Course: Heat Transfer Faculty of Engineering: Program: - PDF document

HEAT TRANSFER Course: Heat Transfer Faculty of Engineering: Program: Petrochemical Level: 2 Monday: 8-10 am Prof. Yehia Hassan Magdy

HEAT TRANSFER Convection Convection is then mode of energy transfer between solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion. The faster the fluid motion, the greater the convection heats transfer. As shown in Figure 1.9, Energy is transferred by convection between the solid’s surfaces and the flowing fluid by convection. The temperature of the film layer of fluid increases. The rate of conviction heat transfer is observed to be proportional to the temperature difference, and is conveniently expressed by Newton’s law ( ) =  = − Q hA T hA T T (1.17) conv surface fluid 1 = R conv hA Flowing fluid Fluid film adjacent to surface Q Stationary Solid Surface Figure 1. 9 Heat transfer by convection Where; h: film coefficient of convective heat transfer, W/m 2 K; A : area of heat transfer parallel to the direction of fluid flow, m2 solid surface temperature, o C or K T s :

HEAT TRANSFER T fluid : flowing fluid temperature, o C or K  T: temperature difference, K thermal resistan ce for convection, ˚C/W R conv The convection coefficient ( h) is not property of the fluid. It is an experimentally determined parameter whose value depends on all variables influencing convection such as the surface geometry, the nature of fluid motion, the properties of the fluid and the bulk fluid velocity. Before the above equation is used to evaluate the convective heat transfer, the fluid flow regime has to be identified; whether it is laminar, transitional or turbulent. Laminar flow of the fluid is encountered at Re <2100. Turbulent flow is normally at Re >4000. Sometimes when Re >2100 the fluid flow regime is considered to be turbulent. If we have a round tube with a liquid flowing in it at a steady state, and if we injected a dye trace with a needle parallel to the axis of the tube, one of two things can happen: a) The dye trace may be smoothly down the tube as a well-defined line, only very slowly becoming thicker which called laminar flow, as shown in Figure 1.10. Figure 1.10 Laminar Flow

HEAT TRANSFER b) The dye trace may flow irregularly down the tube moving back and forth across the diameter of the tube and eventually becoming completely dispersed which called turbulent flow as shown in Figure 1.11. Figure 1.11 Turbulent flow Heat transfer by convection may take the form of either natural or forced convection as shown in Figure 1.12. 1. Natural convection: Natural convection is caused by buoyancy forces due to density differences caused by temperature variations in the fluid. At heating the density change in the boundary layer will cause the fluid to rise and replaced by cooler fluid that also will heat and rise. 2. Forced convection: Forced convection occurs when a fluid flow is induced by an external force, such as a pump, fan or a mixer. Figure 1.12 Forced and Free (Natural) Convection

HEAT TRANSFER In practice, film heat transfer coefficients ( h ) are generally calculated from empirical equations obtained by correlating experimental data with the aid of dimensional analysis. Example 1.8 A fluid flows through a long pipe 2m and 0.5m diameter. The surface and fluid temperature is 55˚C and 25˚C, respectively. Calculate the convection heat transfer if the coefficient convection is 33W/m².K. Solution: From Newton’s law ( ) =  = − Q hA T hA T T conv surface fluid ( ) =    − Q h ( DL ) h T T conv surface fluid =     − = = Q 33 ( 3 . 14 ) ( 0 . 5 ) ( 2 ) ( 55 25 ) 6217 W 6 . 22 kW conv

HEAT TRANSFER Bulk and Film Temperature The rate of convective heat transfer, q, from a solid surface to a surrounding fluid as shown in Figure 1.13 has given by: ( ) =  = − Q hA T hA T T conv surface fluid Figure1.13 Convective heat transfer from a solid surface ( T ) to surrounding fluid T s f Where, h = average convective heat transfer coefficient, W/(m 2 .  K) A = surface area for convective heat transfer, m 2 T = surface temperature of the solid surface, K s T = fluid temperature, K f

HEAT TRANSFER However, in the case of flow thru ducts or pipes (Figure 1.14), it is more convenient to use the bulk temp., T instead of free-stream temperature, T . Thus, for the tube flow depicted in Fig. s f 2, the total energy added can be expressed in terms of bulk temperature difference: ( ) • • − q = m C T T (1.18)  S fluid or in terms of the heat transfer coefficient : =    − q 2 rh dx ( T T ) s fluid Figure 1.14 Total heat transfer expressed in terms of bulk-temperature difference The bulk temperature (T b ) is the mean temperature of the fluid at a given cross-section of the tube. In engineering practice, the bulk temperature is equated to the simple approximate average value: + T T = inlet , f outlet , f T (1.19) b 2 Which is used to calculate the average heat transfer coefficients.

HEAT TRANSFER Film temperature for fluids flowing thru tubes of ducts is the temperature of the fluid film adjacent to the heating surface. It is the average of the temperature of the heating surface and the free-stream temperature of the fluid (Figure 1.15): + T T = s f T (1.20) film 2 Figure 1.15 Film and bulk temperature

HEAT TRANSFER DIMENSIONLESS GROUPS Many of the generalized relationships used in convective heat-transfer calculations have been determined by means of dimensional analysis and empirical considerations. It has been found that certain standard dimensionless groups appear repeatedly in the final equations. Some of the most common dimensionless groups are given below with their names:  DV Reynolds number = Re =  cpµ Prandtl number = Pr = k = Nu = hD Nusselt number k  DV c p = ( Re . Pr ) Peclet number = Pe = k 3  t     = 3 2 D g t D g Grashof number = Gr =  2  2 Where in the SI system: D : pipe diameter, m V : fluid velocity, m/s  : fluid density, kg/m3 fluid dynamic vicosity, N.s/m2 or kg/m.s µ : fluid kinematic viscosity, m2/s  : k : fluid thermal conductivity, W/mK convective heat transfer coefficient, W/m2.K h : cp : fluid specific heat capacity, J/kg.K acceleration of gravity, m/s2 g : Tav. , K – 1 cubical coefficient of expansion of the fluid = 1 ß:

HEAT TRANSFER where; T av is the average absolute temperature of the fluid  t : temperature difference between surface & fluid, K The magnitudes of the above dimensionless groups are the same provided consistent units are used. The characteristic dimension L , D in Reynolds, Nusselt or Grashof number is defined depending on the situation. For a fluid flowing in a tube, its diameter D is used. For a plate, L is used.

HEAT TRANSFER Calculate the Convection Coefficient Heat Transfer for Natural Convection by using empirical relationships Natural or free convection heat transfer occurs whenever a body is placed in a fluid at a higher or lower temperature than that of the body. As a result of the temperature difference, heat flows between the fluid and the body and causes a change in the density of the fluid layers in the vicinity of the surface. The difference in density leads to downward flow of the heavier fluid and upward flow of the lighter. If the motion of the fluid is caused solely by differences in density resulting from temperature gradients, without the aid of a pump or a blower for example, the associated heat transfer mechanism is called natural or free convection. Many processing equipment and devices are cooled by free convection. Free convection is the dominant heat flow mechanism from steam radiators, walls of buildings and steam pipes. The fluid velocities in free convection currents are generally low. Fluid motion generated by natural convection may be laminar or turbulent. Many experiments have been performed to establish the functional relationships for different geometric configurations convecting to various fluids. Generally, it is found that Nu = a ( GrPr ) b (1.21) Where a and b are constants. Laminar and turbulent flow regimes have been observed in natural convection, and transition generally occurs in the range 107 < GrPr < 109 depending on the geometry. Some of the more important formulae obtained for natural convection to or from various geometries as shown in Figure 1.16.

HEAT TRANSFER Figure 1.16 Different geometries and the direction of convective flow for natural convection a. Horizontal Cylinders. Detailed measurements indicate that the convection coefficient varies with angular position round a horizontal cylinder, but for design purposes values given by the following equations are constant over the whole surface area, for cylinders of diameter, d . For laminar flow Nud = 0.525( GrdPr )0.25 (1.22) when 104 < GrdPr < 109 For turbulent flow Nud = 0.129( GrdPr )0.33 (1.23) when 109 < GrdPr < 1012