(Solved): 1. Solve the 1D heat conduction equation without a source term The 1D heat conduction equation wit ...

1. Solve the 1D heat conduction equation without a source term The $$1\mathrm{D}$$ heat conduction equation without a source term can be written as: $$\frac{d}{dx}\left(k\frac{dT}{dx}\right)=0$$ Where $$k$$ is the thermal conductivity, $$T$$ the temperature and $$x$$ the spatial coordinate. Using the Finite Volume Method, use this equation to solve for the temperature $$T$$ in a rod. The rod has a length of $$I=1.5\mathrm{m}$$, a cross-section area of $$A=5\times 10^{?3}{\mathrm{m}}^2$$, the thermal conductivity is $$k=1200\mathrm{W}/\mathrm{Km}$$, and the temperatures at the ends are held constant at $$100^{?}\mathrm{C}$$ and $$600^{?}\mathrm{C}$$, respectively. 2. Solve the $$1\mathrm{D}$$ heat conduction equation with a source term. The 1D heat conduction equation with a source term can be written as: $$\frac{d}{dx}\left(k\frac{dT}{dx}\right)+q=0$$ With $$q$$ being the source term. Using the Finite Volume Method, use this equation to solve for the temperature $$T$$ across the thickness of a flat plate of thickness $$L=4\mathrm{cm}$$. The thermal conductivity is $$k=1.35\mathrm{W}/\mathrm{Km}$$, and the temperatures at the two ends are held constant at $$100^{?}\mathrm{C}$$ and $$300^{?}\mathrm{C}$$, respectively. An electric current creates a constant heat source of $$q=1300\mathrm{kW}/\mathrm{m}$$ B. Solve the 1D convection-diffusion problem The 1D convection-diffusion problem can be written as: $$\frac{d}{dx}(?u?)=\frac{d}{dx}\left(?\frac{d?}{dx}\right)$$ With $$?$$ the property that is being transported, $$u$$ the convection speed, $$?$$ the diffusivity and $$?$$ the density. The length of the domain is $$1.0\mathrm{m}$$, the density is $$1.0\mathrm{kg}/{\mathrm{m}}^3$$, the diffusivity $$0.1\mathrm{kg}/\mathrm{ms}$$. Determine the distribution of $$?$$ for the following cases. i. $$u=0.1\mathrm{m}/\mathrm{s}$$ using 5 cells ii. $$u=2.5\mathrm{m}/\mathrm{s}$$ using 5 cells. iii. $$t=2.5\mathrm{m}/\mathrm{s}$$ using 20 cells For all above 3 questions, please provide workouts and MatLab codes The MatLab code(s) (eg. myFVM.m)