Consider a Brass block (k = 116 W/m °C) as shown in the figure. The entire block is initially at 25°C. The upper surface of the block is exposed to a constant heat flux of 10,000 W/m². The left and bottom side of the block surface is maintained at constant temperature of Ts=30°C. The lower right-side surface of the block is covered with a low-conductivity material so that heat transfer through it is negligible. The L-shaped surface of the block is exposed to ambient temperature of T = 25 °C and the convection heat transfer coefficient is h = 50 W/m².K. Use the finite difference method with a mesh size of Del x = Del y = 10 cm. (a) Using a reasonable time step, determine the temperature of each node with respect to time and plot them in one diagram. (b) Determine the time needed to reach steady state conditions and determine the steady state temperatures. (c) Obtain the finite difference formulation of this problem for steady two-dimensional heat transfer,determine the unknown nodal temperatures by solving those equations and compare them to the temperatures determined from part (b), and (d) Determine the rate of heat transfer from the L- shaped surface by convection in the steady state conditions.

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