heat transfer equation.pptx

this is the derivation of th how heat transfer equation is derived. the book from which this presentation is made is written by m wakil

1. Therefore:   1

2. Syed Muhammad Haris Chapter 5 Lecture 2

3. Heat Flow out of Solid-Plate-Type Fuel Element Assumptions: Thin, Bare and Plate-type fuel element Thermal Conductivity Cross-Sectional Area = Constant y and z dimension infinity = Constant   3

4. Heat Flow out of Solid-Plate-Type Fuel Element (Contd.) 1 (a) First Method to Get Poisson Equation: General Heat Conduction Equation: Poisson Equation: For one-dimension i.e. x-dimension   4

5. Heat Flow out of Solid-Plate-Type Fuel Element (Contd.) 1 (b) Second Method to Get Poisson Equation: Applying Heat Balance:   5

6. Heat Flow out of Solid-Plate-Type Fuel Element (Contd.) 2. Integration to get temperature distribution:   6 3. Boundary Conditions: Surface Temperature:  

7. Heat Flow out of Solid-Plate-Type Fuel Element (Contd.) 4. Heat Conducted out from a plane Between x=0 and x: Total Heat Generated from one side (x=s): As:   7 Total Heat Generated from both sides ( ):  

8. Heat Flow out of Solid-Plate-Type Fuel Element With Clad 5. Effect of Cladding: Cladding thickness = c Thermal Conductivity = Cladding act as extra resistance to heat transfer No heat generated in cladding Heat leaving out of any surface in the direction of heat transfer is constant at steady state If is constant is constant   8

9. Heat Flow out of Solid-Plate-Type Fuel Element With Clad (Contd.) 6. Temperature Differences: Temperature Difference: + Total Heat Generated from one side: Total Heat Generated from both sides:   9

10. Heat Flow out of Solid-Plate-Type Fuel Element With Clad and Coolant 7. Heat transfer form Fuel Element to Coolant: Bulk Coolant Temperature = Heat Transfer Coefficient= h No heat generated in cladding and coolant Heat leaving out of any surface in the direction of heat transfer is constant at steady state If is constant is constant   10

11. Heat Flow out of Solid-Plate-Type Fuel Element With Clad (Contd.) 6. Temperature Differences: Temperature Difference: + Total Heat Generated from one side:   11