HEAT TRANSFER : STEADY STATE HEAT CONDUCTION

1. GENERAL HEAT CONDUCTION EQUATION : Rectangular Coordinates
2. GENERAL HEAT CONDUCTION EQUATION : Cylindrical and Spherical Coordinates
3.BOUNDARY AND INITIAL CONDITIONS
4. STEADY HEAT CONDUCTION IN PLANE WALLS
5. The Thermal Resistance Concept
6. THERMAL CONTACT RESISTANCE
7. GENERALIZED THERMAL RESISTANCE NETWORKS
8. HEAT CONDUCTION IN CYLINDERS & SPHERES
9. CRITICAL RADIUS OF INSULATION

1. HEAT TRANSFER : STEADY STATE HEAT CONDUCTION Prof. Pramod Maurya AP, SCOE, KHARGHAR 1 GENERAL HEAT CONDUCTION EQUATION : Rectangular Coordinates GENERAL HEAT CONDUCTION EQUATION : Cylindrical and Spherical Coordinates BOUNDARY AND INITIAL CONDITIONS STEADY HEAT CONDUCTION IN PLANE WALLS The Thermal Resistance Concept THERMAL CONTACT RESISTANCE GENERALIZED THERMAL RESISTANCE NETWORKS HEAT CONDUCTION IN CYLINDERS & SPHERES CRITICAL RADIUS OF INSULATION

2. Prof. Pramod Maurya AP, SCOE, KHARGHAR 2 1. GENERAL HEAT CONDUCTION EQUATION : Rectangular Coordinates

3. Prof. Pramod Maurya AP, SCOE, KHARGHAR 3 Contd ….

4. Prof. Pramod Maurya AP, SCOE, KHARGHAR 4 ---------- Fourier- Biot equation Contd….

5. Prof. Pramod Maurya AP, SCOE, KHARGHAR 5 2. GENERAL HEAT CONDUCTION EQUATION : Cylindrical Coordinates GENERAL HEAT CONDUCTION EQUATION : Spherical Coordinates

6. Prof. Pramod Maurya AP, SCOE, KHARGHAR 3. BOUNDARY AND INITIAL CONDITIONS 6 The mathematical expressions of the thermal conditions at the boundaries are called the boundary conditions. The temperature at any point on the wall at a specified time also depends on the condition of the wall at the beginning of the heat conduction process. Such a condition, which is usually specified at time t = 0, is called the initial condition.

7. Prof. Pramod Maurya AP, SCOE, KHARGHAR 4. STEADY HEAT CONDUCTION IN PLANE WALLS 7 The energy balance for the wall can be expressed as Separating the variables in the above equation and integrating from x = 0, where T(0) = T1, to x = L, where T(L) = T2, we get

8. Prof. Pramod Maurya AP, SCOE, KHARGHAR 5. The Thermal Resistance Concept 8 The heat conduction through a plane wall can be rearranged as a. Thermal circuit diagram for Conduction only b. Thermal circuit diagram for Convection only

9. Prof. Pramod Maurya AP, SCOE, KHARGHAR 9 c. The thermal resistance network for heat transfer through a plane wall subjected to convection on both sides where U is the overall heat transfer coefficient

10. Prof. Pramod Maurya AP, SCOE, KHARGHAR 10 d. Multilayer Plane Walls

11. Prof. Pramod Maurya AP, SCOE, KHARGHAR 6. THERMAL CONTACT RESISTANCE 11 In reality, a surface is microscopically rough no matter how smooth it appears to be. An interface contain numerous air gaps of varying sizes that act as insulation because of the low thermal conductivity of air Thus, an interface offers some resistance to heat transfer, and this resistance per unit interface area is called the thermal contact resistance, Rc

12. Prof. Pramod Maurya AP, SCOE, KHARGHAR 7. GENERALIZED THERMAL RESISTANCE NETWORKS 12 Thermal resistance network for two parallel layers b) Thermal resistance network for combined series-parallel arrangement

13. Prof. Pramod Maurya AP, SCOE, KHARGHAR 8. HEAT CONDUCTION IN CYLINDERS & SPHERES 13 A. cylindrical layer Where, A = 2 π rL integrating from r = r 1 , where T ( r 1 ) = T 1 , to r = r 2 , where T ( r 2 ) = T 2 , gives Where B. Spherical layer Where C. Cylindrical (or Spherical) shell subjected to convection

14. Prof. Pramod Maurya AP, SCOE, KHARGHAR CONTD… 14 C. Cylindrical (or Spherical) shell subjected to convection for a cylindrical layer for a spherical layer

15. Prof. Pramod Maurya AP, SCOE, KHARGHAR CONTD… 15 D. Multilayered Cylinders and Spheres The interface temperature T 2 between the first and second cylindrical layers can be determined from

16. Prof. Pramod Maurya AP, SCOE, KHARGHAR 8. CRITICAL RADIUS OF INSULATION 16 From thermal network, the heat transfer rate : differentiating above equation with respect to r 2 and equating it to zero A. For Cylinder A. For Sphere

17. Prof. Pramod Maurya AP, SCOE, KHARGHAR THANK YOU 17