Question

Consider a large uranium plate of thickness 5 cm and thermal conductivity k = 28 W/m...

Consider a large uranium plate of thickness 5 cm and thermal conductivity k = 28 W/m K in which heat is generated uniformly at a constant rate of q˙ = 6 × 10^5 W/m^3 . One side of the plate is insulated while the other side is subjected to convection in an environment at 30◦C with a heat transfer coefficient of h = 60 W/m2 K. Considering six equally spaced nodes with a nodal spacing of 1 cm,

(a) Sketch the given geometry and indicated nodal positions, labeling them 1 through 6 with node 1 located at the insulated wall.

(b) Using the energy balance, or finite volume method, derive the finite difference equations for each of the nodes,

(c) Solving the simultaneous algebraic equations, determine the steady-state temperature distribution.

(d) Determine the temperature predicted by an exact analytical solution at each of the finite-volume centers (node).

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