Consider a 5-m-long Titanium block 30 cm high and 50 cm wide. The entire block is...

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Consider a 5-m-long Titanium block 30 cm high and 50 cm wide. The entire block is initially at 25°C. The block is completely submerged in iced water at 0°C that is well stirred, and the heat transfer coefficient is so high that the temperatures on both sides of the block can be taken to be 0°C. The bottom surface of the bar is covered with a low-conductivity material so that heat transfer through the bottom surface is negligible. The top surface of the block is heated uniformly by a 6 kW resistance heater. Using the finite difference method with a mesh size of Ax Ay = 10 cm and taking advantage of symmetry, %3D (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 block to the iced water in the steady state conditions. 6 kW heater Insulation 0000000 0°C 0°C }10cm 10cm Insulation Consider a 5-m-long Titanium block 30 cm high and 50 cm wide. The entire block is initially at 25°C. The block is completely submerged in iced water at 0°C that is well stirred, and the heat transfer coefficient is so high that the temperatures on both sides of the block can be taken to be 0°C. The bottom surface of the bar is covered with a low-conductivity material so that heat transfer through the bottom surface is negligible. The top surface of the block is heated uniformly by a 6 kW resistance heater. Using the finite difference method with a mesh size of Ax Ay = 10 cm and taking advantage of symmetry, %3D (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 block to the iced water in the steady state conditions. 6 kW heater Insulation 0000000 0°C 0°C }10cm 10cm Insulation

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