Convection

Convective Heat-Transfer Coefficient When the fluid outside the solid surface is in forced or natural

convective motion, we express the rate of heat transfer from the solid to the fluid, or vice versa, by the following equation:

=

Where q is the heat transfer rate, A is the area, Tw is the temperature of the solid surface, Tf is the average or bulk temperature of the fluid flowing past, and h is the convective heat-transfer coefficient

Convective Heat-Transfer Coefficient The coefficient h is a function of the system geometry, fluid

properties, flow velocity, and temperature difference. In many cases, empirical correlations are available to predict this coefficient, since it often cannot be predicted theoretically.

Combined Convection and Conduction and Overall Coefficients

In many practical situations the surface temperatures (or boundary conditions at the surface) are not known, but there is a fluid on both sides of the solid surfaces. Consider the plane wall:

Combined Convection and Conduction and Overall Coefficients

The heat-transfer rate is given as

Combined Convection and Conduction and Overall Coefficients

Expressing 1/hiA, xA/kAA, and 1/hoA as resistances and combining the equations as before,

Combined Convection and Conduction and Overall Coefficients

The overall heat transfer by combined conduction and convection is often expressed in terms of an overall heat-transfer coefficient U defined by

q = UAToverall

Where Toverall = T1 T4 and U is

Combined Convection and Conduction and Overall Coefficients

A more important application is heat transfer from a fluid outside a cylinder, through a metal wall, to a fluid inside the tube. Consider the following figure:

Combined Convection and Conduction and Overall Coefficients

Using the same procedure as before, the overall heat-transfer rate through the cylinder is

Combined Convection and Conduction and Overall Coefficients

The overall heat-transfer coefficient U for the cylinder may be based on the inside area Ai or the outside area Ao of the tube. Hence,

Example

A gas at 450K is flowing inside a 2-in. steel pipe, schedule 40. the pipe is insulated with 51mm of lagging having a mean k=0.0623 W/mK. The convective heat transfer coefficient of the gas inside the pipe is 30.7 W/m2K and the convective coefficient on the outside of the lagging is 10.8. The air is at a temperature of 300K. Calculate the heat loss per unit length of 1 meter of pipe using resistances.

FORCED CONVECTION HEAT TRANSFER INSIDE PIPES

Forced Convection Heat Transfer Inside Pipes In most situations involving a liquid or a gas in heat transfer,

convective heat transfer usually occurs as well as conduction. In most industrial processes where heat transfer is occurring, heat is being transferred from one fluid through a solid wall to a second fluid.

Forced Convection Heat Transfer Inside Pipes The type of fluid flow, whether laminar or turbulent, of the

individual fluid has a great effect on the heat-transfer coefficient h, which is often called a film coefficient, since most of the resistance to heat transfer is in a thin film close to the wall. The more turbulent the flow, the greater the heat-transfer coefficient.

Forced Convection Heat Transfer Inside Pipes Most of the correlations fro predicting film coefficients h are

semiempirical in nature and are affected by the physical properties of the fluid, the type and velocity of flow, the temperature difference, and the geometry of the specific physical system. Some approximate values for convective coefficients were presented in Table 4.1-2 of your Geankoplis book.

Forced Convection Heat Transfer Inside Pipes To correlate the data for heat-transfer coefficients,

dimensionless numbers such as the Reynolds and Prandtl numbers are used. The Prandtl number is the ratio of shear component of diffusivity from momentum (/) to the diffusivity for heat (k/cp) and physically relates the relative thicknesses of the hydrodynamic layer and thermal boundary layer:

Forced Convection Heat Transfer Inside Pipes The dimensionless Nusselt number is used to relate data for

the heat transfer coefficient h to the thermal conductivity k of the fluid and a characteristic dimension D:

Heat-Transfer Coefficient for Laminar Flow Inside a Pipe This equation holds for (NReNPrD/L) > 100

Heat-Transfer Coefficient for Laminar Flow Inside a Pipe In laminar flow the average coefficient ha depends strongly on

heated length. The average(arithmetic mean) temperature drop Ta is used in the equation to calculate the heat-transfer rate q:

Heat-Transfer Coefficient for Turbulent Flow Inside a Pipe The following equation has been found to hold for tubes but is

also used for pipes. It holds for a NRe>6000, a NPr between 0.7 and 16000, and L/D>60.

Heat-Transfer Coefficient for Transition Flow Inside a Pipe In the transition region for Reynolds number between 2100

and 6000, the empirical equations are not well defined. No simple equation exists for accomplishing a smooth transition from heat transfer in laminar flow to that in turbulent flow.

Heat-Transfer Coefficient for Transition Flow Inside a Pipe Consider the following plot:

Heat-Transfer Coefficient for Transition Flow Inside a Pipe The plot presented represents an approximate relationship to

use between the various heat-transfer parameters and the Reynolds number between 2100 and 6000.

Example

Air at pressure of 101.3 kPa and a temperature of 288.8 K is flowing inside a pipe at 3.05 m/s. The plate length in the direction of flow is 5 meters and is at 333.2 K. calculate the heat transfer coefficient . The pipe is 2 in schedule 80, 308 stainless steel pipe.

NATURAL CONVECTION HEAT TRANSFER

Natural Convection Heat Transfer

Natural convection heat transfer occurs when a solid surface is in contact with a gas or liquid which is at a different temperature from the surface. Density differences in the fluid arising from the heating process provide the buoyancy force required to move the fluid. Free or natural convection is observed as a result of the motion of the fluid.

Natural Convection from Vertical Planes and Cylinders For an isothermal vertical surface or plate with height L less

than 1 meter, the average natural convection heat-transfer coefficient can be expressed by the following general equation:

Natural Convection from Vertical Planes and Cylinders The Grashof number can be interpreted physically as a

dimensionless number that represents the ratio of the buoyancy forces to the viscous forces in free convection and plays a role similar to that of the Reynolds number in forced convection

Example

A vertical cylinder 76.2mm in diameter and 121.9mm high is maintained at 397.1 K at its surface. It loses heat by natural convection to air at 294.3 K. Heat is lost from the cylindrical side and the flat circular end at the top. Calculate the heat loss neglecting radiation losses. The equivalent L to use for the top flat surface is 0.9 times the diameter.

Natural Convection From Horizontal Cylinders and Natural Convection From Horizontal Plates

Refer to Table 4.7-1, Geankoplis

Example

A horizontal tube carrying hot water has a surface temperature of 355.4 K and an outside diameter of 25.4mm. The tube is exposed to room air at 294.3 K. What is the natural convection heat loss for a 1 meter length of pipe.

INTRODUCTION TO RADIATION HEAT TRANSFER

Nature of Radiant Heat Transfer

Radiation, which may be considered to be energy streaming through space at the speed of light, may originate in various ways. Some types of material will emit radiation when they are treated by external agencies, such as electron bombardment, electric discharge, or radiation of definite wavelengths. All substances at temperatures above absolute zero emit radiation that is independent of external agencies. Radiation that is the result of temperature only is called thermal radiation.

Nature of Radiant Heat Transfer In an elementary sense the mechanism of radiant heat-

transfer is composed of three distinct steps or phases:

1. The thermal energy of a hot source, such as wall of a furnace at T1 is converted into energy in the form of electromagnetic-radiation waves.

2. These waves travel through the intervening space in straight lines and strike a cold object at T2 such as a furnace tube containing water to be heated.

3. The electromagnetic waves that strike the body are absorbed by the body and converted back to thermal energy or heat.

Absorptivity and Black Bodies

When thermal radiation (such as light waves) falls upon a body, part is absorbed by the body in the form of heat, part is reflected back to space, and part may actually be transmitted through the body. The fraction of the radiation falling on a body that is reflected is called reflectivity . The fraction that is absorbed is called the absorptivity . The fraction that is transmitted is called the transmissivity . The sum of these fractions must be unity, or

+ + = 1

Absorptivity and Black Bodies

A black body is defined as one that absorbs all radiant energy and reflects none. Hence, =0, =0, and =1 for black bodies.

As stated previously, a black body absorbs all radiant energy falling on it and reflects none. Such a black body also emits radiation, depending on its temperature, and does not reflect any. The ratio of the emissive power of a surface to that of a black body is called emissivity and is 1.0 for a black body. Kirchoffs Law states that at the same temperature T1, 1, and 1 of a given surface are the same,

1= 1

This also holds true for any black or nonblack solid surface.

Radiation from a Body and Emissivity The basic equation for heat transfer by radiation from a

perfect black body with an emissivity equal to 1.0 is

Radiation from a Body and Emissivity For a body that is not a black body and has an emissivity less

than 1.0, the emissive power is reduced by , or

Substances that have emissivities of less than 1.0 are called gray bodies when the emissivity is independent of the wavelength. All real materials have an emissivity of less than 1.0.

Radiation to a Small Object from Surroundings In the case of a small gray object of area A1 at temperature T1

in a large enclosure at a higher temperature T, there is net radiation to the small object. Example of this is a loaf of bread in an oven receiving radiation from the walls around it. The net heat of absorption happening is given by the simplified Stefan-Boltzmann equation:

Example

A loaf of bread having a surface temperature of 100C is being baked in an oven whose walls and the air are at 200C. The bread moves continuously through the large oven on an open chain belt conveyor. The emissivity of the bread is estimated as 0.85 and the loaf can be assumed a rectangular solid 11 cm by 11 cm by 30 cm. Calculate the radiation heat transfer to the bread, assuming that it is small compared to the oven and neglecting natural convection heat transfer.