of the upper side of the iron cylinder at 300oC. Show 3 proofs that heat transfer occurs transiently

An external wall of a building has a U value of 0.50 W/m^2K. The indoor temperature is21 degrees C and the outdoor temperature is -2.0 degrees C The steady-state heat loss is calculated to be 11.5W/m^2 The wall contains a layer of insulation 40 mm thick with a conductivity of0.035 W/mK. What would the insulation thickness need to be in order toreduce the steady state heat loss by 50%? answer = 0.11m ​​​​​​​please show all working

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=