Pengantar Perpindahan Panas Konveksi Pertemuan 1 dan 2.pptx

Dasar Dasar perpindahan Panas konveksi

1. Chapter 6 FUNDAMENTALS OF CONVECTION Agung Sugiharto, M.Eng Copyright © 2011 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Heat and Mass Transfer: Fundamentals & Applications Fourth Edition Yunus A. Cengel, Afshin J. Ghajar McGraw-Hill, 2011

2. Objectives Memahami tenting mekanisme fisik peristiwa konveksi dan klasifikasinya Visualisai bagaimana velocity dan thermal boundary layers terbentuk pada aliran diatas flat plate Memahami tentang Bilangan tak berdimensi Reynolds, Prandtl, and Nusselt Perbedaan antara aliran laminar dan turbulent flows Menyusun PD pada kasus konveksi Persamaan talk berdimensi pada konveksi Analogi antara momentum dan heat transfer

3. Pertemuan I

4. PHYSICAL MECHANISM OF CONVECTION Konduksi dan konveksi keduanya membutuhkan kehadiran materi sebagai medium penghantar Konveksi pada media mengalir seperti konduksi pada media padat . Transfer panes melalui padatan selalu berupa konduksi . Transfer panas pada aliran fluida adalah disebabkan oleh konveksi baik ada atau tidak ada transfer panas konduksi . Oleh karena itu, konduksi dalam fluida dapat dilihat sebagai kejadian khusus pada konveksi tergantung pada keadaan aliran fluidanya .

5. Keceptan transfer panas melalui fluida sebagian besasr adalah oleh konveksi dibandingkan karena koduksi Semakin besar kecepatan fluida semakin besar kecepatan transfer panasnya .

6. Transfer konveksi sangat dipengaruhi oleh sifat fluidanya dynamic viscosity , thermal conductivity , density , dan specific heat , juga fluid velocity . Juga tergantung geometry dan roughness dari permukaan padatan, Jenis aliran fluida juga berpengaruh (laminer, turbulen). Convection heat transfer coefficient, h : Kecepatan transfer panas antara permukaan padatan dan fluida per satuan luas padatan per satuan temperatur Newton’s law of cooling

7. The development of a velocity profile due to the no-slip condition as a fluid flows over a blunt nose. A fluid flowing over a stationary surface comes to a complete stop at the surface because of the no-slip condition. No-slip condition: Fluida yang kontak langsung dengan permukaan padatan dianggap tidak bergerak. Boundary layer: Area aliran didekat permukaan padatan akan membentuk distribusi kecepatan dan ini sangat berpengaruh. Sifat fluida yang mempengaruhi pembentukan boundary layer adalah viscosity .

8. Implikasi dari permukaan padatan yang tidak licin adalah transfer panas yang terjadi dari padatan ke fluida adalah hanya konduksi , dikarena fluida bergerak maka Penentuan convection heat transfer coefficient ketika distribusi temperatur terjadi pada fluida adalah Koefisien transfer panas konveksi, secara umum, bervariasi sepanjang aliran fluida ( x -direction). Sehingga koefisien transferpanas konveksi rata-rata ( average / mean) pada permukaan adalah ditentukan dengan menghitung rata-rata berdasar koefisien transfer panas local pada permukaan A s atau sepanjang L

9. Bilangan Nusselt ( Nusselt Number ) Heat transfer through a fluid layer of thickness L and temperature difference D T. Pada konveksi, adalah lebih mudah ketika dilakukan analisis persamaan tak berdimensi dengan mengkombinasikan variabel-variabel yang relevan, sehingga dapat mengurangi jumlah total variabel (khususnya variabel yang tak diketahui). Nusselt number: Dimensionless convection heat transfer coefficient L c characteristic length Bilangan Nusselt menggambarkan transfer panas melalui lapisan fluida sebagai hasil relatif antara konveksi dan konduksi yang terjadi pada permukaan lapisan fluida. Semakin besar bilangan Nusselt, semakin efektif transfer konveksi terjadi. Bilangan Nusselt Nu = 1 untuk lapisan fluida yang mana transfer panas terjadi hanya berupa konduksi.

10. 11 Klasifikasi Aliran Fluida Viscous versus Inviscid Regions of Flow Viscous flows: Aliran dimana efek dari gesekan fluida sangat signifikan. Inviscid flow regions: Dalam prakteknya tidak terbentuk region (khususnya daerah yang jauh dari permukaan padatan) The flow of an originally uniform fluid stream over a flat plate, and the regions of viscous flow (next to the plate on both sides) and inviscid flow (away from the plate).

11. 12 Internal versus External Flow External flow over a tennis ball, and the turbulent wake region behind. External flow: Aliran fluida diatas permukaan padatan berupa plate, atau pipa Internal flow: Aliran fluida pada pipa. Water flow in a pipe is internal flow, and airflow over a ball is external flow . The flow of liquids in a duct is called open-channel flow if the duct is only partially filled with the liquid and there is a free surface.

12. 13 Compressible versus Incompressible Flow Incompressible flow: Jika densitas dari fluida yang mengalir cenderung konstan (e.g., liquid flow). Compressible flow: Jika densitas dari fluida yang mengalir berubah sepanjang aliran (e.g., high-speed gas flow) Ma = 1 Sonic flow Ma < 1 Subsonic flow Ma > 1 Supersonic flow Ma >> 1 Hypersonic flow Aliran Gas seringkali dianggap incompressible jika perubahan density terjadi kurang dari 5% biasanya terjadi pada kecepatan dibawah kecepatan suara (Ma < 0.3.) Oleh karena itu , efek compressibilitasnya diabaikan pada kecepatan dibawah 100 m/s.

13. 14 Laminar versus Turbulent Flow Laminar flow: Aliran yang sangat uniform. Aliran fluida yang sangat kental biasnya berbentuk laminer. Turbulent flow: TBiasa terjadi pada aliran fluida yang berkecepatan tinggi. aliran fluida yang tidak kental biasanya turbulent. Transitional flow: aliran antara laminer dan trubulent. Laminar, transitional, and turbulent flows.

14. 15 Natural (or Unforced) versus Forced Flow Forced flow: Aliran fluida yang disebabkan adanya pemompaan. Natural flow: Aliran fluida tanpa pompa In this schlieren image, the rise of lighter, warmer air adjacent to her body indicates that humans and warm - blooded animals are surrounded by thermal plumes of rising warm air.

15. 16 Steady versus Unsteady Flow Term st eady artinya no change at a point with time . Lawan dari steady adalah unsteady . Term uniform artinya no change with location sepanjang region tertentu. Term periodic mengacu pada jenis aliran unsteady yang kadang kadang steady. Beberapa peralatan seperti turbines, compressors, boilers, condensers, dan heat exchangers yang dioperasikan dalam jangka panjang pada kondisi yang sama bisa dianggap sebagai steady-flow devices .

16. 17 One-, Two-, and Three-Dimensional Flows A flow field is best characterized by its velocity distribution . A flow is said to be one-, two-, or three-dimensional if the flow velocity varies in one, two, or three dimensions, respectively. However, the variation of velocity in certain directions can be small relative to the variation in other directions and can be ignored . The development of the velocity profile in a circular pipe. V = V ( r , z ) and thus the flow is two-dimensional in the entrance region, and becomes one-dimensional downstream when the velocity profile fully develops and remains unchanged in the flow direction, V = V ( r ).

17. 18 VELOCITY BOUNDARY LAYER Velocity boundary layer: Region aliran diatas plate pada jarak d yang mana efek gesekan lapisan fluida diabaikan (menurun). boundary layer thickness , d , umumnya didefinisikan sebagai jarak y dari permukaan padatan yang kecepatannya (u = 0.99 V) . Secara imaginer garis u = 0.99 V membagi aliran pada dua region: Boundary layer region: Efek kekentalan dan perubahan kecepatan sangat berpengaruh. Irrotational flow region: Efek gesekan diabaikan dan kecepatan dianggap konstan.

18. Wall Shear Stress Shear stress: Gaya gesek persatuan luas. Untuk kebanyakan fulida adalah proporsional dengan gradien kecepatan velocity gradient , dan shear stress pada permukaan dinding: Fluida yang mengikuti persamaan diatas disebut Newtonian Fluids . Kebanyakan fulida seperti udara, air, gasoline dan minyak adalah Newtonian fluids. Darah dan plastik adalah non-Newtonian fluids. m dynamic viscosity kg/m × s or N × s/m 2 or Pa × s 1 poise = 0.1 Pa × s

19. The viscosity of a fluid is a measure of its resistance to deformation , and it is a strong function of temperature. C f friction coefficient or skin friction coefficient The friction coefficient is an important parameter in heat transfer studies since it is directly related to the heat transfer coefficient and the power requirements of the pump or fan. Wall shear stress: Friction force over the entire surface: Kinematic viscosity, m 2 /s or stoke 1 stoke = 1 cm 2 /s = 0.0001 m 2 /s

20. 22 THERMAL BOUNDARY LAYER Thermal boundary layer on a flat plate (the fluid is hotter than the plate surface). A thermal boundary layer develops when a fluid at a specified temperature flows over a surface that is at a different temperature. Thermal boundary layer: The flow region over the surface in which the temperature variation in the direction normal to the surface is significant. The thickness of the thermal boundary layer d t at any location along the surface is defined as the distance from the surface at which the temperature difference T − T s equals 0.99( T ¥ − T s ). The thickness of the thermal boundary layer increases in the flow direction, since the effects of heat transfer are felt at greater distances from the surface further down stream. The shape of the temperature profile in the thermal boundary layer dictates the convection heat transfer between a solid surface and the fluid flowing over it.

21. 23 Prandtl Number The relative thickness of the velocity and the thermal boundary layers is best described by the dimensionless parameter Prandtl number The Prandtl numbers of gases are about 1, which indicates that both momentum and heat dissipate through the fluid at about the same rate. Heat diffuses very quickly in liquid metals (Pr << 1) and very slowly in oils (Pr >> 1) relative to momentum. Consequently the thermal boundary layer is much thicker for liquid metals and much thinner for oils relative to the velocity boundary layer.

22. 25 LAMINAR AND TURBULENT FLOWS Laminar and turbulent flow regimes of candle smoke. The behavior of colored fluid injected into the flow in laminar and turbulent flows in a pipe. Laminar: Smooth streamlines and highly ordered motion. Turbulent: Velocity fluctuations and highly disordered motion. Transition: The flow fluctuates between laminar and turbulent flows. Most flows encountered in practice are turbulent. Laminar flow is encountered when highly viscous fluids such as oils flow in small pipes or narrow passages.

23. 26 Reynolds Number The transition from laminar to turbulent flow depends on the geometry , surface roughness , flow velocity , surface temperature , and type of fluid . The flow regime depends mainly on the ratio of inertia forces to viscous forces ( Reynolds number ). The Reynolds number can be viewed as the ratio of inertial forces to viscous forces acting on a fluid element. Critical Reynolds number, Re cr : The Reynolds number at which the flow becomes turbulent. The value of the critical Reynolds number is different for different geometries and flow conditions. At large Reynolds numbers , the inertial forces, which are proportional to the fluid density and the square of the fluid velocity, are large relative to the viscous forces, and thus the viscous forces cannot prevent the random and rapid fluctuations of the fluid (turbulent). At small or moderate Reynolds numbers , the viscous forces are large enough to suppress these fluctuations and to keep the fluid “in line” (laminar).

24. HEAT AND MOMENTUM TRANSFER IN TURBULENT FLOW Most flows encountered in engineering practice are turbulent, and thus it is important to understand how turbulence affects wall shear stress and heat transfer. However, turbulent flow is a complex mechanism dominated by fluctuations, and the theory of turbulent flow is still not fully understood. Therefore, we must rely on experiments and the empirical or semi-empirical correlations developed for various situations. Turbulent flow is characterized by disorderly and rapid fluctuations of swirling regions of fluid, called eddies , throughout the flow. These fluctuations provide an additional mechanism for momentum and energy transfer. The swirling eddies transport mass, momentum, and energy to other regions of flow much more rapidly than molecular diffusion, greatly enhancing mass, momentum, and heat transfer. Turbulent flow is associated with much higher values of friction, heat transfer, and mass transfer coefficients.

25. Pertemuan II

26. DERIVATION OF DIFFERENTIAL CONVECTION EQUATIONS

27. The Continuity Equation

28. The Momentum Equations

29. Conservation of Energy Equation

30. SOLUTIONS OF CONVECTION EQUATIONS FOR A FLAT PLATE

31. The Energy Equation

32. NONDIMENSIONALIZED CONVECTION EQUATIONS AND SIMILARITY

33. FUNCTIONAL FORMS OF FRICTION AND CONVECTION COEFFICIENTS

34. ANALOGIES BETWEEN MOMENTUM AND HEAT TRANSFER

35. 57 Some important results from convection equations The velocity boundary layer thickness The local skin friction coefficient The thermal boundary layer thickness Local Nusselt number Reynold analogy Modified Reynold analogy or Chilton-Colburn analogy

36. 58 Summary Physical Mechanism of Convection Nusselt Number Classification of Fluid Flows Velocity Boundary Layer Wall shear sttress Thermal Boundary Layer Prandtl Number Laminar and Turbulent Flows Reynolds Number Heat and Momentum Transfer in Turbulent Flow Derivation of Differential Convection Equations Solutions of Convection Equations for a Flat Plate Nondimensionalized Convection Equations and Similarity Functional Forms of Friction and Convection Coefficients Analogies Between Momentum and Heat Transfer