Fundamentals of Heat Transfer Muammad Rasid Usman Institute of Cemical Engineering and Tecnology University of te Punjab, Laore. Figure taken from: ttp://eatexcanger-design.com/20/0/06/eat-excangers-6/ Dated: 7-Jan-202
Course contents final term Convection eat transfer: Free and forced convection. Rate equation for convective eat transfer coefficient. Brief description of ydrodynamic boundary layer and eat transfer coefficient. Units of eat transfer coefficient. Individual and overall eat transfer coefficients: plane wall and ollow cylinder. Numerical problems regarding overall eat transfer coefficient. Determination of eat transfer coefficient. Description of various eat transfer correlations. Log mean temperature difference. Numerical problems involving log mean temperature difference. Heat transfer in coiled and jacketed agitated vessels. Introduction to boiling and condensation. Types of boiling: Pool boiling and film boiling. Critical tickness of insulation. Brief description of eat transfer equipment: Heat excangers, furnaces, and evaporators. Radiation eat transfer: Basics of radiation eat transfer. Stefan-Boltzmann Law. Kircoff s law. Radiation eat transfer coefficient. Radiation to a small object from surroundings. View factors in radiation. Radiation in absorbing gases. 2
Te text book Please read and consult to know and learn. Geankoplis, C.J. (2003). Transport processes and separation process principles: includes unit operations. 4 t ed. Prentice- Hall International, Inc. 3
Convection eat transfer 4
Types of convective eat transfer Free or natural convection eat transfer Forced convection eat transfer 5
Free or natural convection eat transfer If te fluid motion is caused by itself due to difference in densities at two different points suc a process is natural or free convection eat transfer. Te density differences may be caused by temperature differences or concentration differences at two locations. In natural convection, no mecanical means are used to produce convective currents and convective mixing is a solely due to natural motion of te fluid. Boiling of milk and water and eating distant parts of a room in te presence of a room eater are common daily examples. 6
Forced convection eat transfer If te fluid motion is caused by some external or mecanical means te eat transfer is due to forced convection. Pumps, blowers, fans, agitation devices suc as impellers are employed for forced convection eat transfer. gitation using impellers in reaction vessels and pumping of fluids, at ig velocity, in eat excangers devices are te examples of forced convection. 7
Free and forced convection eat transfer In wic of te following cases do you expect greater rate of eat transfer?. Free convection 2. Forced convection 8
Newton s rate equation Rate of eat transfer per unit area is equal to te product of eat transfer coefficient and temperature difference between te eated surface and fluid far from te surface. q ( T s Tf ) q ( T s Tf ) q T f T s 642-727 9
Heat conduction troug a multilayer (composite) ollow cylinder-4: Problem (modified)-7 [p. 7, 2] ir at 20 C blows over a ot plate 50 by 75 cm wile maintained at 250 C. Te convection eat transfer coefficient is 25 W/m 2 K. Calculate te rate of eat transfer. Wat if eat transfer coefficient for te system is very ig or very low suc as 200 W/m 2 K and 0. W/m 2 K respectively. Wat is te direction of eat flow. T air = 20 C ir 75 cm 50 cm T s = 250 C 0
Heat transfer coefficient From te Newton s rate equation, it may be said tat eat transfer coefficient is te ability of te system, for wic it is defined, to transfer eat. Wat are te units of eat transfer coefficient?
Units of eat transfer coefficient SI units: J/s m 2 K or W/m 2 K W/m 2 K is equal to W/m 2 C Englis system: Btu/ ft 2 F Compare units of termal conductivity and eat transfer coefficient. 2
Heat transfer coefficient based on film model: Hydrodynamic boundary layer [p.58, 6] Fully developed boundary layer 3
Heat transfer coefficient based on film model Consider tickness of te film as Δx and k as te termal conductivity of te fluid (material of te film), ten it may be written tat k x Te main resistance to eat transfer is in tis film. Te eat transfer coefficient is sometimes called film coefficient. Note: Liquids and gases ave low termal conductivity. 4
Heat transfer coefficient based on film model Excerpt (p. 3.2) from Heat transfer by K.. Gavana, 8 t ed., Nirali Prakasan, Pune (2008). 5
Heat transfer coefficient based on film model For convective eat transfer, te film model suggests tat were ever a fluid flows past a solid surface tere is a film formed adjacent to te wall and tat tere is no turbulence in tis film and tis film offers te only resistance to eat transfer. It is important to mention ere tat for te film model, in te turbulent region (beyond te film) of a fluid tere is no problem for eat transfer, i.e. due to intense mixing, eat transfer is greatly enanced and tere is no temperature differential. 6
pproximate magnitudes of some eat transfer coefficients [] 7
Heat transfer coefficient based on film model Condensing steam (saturated steam) as ig eat transfer coefficient in contrast to supereated steam tat is wy a process engineer would like to eat a system using condensing steam and not by supereated steam. supereated steam beaves like a gas and you know gases ave low eat transfer coefficients. 8
Individual and overall eat transfer coefficients: plane wall [p. 249, ] Outside film resistance Inside film resistance Wall resistance 9
Individual and overall eat transfer coefficients: plane wall [p. 249, ] For inside film resistance: q i ( T T2) For wall resistance: q k ( T2 T 3) x For outside film: q ( T 3 T4) Wat if we ave two walls? o 20
2 Individual and overall eat transfer coefficients: plane wall [p. 249, ] i o k x T T q 4 k x T T q o i 4 te resistancein series all Sumof Overall temperature difference rate Heat
22 Individual and overall eat transfer coefficients: plane wall Reciprocal of overall resistance is overall conductance and frequently written in terms of overall eat transfer coefficient. i o k x U i o k x U ( 4) T T U q, k x U o i
Individual and overall eat transfer coefficients: plane wall Case : Wat if tickness of te wall wit ig termal conductivity is very small? Case 2: If one of te two film coefficients is a small value compared to te oter, ten major resistance is offered by te one wit small value and te coefficient is called as controlling film coefficient. Wat will be te form of te eat rate equation if i >>> o? Case 3: Wat if tere are a number of plane walls in series? Tink oter cases! 23
Individual and overall eat transfer coefficients: ollow cylinder Pipe wall resistance Outside fluid film resistance r 2 r Inside fluid film resistance 24
Individual and overall eat transfer coefficients: ollow cylinder q i i T T4 ln( r2 / r ) 2 k L o o Overall temperature difference Heat rate Sumof all te resistancein series 25
Individual and overall eat transfer coefficients: ollow cylinder U i i ln( r2 / r 2 k ) L o o Wic? Unlike plane wall, te inside and outside surface areas are different for cylindrical geometry. Te overall eat transfer coefficient is terefore as to be defined eiter on outside or inside surface of te ollow cylinder. 26
27 Individual and overall eat transfer coefficients: ollow cylinder o o i i i i L k r r U 2 ) / ln( 2 o o i i o o L k r r U 2 ) / ln( 2
References. Geankoplis, C.J. (2003). Transport processes and separation process principles: includes unit operations. 4 t ed. Prentice-Hall International, Inc. 2. Holman, J.P. (200). Heat transfer. 0 t ed. McGraw-Hill Higer Education, Singapore. 3. Cengel, Y.. (2003). Heat transfer: practical approac. 2 nd ed. McGraw-Hill. 4. Incropera, F.P.; DeWitt, D.P.; Bergman, T.L.; Lavine..S. (2007) Fundamentals of eat and mass transfer. 6 t ed. Jon Wiley & Sons, Inc. 5. Kern, D.Q. (965). Process eat transfer. McGraw-Hill International Book Co., Singapore. 6. McCabe, W.L.; Smit, J.C.; Harriott, P. (993). Unit operations of cemical engineering. 5 t ed. McGraw-Hill, Inc., Singapore. 7. Coulson, J.M.; Ricardson, J.F.; Backurst, J.R.; Harker, J.H. (999). Coulson and Ricardson s Cemical engineering: Fluid flow, eat transfer and mass transfer. vol.. 6 t ed. Butterwot-Heinemann, Oxford. 8. Staff of Researc and Education ssociation. (984). Te eat transfer problem solver. Researc and Education ssociation, New Jersey. 9. Kreit, F.; Manglik, R.M.; Bon, M.S. (20). Principles of eat transfer, 7 t ed., Cengage learning. 0. Mills.F. (995). Heat and mass transfer. Ricard D. Irwin, Inc. 28