The following figure shows a schematic of a plate fuel element. The fuel is cladded in...

 

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The following figure shows a schematic of a plate fuel element. The fuel is cladded in thin metallic clad sheets, with perfect contact between the fuel and the cladding (i.e., no gap between the fuel and cladding). The width of the fuel region is 2a, and the fuel plate can be considered very thin since the width of the fuel is much smaller than its dimensions in y- and z- directions. The volumetric heat generation in the fuel region q" can be considered uniform. The clad thickness on both sides of the fuel is given as de, and the thermal conductivities of the fuel and cladding can be assumed independent of their temperatures, i.e., being constant kj and ke, respectively. Cooling is being pro- vided to the fuel plate by flowing coolant on both sides of the fuel plate. Assume the bulk mean temperatures of the coolant on the left and right sides of the fuel plates, Tm,L and Tm,R are the same. The convective heat transfer coefficients from the cladding sur- face to the coolant for the left and right sides of the fuel plates are hy and hg, respectively. a) Develop a formula to calculate the maximum fuel temperature as a function of the parameters given above and the r-location at which the maximum fuel temperature will occur (25 points). b) Find the r-location at which the maximum fuel temperature will occur. Make sure that when hy and he are the same, the maximum fuel temperature will occur at z=0 as shown in the figure (15 points). c) If h=10h R, sketch the temperature profile in the fuel and cladding regions. Show clearly where the maximum temperature is and what the slope of the temperature is at the boundary (between cladding and coolant, and fuel and cladding) (10 points). Ta Fuel Ta Figure 0.4 Clad Too The following figure shows a schematic of a plate fuel element. The fuel is cladded in thin metallic clad sheets, with perfect contact between the fuel and the cladding (i.e., no gap between the fuel and cladding). The width of the fuel region is 2a, and the fuel plate can be considered very thin since the width of the fuel is much smaller than its dimensions in y- and z- directions. The volumetric heat generation in the fuel region q" can be considered uniform. The clad thickness on both sides of the fuel is given as de, and the thermal conductivities of the fuel and cladding can be assumed independent of their temperatures, i.e., being constant kj and ke, respectively. Cooling is being pro- vided to the fuel plate by flowing coolant on both sides of the fuel plate. Assume the bulk mean temperatures of the coolant on the left and right sides of the fuel plates, Tm,L and Tm,R are the same. The convective heat transfer coefficients from the cladding sur- face to the coolant for the left and right sides of the fuel plates are hy and hg, respectively. a) Develop a formula to calculate the maximum fuel temperature as a function of the parameters given above and the r-location at which the maximum fuel temperature will occur (25 points). b) Find the r-location at which the maximum fuel temperature will occur. Make sure that when hy and he are the same, the maximum fuel temperature will occur at z=0 as shown in the figure (15 points). c) If h=10h R, sketch the temperature profile in the fuel and cladding regions. Show clearly where the maximum temperature is and what the slope of the temperature is at the boundary (between cladding and coolant, and fuel and cladding) (10 points). Ta Fuel Ta Figure 0.4 Clad Too