A wall 0.12 m thick having thermal diffusivity of 15 10-6 m2/s is initially at temperature of 85oC.Suddenly one face temperature lowered to a temperature of 20 oC while other face is perfectly insulated.Using explicit finite difference method, write descretization equation for space and time steps of 30 mmand 300 s respectively.

A box with a total surface area of 1.20 m2 and a wall thickness of 4.00 cm is made of an insulatingmaterial. A 10.0-W electric heater inside the box maintains the inside temperature at 15.0°C abovethe outside temperature. Find the thermal conductivity k of the insulating materi

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.

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.

35 | P a g eC h e s s48-In order to conserve energy, it is decided to increase the R-value of an outside wall from 0.36 (m^2*Celsius)/(J/s) by addingan inexpensive layer of sheathing on the inside of the wall whichhas an R-value of 0.62 (m^2*Celsius)/(J/s). When thetemperature difference between the inside and outside is 20°C,by what percentage is the rate of energy transfer through the wallreduced by this added insulation?a. 37%b. 58%c. 63%d. this cannot be found without knowing the area of the wallANS:C

An object, heated up to 80 0C and kept in an environment of 30 0C, the rate of temperature fall ofinitial temperature is 5 0C s-1.If the environmental temperature is reduced by 10 0C, What is therate of temperature fall of initial temperature.