3 convection (ensc 14a)

7/24/2019 3 Convection (ENSC 14a)

1/43

Engr FRANCIS M MULIMBAYAN

BSAE

INSTRUCTOR 4

ENSC 15

Fundamentals of Heat Transfer

Department of Engineering Science

University of the Philippines

Los BanosCollege, Los Banos, Philippines

Heat Transfer by

Convection


2/43

Convection

o occurs between a solid surface and a moving fluid

o combination of heat diffusion (conduction) and bulk motion ofmolecules (advection)

o dominant form of heat transfer in fluids

o requires presence of material medium

o enhanced heat transfer due to fluid motion

2

Introduction

Convective Heat Transfer

Prepared by Engr. F. M. Mulimbayan


3/43

Types of Convection

o Forced Convection

o occurs when fluid motion is

induced by an external meanssuch as pump or fan

o Natural Convection

o

brought by buoyancy forces dueto density differences caused bytemperature variations in thefluid

3

Introduction




4/43

Classification of Fluid Flowso Viscous vs. Inviscid Flow

o Viscous flow the effect of viscosity is significant

o

Inviscid flow flow with zero viscosityo Internal vs. External Flow

o Internal flow through tubes or ducts in which the fluid is completelybounded by solid surface

o External flow of unbound fluid over a surface

o Open-channel flow though tubes or ducts or channels in which fluidis not completely bounded by the solid surface

o Laminar vs. Turbulent Flow

o Laminar highly ordered fluid motion

o Turbulent disordered fluid motion

4

Introduction




5/43

Physical Mechanism of Convectiono Convection strongly depends on the following:

o fluid properties (, k, , and )o fluid velocityo geometry of the exposed surface

o type of fluid flow

o Newtons Law of Cooling

=

The crux of the convection problem is to find the heat transfer coefficient forthe situation at hand.

5

Introduction




6/43

Nusselt Number

=

where: = heat transfer coefficient, W/m2-K = characteristic length, m = thermal conductivity, W/m-K

6

Dimensionless Parameters




7/43

Reynolds Number

=

=

where:

= density, kg/m3 = free stream velocity, m/s = characteristic length, m

= dynamic viscosity, kg/m-s = kinematic viscosity, m2/s =

7





8/43

Prandtl Number

=

=

where: = kinematic viscosity, m2/s =

= thermal diffusivity, m2/s =

= dynamic viscosity, kg/m-s

= specific heat, J/kg-K = thermal conductivity, W/m-K

8





9/43

Grashof Number

=

where:

= gravitational acceleration (9.81 m/s2) = characteristic length, m = kinematic viscosity, m2/s

= surface temperature, = fluid temperature far from the surface, = coefficient of volume expansion

=

ideal gases

9





10/43

Rayleigh Number, Ra =

Correlation of Datao a convenient and relatively simple relation for the correlation of

experimental data is to assume an equation of the form:

=

o where C, m and n depend on the surface geometry and the flowcondition.

10





11/43

11

Nature of Convection Problems


Convection

Natural Forced

External

Flow overFlat Plates

Flow overspheres

Flow acrosscylinders

Internal

Constant or constant

Turbulentor Laminar

flow

Developingor fully-

developed



12/43

Natural Convectiono Brought by buoyancy forces due to density differences caused by

temperature variations in the fluid

Applicationso Found in equipment that are designed to operate without the

use of any fluid mover

Mean Film Temperature,o Temperature at which all fluid properties in natural convection

are evaluated

=

2

12

Natural Convection




13/43

Nusselt Equations (See Table 9-1)

o depends on the geometry and orientation of the surface ,variation of temperature on the surface and thermo-physical

properties of the fluid.

=

= ,

Convective Heat Transfer Coefficient =

13

Natural Convection




14/43

14

Natural Convection




15/43

15

Natural Convection




16/43

16

Natural Convection




17/43

17

Natural Convection




18/43

18

Natural Convection




19/43

Sample Problems

1. The outside diameter of a horizontal steel pipe is 4.6 cm.The pipe is located in a room where the ambient

temperature is 20C. The exterior surface temperature ofthe pipe is 40C. Determine the heat transfer rate from thepipe per unit length of the pipe.

19

Natural Convection




20/43

Sample Problems

2. A small holding tank in a chemical plant contains acorrosive liquid that is maintained at a temperature of

120F by means of an electrical heater. The heating elementconsists of a refractory disk 2 ft in diameter situated at thebottom of the tank. Estimate the power required, in Btu/hrto maintain the surface of the heating element at 160F. The

properties of the corrosive liquid at 140F are: = 4.8, = 0.023ft2/h, = 0.4Btu/h-ft-F and = 0.000125R-1.Use = 32.2ft/s2.

20

Natural Convection




21/43

External Forced Convectiono Involves flow of unbound fluid over a surface.

Applications:o Used in mechanical and thermal design of many engineering systems

such as aircraft, automobiles, buildings, electronic components andturbine blades.

Flow over Flat plates

o Laminar: R e < 5 1 0

=

= 0.664//

o Turbulent: R e > 5 1 0

=

= 0.037. 871 /

21

External Forced Convection




22/43

Flow across a single cylinder

Flow over spheres

= 2 0.4/

0.06/.

o The Nusselt equation above is valid

only if 0.71 380,3.5 7.6 10and 1.0

3.2.o All properties are evaluated at free

stream temperature except

22





23/43

Sample Problems1. A small heater in the form of an electrically heated wire is

crossed back and forth in front of a fan which blows air over it ata mean velocity of 15 ft/s. The surface temperature of the wire

should not exceed 1300F. The air temperature is 60F. Theheater is to generate 3412.3 Btu/hr. Determine the length of acircular wire whose diameter is 1/32 inch.

2. The components of an electronic system are located in a 1.25-m-long horizontal duct whose cross-section is 18 cm x 18 cm. Thecomponents in the duct are not allowed to come into directcontact with cooling air, and thus are cooled by air at 28Cflowing over the duct with a velocity of 200 m/min. If the surfacetemperature of the duct is not to exceed 72C, determine thetotal power rating, in W of the electronic devices that can bemounted into the duct.

23





24/43

Sample Problems3. The top surface of the passenger

car of a train moving at a velocity of70 km/h is 2.8 m wide and 8 m

long. The top surface is absorbingsolar radiation at a rate of 200W/m2, and the temperature of theambient air is 30C. Assuming theroof of the car to be perfectlyinsulated and the radiation heat

exchange with the surroundings tobe small relative to convection,determine the equilibriumtemperature of the top surface ofthe car.

24





25/43

Internal Forced Convectiono Involves flow through a closed conduit that is sufficiently long to

effect the desired heat transfer

Applications:o Commonly used in heating and cooling applications

Different flow sectionso Pipes has circular cross-sections

o Ducts has non-circular cross-sections

o Tubes pipes with small diameter

25

Internal Forced Convection



f


26/43

Mean Velocity

o Velocity which remainsconstant for incompressible

flow when the crosssectional area of the tube isconstant

=

26




f


27/43

Mean Temperature

o When a fluid is heated as itflows through a tube, the

temperature of the fluid atany cross-section changesfrom at the surface of thewall to some minimum atthe tube center.

o The temperature profile willchange whenever the fluid isheated or cooled.

27




C f


28/43

Bulk Mean Temperatureo Temperature where all fluid properties in internal flow are evaluated

= 2

o where:

= mean inlet temperature = mean outlet temperature

28




C i H T f


29/43

Velocity Profile

29




C i H T f


30/43

Velocity Profile

o Hydrodynamic entrance region

region from the tube inlet to the point at which the boundary layer

merges at the centerlineo Hydrodynamic entry length,

length of the hydrodynamic region

o Hydrodynamically developing flow

flow in the entrance regiono Hydrodynamically fully developed region

region beyond the entrance region in which the velocity profile isfully developed and remains unchanged

30




C i H T f


31/43

Temperature Profile

31




C ti H t T f


32/43

Temperature Profileo Thermal entrance region

region of flow over which the thermal boundary layer develops andreaches the tube center.

o Thermal entry length, length of thermal entrance region

o Thermally Developing Flow flow in the thermal entrance region where the temperature profile

developso Thermally fully-developed Region

region beyond the thermal entrance region in which the dimensionless

temperature profile expressed as

remains unchanged

32




C ti H t T f


33/43

Fully-developed Flow

o region in which the flow is both hydrodynamically andthermally developed and thus both the velocity and

dimensionless temperature profile remains unchanged. Entry Length

o distance from the tube entrance where the friction coefficientreaches within about 2% of the fully developed value.

Laminar: = 0.05 = 0.05 =

Turbulent: 10

33




C ti H t T f


34/43

General Thermal Analysis

o In the absence of work, the conservation of energy equation forsteady flow of a fluid in a tube can be expressed as:

=

34






35/43

The thermal conditions at the surface can usually beapproximated with reasonable accuracy to be:

o

Constant surface temperature (constant ) Realized when a phase change process such as boiling and

condensation occurs at the outer surface of the tube

o Constant surface heat flux (constant ) Realized when the tube is subjected to uniform radiation or electric

resistance heating

=

35






36/43

Constant

= =

=

ln

=

36






37/43

Constant

= =

=

= , = ,

, =

, =

37






38/43

Pumping Power Requirement

o Volume flow rate: =

o Friction Factor, For fully-developed laminar flow (or at least hydrodynamically

fully-developed) in tubes - Use Table 8-1.

For turbulent flow in tubes: = 0.790 ln Re 1.64 10 < R e < 1 0

o Pressure Drop,

=

2

=

38






39/43

39




Laminar Flow

Developing

flow

Use Equation 1

(constant Ts)

Fully-

developed flow

Table 8-1

(constant Ts and

qs)

Turbulent Flow

Developing

flow

See Note 1

(constant Ts and

qs)

Fully-

developed flow

Use Equation 2

(constant Ts and

qs)




40/43

For developing, laminar flow in entrance region for circulartube assuming constant Ts

Equation 1: Nu = 3.66 . D/L

+. D/L /

For fully-developed turbulent flow in smooth tubes

Equation 2: Nu = 0.023Re/Pr

= 0.4 for heating ( > )

= 0.3 for cooling < Note 1: For developing, turbulent flow in smooth tubes, use

Equation 2.

40






41/43

41



Heat Transfer Coefficient

o can be computed once theNusselt value is known,

=


o Constant = o Constant = , = ,




42/43

Sample Problems

1. Water is to be heated from 10C to 80C as it flows througha 4-cm-internal-diameter, 18-m-long tube. The tube is

equipped with an electric resistance heater, which providesuniform heating throughout the surface of the tube. Theouter surface of the heater is well-insulated, so that insteady operation all the heat generated in the heater istransferred to the water in the tube. If the system is to

provide hot water at a rate of 2.4 L/min, determine thepower rating of the resistance heater and estimate the innersurface temperature of the pipe at the exit. Also, computethe pressure drop in the tube.

42






43/43

Sample Problems

2. An air heater for an industrial application consists of an insulated, concentrictube annulus, for which air flows through a thin-walled inner tube. Saturatedsteam flows through the outer annulus, and condensation of the steammaintains a uniform temperature Ts on the tube surface. Consider conditionsfor which atmospheric air enters a 50-mm diameter tube at a temperature of15C and a flow rate of = 0.03 kg/s, while saturated steam at 2.5 bars

condenses on the outer surface of the tube.

43



If the length of the annulus is = 5m what is theoutlet temperature and heat gain of air? What isthe mass rate at which condensate leaves theannulus? Also, determine the LMTD, pressure

drop and the power requirement of the pump toovercome this pressure drop. From thethermodynamic property table, at = 2.5 bars,the saturation temperature and the latent heat offusion are 127.43C and 2181.55 J/kg, respectively

3 convection (ensc 14a)

Documents