UNIT - - 3-Heat Transfer - CONDUCTION.pptx

Short Notes on Conduction

1. 1 Kongunadu college of engineering and technology (AUTONOMOUS) (Approved by AICTE, New Delhi, Affiliated to Anna University, Chennai, Accredited by NAAC B++ Grade , Accredited by NBA, Recognized by UGC with 2(f) & 12(B) An ISO 9001:2015 certified Institution) Namakkal - Trichy Main Road, Thottiam , Trichy - 621215 24AG301 THERMODYNAMICS AND HEAT TRANSFER Prepared by, Dr. P. DINESHKUMAR , M.E., Ph.D., Assistant Professor, Department of Agricultural Engineering, Kongunadu College of Engineering and Technology, Trichy .

2. SYLLABUS UNIT III – CONDUCTION General Differential equation of Heat Conduction– Cartesian and Polar Coordinates – One Dimensional Steady State Heat Conduction – Plane and Composite Systems – Extended Surfaces – Unsteady Heat Conduction – Lumped Analysis. Dr.P.DINESHKUMAR, AP / AGE / KNCET

3. UNIT III – CONDUCTION Dr.P.DINESHKUMAR, AP / AGE / KNCET

4. HEAT TRANSFER Heat transfer can be defined as the transmission of energy from one region to another region due to temperature difference . Dr.P.DINESHKUMAR, AP / AGE / KNCET

5. MODES OF HEAT TRANSFER Conduction Convection Radiation Dr.P.DINESHKUMAR, AP / AGE / KNCET

6. CONDUCTION ‘Conduction’ is the transfer of heat from one part of a substance to another part of the same substance, or from one substance to another in physical contact with it, without appreciable displacement of molecules forming the substance. In solids, the heat is conducted by the following two mechanisms. By lattice vibration By transport of free electrons Dr.P.DINESHKUMAR, AP / AGE / KNCET

7. CONVECTION Convection is the transfer of heat within a fluid by mixing of one portion of the fluid with another. Convection is possible only in a fluid medium and is directly linked with the transport of medium itself. Free or natural convection Forced convection Dr.P.DINESHKUMAR, AP / AGE / KNCET

8. RADIATION The heat transfer from one body to another without any transmitting medium is known as radiation. It is a electromagnetic wave phenomenon. Dr.P.DINESHKUMAR, AP / AGE / KNCET

9. FOURIER LAW OF CONDUCTION The rate of flow of heat through a simple homogeneous solid is directly proportional to the area of the section at right angles to the direction of heat flow, and to change of temperature with respect to the length of the path of the heat flow. Dr.P.DINESHKUMAR, AP / AGE / KNCET

10. K = Constant of proportionality and is known as thermal conductivity of the body. The – ve sign of K is to take care of the decreasing temperature along with the direction of increasing thickness or the direction of heat flow. The temperature gradient dt/dx is always negative along positive x direction and therefore the value of Q becomes + ve . Dr.P.DINESHKUMAR, AP / AGE / KNCET

11. THERMAL CONDUCTIVITY The amount of energy conducted through a body of unit area, and unit thickness in unit time when the difference in temperature between the faces causing heat flow is unit temperature difference. Unit: W/mK or W/m°C Dr.P.DINESHKUMAR, AP / AGE / KNCET

12. GENERAL HEAT CONDUCTION EQUATION IN CARTESIAN CO-ORDINATES Dr.P.DINESHKUMAR, AP / AGE / KNCET

13. Case( i ). No Heat Sources This equation known as diffusion equation (or) Fourier’s equation. Case (ii): Steady State Conditions: Dr.P.DINESHKUMAR, AP / AGE / KNCET

14. Case (iii): One Dimensional Steady State Heat Conduction Case (iv): Two dimensional steady state heat conduction Case(v): Unsteady state, one dimensional without internal heat generation Dr.P.DINESHKUMAR, AP / AGE / KNCET

15. General Heat Conduction Equation in Polar (or) Cylindrical Co - Ordinates Dr.P.DINESHKUMAR, AP / AGE / KNCET

16. CONDUCTION OF HEAT THROUGH A SLAB OR PLANE WALL Dr.P.DINESHKUMAR, AP / AGE / KNCET

17. Dr.P.DINESHKUMAR, AP / AGE / KNCET

18. CONDUCTION OF HEAT THROUGH A HOLLOW CYLINDER Dr.P.DINESHKUMAR, AP / AGE / KNCET

19. CONDUCTION OF HEAT THROUGH A HOLLOW SPHERE Dr.P.DINESHKUMAR , AP / AGE / KNCET

20. PROBLEM 1 A wall of 0.6 m thickness having thermal conductivity of 1.2 W/m K. The wall is to be insulated with a material having an average thermal conductivity of 0.3 W/m K. Inner and outer surface temperature are 1000ºC and 10ºC respectively. If heat transfer rate is 1400 W/m 2 Calculate the thickness of insulation. Dr.P.DINESHKUMAR, AP / AGE / KNCET

21. Newton’s Law of Cooling Heat transfer by convection is given by Newton’s law of cooling h= coefficient of convective heat transfer Dr.P.DINESHKUMAR, AP / AGE / KNCET

22. COEFFICIENT OF CONVECTIVE HEAT TRANSFER The coefficient of convective heat transfer ‘h’ (also known as film heat transfer coefficient) may be defined as ‘‘the amount of heat transmitted for a unit temperature difference between the fluid and unit area of surface in unit time.’’ Dr.P.DINESHKUMAR, AP / AGE / KNCET

23. PROBLEM 2 The wall of a cold room is composed of three layer. The outer layer is brick 30 cm thick the middle layer is cork 20 cm thick. The inside layer is cement 15 cm thick. The temperature of the outside air is 25°C and on the inside air is -20°C. The film co-efficient for outside air and brick is 55.4 W/m 2 k. Film co-efficient for inside air and cement is 17W/m 2 K. Find the heat flow rate. K for brick = 2.5 W/ mK K for cork = 0.05 W/ mK K for cement = 0.28 W/ mK Dr.P.DINESHKUMAR, AP / AGE / KNCET

24. PROBLEM 3 A wall is constructed of several layers. The first layer consists of masonary brick 20 cm thick of thermal conductivity 0.66 W/ mK , The second layer consists of 3 cm thick mortar of thermal conductivity 0.6 W/ mK the third layer consists of 8 cm thick line stone of thermal conductivity 0.58 W/ mK and the outer layer consists of 1.2 cm thick plaster of thermal conductivity 0.6 W/ mK. The heat transfer co-efficient on the interior and exterior of the wall are 5.6 W/m 2 K and 11 W/m 2 K respectively. Interior room temperature is 22°c and outside air temperature is -5°C Calculate: a) Overall heat transfer co-efficient b) Overall Thermal resistance c) The rate of heat transfer d) The temperature at the junction between the motor and line stone. Dr.P.DINESHKUMAR, AP / AGE / KNCET

25. PROBLEM 4 A hollow cylinder 5cm inner diameter and 10cm outer diameter has inner surface temperature of 200 °C and outer surface temperature 100 °C . Determine heat flow through cylinder per meter length. Also determine the temperature the point half way between the inner and outer surface take K = 1W/mk. Dr.P.DINESHKUMAR, AP / AGE / KNCET

26. PROBLEM 4 Air at 90 °C flow in a copper tube of 5cm inner diameter with thermal conductivity 380W/ mK and with 0.7cm thick wall which heated from outside water 120 °C . A scale 0.4cm thick deposited outer surface tube whose thermal conductivity 1.82W/ mK. The air water side surface conductance 220W/m 2 K and 3650W/m 2 K respectively. Calculate Over all heat transfer co-efficient Water to air heat transfer Q Temperature drop a cross scales deposit (𝑇 3 −𝑇 2 ) Dr.P.DINESHKUMAR, AP / AGE / KNCET

27. Dr.P.DINESHKUMAR, AP / AGE / KNCET

28. PROBLEM 5 A steel pipe of 120mm inner diameter, 140mm outer diameter with thermal conductivity 55 W/m °C is covered with two layer of insulation each having a thickness of 55mm. The thermal conductivity of the first insulation material is 0.05w/ mk and that of second is 0.11w/mk. The temperature of the inside and outside tube are 240 °C and 60 °C . Calculate the loss of heat per meter length of pipe and the interface temperature between two layer of insulation. Dr.P.DINESHKUMAR, AP / AGE / KNCET

29. A steel pipe of 170mm diameter and 190mm outer diameter with thermal conductivity 55W/ mK in covered with two layer of insulation. The thickness of the first and second layer thickness are 25mm (K=0.1W/ mK ) and 40mm (K=0.18W/ mK ). The temperature of the steam and inner surface of the steam pipe in 320°C and outer surface of the insulation in 80°C. Ambient air temperature in 25°C. The surface co-efficient for inside and outside surface are 230W/m 2 K and 6W/m 2 K respectively. Determine the heat loss per meter length of steam pipe and layer conduct temperature and also calculate the overall heat transfer co-efficient. Dr.P.DINESHKUMAR, AP / AGE / KNCET PROBLEM 6

30. Dr.P.DINESHKUMAR, AP / AGE / KNCET

31. TRANSIENT HEAT CONDUCTION (OR) UNSTEADY HEAT CONDUCTION If the temperature of a body does not vary with time, it is used to be in a steady state. But if there is an abrupt change in its surface temperature, it attains a steady state after some period. During this period The temperature varies with time and the body is said to be in an unsteady or transient state. Transient heat conduction occur in cooling of IC engines, automobile engines, boiler tubes, heating and cooling of metal billets, rockets nozzles, electric irons etc. Dr.P.DINESHKUMAR, AP / AGE / KNCET

32. BIOT NUMBER The ratio of internal conduction resistance to the surface convection resistance is known as Biot Number. Dr.P.DINESHKUMAR, AP / AGE / KNCET

33. Dr.P.DINESHKUMAR, AP / AGE / KNCET

34. Lumped Heat Analysis [Negligible Internal Resistance] The process in which the internal resistance is assumed as negligible in compression with its surface resistance is known as Newtonian heating or cooling process. In a Newtonian heating or cooling process the temperature is considered to be uniform at a given time. Such an analysis is called lumped parameter analysis. Dr.P.DINESHKUMAR, AP / AGE / KNCET

35. Where, T −Initial temperature of the solid,K T−Intermediate temperature of the solid,K T ∞ −Surface temperature of teh solid (or)Final temperature of the solid,K h−Heat transfer co− efficient,W /m 2 K A−Surface area of the body,m 2 P−Density of the body,kg /m 3 V−volume of the body,m 3 C p −specific heat of the body,J /kg K t− Time,s Dr.P.DINESHKUMAR, AP / AGE / KNCET

36. A copper rod of outer diameter 20mm initially at a temperature of 380ºC is suddenly immersed in a water at 100ºC. Determine the time required for the rod to reach 210ºC. Take convective heat transfer co-efficient is 95 W/m 2 K. Dr.P.DINESHKUMAR, AP / AGE / KNCET PROBLEM 7

37. PROBLEM 8 A 5 cm thick copper slab is at 200ºC initially and it is suddenly immersed in water. So its surface temperature is lowered to 90ºC. In one test run the initial temperature is decreased by 40ºC and the time taken is 6 minutes. Determine the heat transfer co-efficient by using lumped capacity method of analysis. Dr.P.DINESHKUMAR, AP / AGE / KNCET

38. PROBLEM 9 An aluminum sphere weighing 7kg and initially at a temperature of 320 ºC is suddenly immersed in a liquid at 25 ºC . The convective heat transfer co-efficient is 50W/m 2 K. Determine the time required for the sphere to reach 100 ºC . Dr.P.DINESHKUMAR, AP / AGE / KNCET

39. PROBLEM 10 An aluminum (K = 160W/ mºC , ρ = 2790 kg/m 3 , Cp = 0.88 kJ/ kgºC ) of thickness, L = 3cm and at a uniform temperature of 225ºCis suddenly immersed at time t = 0 in a well stirred fluid maintained at a constant temperature 𝑻 ∞ =𝟐𝟓 ºC 𝒕𝒂𝒌𝒆 𝒉=𝟑𝟐𝟎𝑾/𝒎 𝟐 ºC . Determine the time required for the centre of the place to reach 50ºC. Dr.P.DINESHKUMAR, AP / AGE / KNCET

40. EXTENDED SURFACES (OR) FINS It is possible to increase the heat transfer rate by increasing the surface of heat transfer. The Surface used for increasing heat transfer are called extended surface or fins. Dr.P.DINESHKUMAR, AP / AGE / KNCET

41. TYPES OF FINS Dr.P.DINESHKUMAR, AP / AGE / KNCET

42. APPLICATIONS Cooling of electronic components Cooling of motor cycle engines Cooling of small capacity compressors Cooling of transformers Cooling of radiators and refrigerator etc. Dr.P.DINESHKUMAR, AP / AGE / KNCET

43. FIN EFFICIENCY The efficiency of a fin is defined as the ratio of actual heat transferred by the fin to the maximum possible heat transferred by the fin. Dr.P.DINESHKUMAR, AP / AGE / KNCET

44. FIN EFFECTIVENESS It is defined as the ratio of heat transfer with fin to heat transfer without fin. Dr.P.DINESHKUMAR, AP / AGE / KNCET

45. FORMULAE USED Infinitely long fin (or) long fin Dr.P.DINESHKUMAR, AP / AGE / KNCET

46. PROBLEM 11 Find the heat loss from a rod of 3 mm in diameter and infinitely long when its base is maintained at 140°C. The conductivity of the material is 150 W/ mK and the heat transfer co – efficient on the surface of the rod is 300 W/m 2 K. The temperature of the air surrounding the rod is 15°C Dr.P.DINESHKUMAR, AP / AGE / KNCET

47. PROBLEM 12 A long rod 5 cm diameter its base it connected to a furnace wall at 150° C while the end is projecting into the room, at 20°C. The temperature of the rod at distance of 20 cm apart from its base is 60°C. the conductivity of the material is 200 W/ mK. Determine connective heat transfer co-efficient. Dr.P.DINESHKUMAR, AP / AGE / KNCET