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

Heat and Mass Transfer: Fundamentals and Applications

5th Edition

ISBN: 9780073398181

Author: Yunus A. Cengel Dr., Afshin J. Ghajar

Publisher: McGraw-Hill Education

See similar textbooks

Question

Chapter 2, Problem 100P

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 99P

Chapter 2, Problem 101P

Students have asked these similar questions

A turbocharged engine with a compression ratio of 8 is being designed using an air standard cycle. The ambient air is assumed to be 300K and 100 kPa. The temperature at the end of the compression in the cylinder is desired to be 1000K, assuming no combustion prior to reaching TDC. At the end of the cylinder expansion the temperature is also desired to be 1000K. If both the turbine and the compressor have mechanical efficiencies of 80%, what will be the pressure ratio of the compressor and what will be the turbine exhaust temperature?

Q6: A turbocharged engine with a compression ratio of 8 is being designed using an air standard cycle. The ambient air is assumed to be 300K and 100 kPa. The temperature at the end of the compression in the cylinder is desired to be 1000K, assuming no combustion prior to reaching TDC. At the end of the cylinder expansion the temperature is also desired to be 1000K. If both the turbine and the compressor have mechanical efficiencies of 80%, what will be the pressure ratio of the compressor and what will be the turbine exhaust temperature?

Q5: A 5.6 litre V8 engine with a compression ratio of 9.4:1 operates on an air-standard Otto cycle at 2800 RPM, with a volumetric efficiency of 90 % and a stoichiometric air-fuel ratio using gasoline. The exhaust flow undergoes a temperature drop of 44ºC as it passes through the turbine of the supercharger. Calculate (a) mass flow rate of exhaust gas and (b) power available to drive the turbocharger compressor.

Chapter 2 Solutions

Heat and Mass Transfer: Fundamentals and Applications

Ch. 2 - How does transient heat transfer from steady heat...Ch. 2 - Is heat transfer a scalar or a vector quantity?...Ch. 2 - Does a hear flux vector at a point P on an...Ch. 2 - From a heat transfer point of view, what is the...Ch. 2 - What is heat generation in a solid? Give examples.Ch. 2 - Heat generation is also referred to as energy...Ch. 2 - In order to size the compressor of a new...Ch. 2 - In order to determine the size of the heating...Ch. 2 - Consider a round potato being baked in an oven....Ch. 2 - Consider an egg being cooked in boiling water in a...

Knowledge Booster