Explanation Given: Maximum temperature of the fuel rod is 200 ° C , thermal conductivity of rod is 30 W/mk , inside diameter is 2 cm ,heat generation is 100 MW/m 3 ,convection heat transfer coefficient is 2500 W/m 2 k and cooling water temperature is 75 ° C . Concept used: Expression heat transfer through plate is given as follows: q = − k d T d r ...... (1) Here, heat flux is q , thermal conductivity is k , temperature difference is Δ T and thickness is L . Expression for heat equation for cylinder with heat generation is given as follows: d d r ( r d T d r ) = − q g r k ...... (2) Here, heat generation is q g temperature is T and radial distance is r . Expression heat transfer in convection mode is given as follows: q = h ( T ( r o ) − T ∞ ) ...... (3) Here, convection coefficient is h , exposed surface area is A , surface temperature T ( r 1 ) and ambient temperature is T ∞ . Calculation: Integrate the equation (2) as follows: ∫ d d r ( r d T d r ) = ∫ − q g r k d T d r = − q g r 2 k + C 1 r Again, integrate the above equation as follows: ∫ d T = ∫ ( − q g r 2 k + C 1 r ) d r T = − q g r 2 4 k + C 1 ln r + C 2 Substitute boundary condition d T d r = 0 at r = 0 in thermal gradient equation. d T d r = − q g r 2 k + C 1 r 0 = − q g × 0 2 k + C 1 0 C 1 = 0 Substitute boundary condition d T d r = d T ( r o ) d r at r = r o in thermal gradient equation. d T d r = − q g r 2 k + C 1 r d T ( r o ) d r = − q g r o 2 k + C 1 r o d T ( r o ) d r = − q g r o 2 k + 0 r o d T ( r o ) d r = − q g r o 2 k Substitute boundary condition T = T ( r o ) at r = r o in temperature profile. T ( r o ) = − q g r o 2 4 k + C 1 ln r o + C 2 T ( r o ) = − q g r o 2 4 k + 0 × ln r o + C 2 T ( r o ) = − q g r o 2 4 k + C 2 For steady state, the heat conduction and heat convection are equal

6th Edition

ISBN: 9781260439991

Author: CENGEL

Publisher: MCG

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Chapter 2, Problem 104P

To determine

The formula for temperature variation in the fuel rod, temperature at inner surface of the pipe and comparison with maximum operating temperature of the fuel rod.

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Chapter 2, Problem 103P

Chapter 2, Problem 105P

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