Consider a brick wall (Fig. P10.1) of thicknessL=30 cm,k=0.7 W/m ∘ C. The inner surface is at28 ∘ Cand the outer surface is exposed to cold air at−15 ∘ C. The heat-transfer coefficient associated with the outside surface ish=40 W/m 2 ⋅ ∘ C. Determine the steadystate temperature distribution within the wall and also the heat flux through the wall. Use a two-element model, and obtain the solution by hand calculations. Assume onedimensional flow. Then prepare input data and run program HEAT1D.

Consider an electric space heater with dimensions 100 cm x 50 cm x 20 cm as shown inthe figure. The space heater is exposed to quiescent (still) air at 20 C. If the frontsurface of the heater (100 cm x 50 cm) is at temperature 𝑇𝑠 = 80 𝐶, find the heatconvected to the room via natural convection by following the steps below. Assume thatall other surfaces of the heater are completely insulated (in other words, only considerthe large rectangular surface facing the room).1. At which temperature will you evaluate the properties of air? Find the values ofkinematic viscosity 𝜈, the Prandtl number 𝑃𝑟, and the thermal conductivity 𝑘 atthis temperature. Interpolate if needed.2. What is the value of the volume expansion coefficient 𝛽?3. Find the Grashof number for this problem.4. Find the Rayleigh number for this problem.5. Find the average Nusselt number 𝑁𝑢.6. Find the average convection coefficient ℎ.7. Find the heat convected away from the front surface of the space heater 𝑄̇𝑐𝑜𝑛𝑣.

Task DetailsThroughout this assignment, all variables are non-dimensionalised. The heat transfer system can beapproximated by the following partial differential equation (PDE) in time and space:𝜕Θ𝜕𝑡 + 𝑐 𝜕Θ𝜕𝑥 − 𝑑 𝜕 ! Θ𝜕𝑥 ! = 0, 𝑥 ∈ [0, 1], 𝑡 ∈ [0, 3], (1)where Θ is a non-dimensional temperature, 𝑡 is time, 𝑥 is a spatial coordinate with inlet at 𝑥 = 0 andoutlet at 𝑥 = 1, 𝑐 is a convection speed, and 𝑑 is a positive thermal diffusivity. Boundary conditionsare specified below, and they are different for tasks 1 and 2. The following initial condition applies:Θ(𝑥, 𝑡 = 0) = 𝜏 cos(2𝜋 𝑘 𝑥) , (2)where 𝑘 is an integer wave number. The PDE defined by equations (1) and (2), should be solved by aMATLAB script and/or functions using a suitable Runge-Kutta time-integration scheme and finite-difference spatial discretization of 𝑥 (do not exceed 4th order in time and space).1. (a) Take 𝑑 = 0, 𝜏 = 1 and apply periodic boundary conditions in 𝑥 as well as convectionspeeds c ∈ [0.1,0.3]. Run a total of 𝑁 simulations for 𝑘 = 2, each one with a different c, andrepeat the same for 𝑘 = 3, then store the temperatures Θ(𝑡 = 3, 𝑥 = 1), respectively.Choose appropriate spatial and temporal step sizes, and hence CFL number, and keep thischoice for all simulations, respectively, and briefly explain this choice in the written report,considering numerical stability and accuracy.

How is the temperature rise calculated in the thermal network model?Question 5Answera.Using finite element analysisb.Using distributed heat sourcesc.Ignoring heat sourcesd.Using differential equations

A brass rod with a length of 20.0 cm is placed side by side with an aluminum rod with a length of 20.0 cm, and this system is placed between a hot temperature of 150 °C and a cold temperature of −10.0 °C. The thermal conductivities of the brass and the aluminum are 100 W/m °C and 230 W/m °C, respectively. The rods have the same cross-sectional area of 20.0 cm2. What is the rate of heat flow from the hot temperature to the cold temperature?

1.Question 1What causes heat transfer?1 pointA difference in mass flowA difference in temperatureWork transferA difference in specific volume