**FE 546 Thermal Process Engineering**

# Heat Transfer

Heat Transfer by Convection and Radiation

Heat Transfer by Convection

Convective heat transfer inside containers results either from the natural effects of changes in density in the liquid induced by changes in temperature at the container walls (free or natural convection) or by creating motion in the container contents by axial or end-over-end rotation (forced convection).

# Mechanism of Natural Convection

# The process of natural convection initially involves heat transferred by conduction into the outer layers of fluid adjacent to the heated wall; this results in a decrease in the density, and the heated fluid layer rises.

When it reaches the top of the liquid at the headspace, the induced fluid motion causes it to fall in the central core, the displaced hot fluid at the wall being replaced by colder fluid in the core.

As the temperature of the can contents becomes more uniform and the driving force smaller, the fluid velocity tends to decrease and eventually, when the fluid becomes uniformly heated, the motion ceases. Idealized representation of convection currents in a can of liquid

In the upper part of the container the hot liquid is being pumped by the heated fluid rising in the boundary layer, and being placed on the cold liquid in the core.

Simultaneously, in the case of a vertical container, there is also heat rising from the bottom end of the can, which produces mixing eddies in the bulk of the fluid.

Datta (1985) has shown that as result of instabilities in the temperature distribution, regular bursts of hot liquid occur on the base of the container. This phenomenon is known as Bernard convection.

The mechanism of unsteady-state convection is very complex and varies with time of heating and/or cooling; consequently it is very difficult to model precisely.

Hiddink (1975) used a flow visualizing technique with metallic powders in liquids in containers with light- transmitting walls, to highlight the streamlines in the bulk of the fluid.

Blaisdell (1963), have used thermocouples at several points in the containers to plot the temperature profiles.

Guerrei (1993) has discussed the internal flow patterns in convection-heating bottles of cylindrical and square shape, using the concept of a double-layer system of rising hot liquid on the wall of the container which discharge into a central volume. The point-of- slowest-heating was shown to be 0.006 m from the wall of an 0.06 m internal diameter container.

The most important point, from a practical safety point of view, is where the slowest heating point is situated.

While the discussion has been concerned with convection heating/cooling inside containers, there is also the problem of convection heating on the outside, from the heating or cooling medium to the container wall.

In the case of pure steam heating, condensation of steam on the container wall surface raises the temperature of the surface almost immediately to that of the steam and, consequently, no problem arises.

If, however, the steam contains air, either as an adulterant or intentionally, then the velocity of the mixture over the surface will affect the temperature of the surface and a more complex situation will arise.

Similarly, if water is used for heating, and also for cooling, then the wall temperature will be affected by the velocity of the heat transfer medium.

In all cases, except for condensing pure steam, it is necessary to consider external convective heat transfer to the outer surface of the container.

# Basic Concepts in Convection Heat Transfer

# Mathematical models for the prediction of temperatures in the heating of canned foods by convection are necessary in order to determine the process requirements.

There are three approaches to convective heat transfer:

1) the film theory

2) the use of dimensionless numbers

3) the more rigorous mathematical treatment of the basic fluid dynamic and heat transfer models.

# 1) Film Theory

# The idealized temperature profile for a material being heated by a fluid and separated by a container wall Thus if T1 is the temperature of the heating medium and T4 is the temperature in the bulk of the fluid being heated, and the average film temperatures are T2 and T3, then an overall heat-transfer coefficient U (alternatively denoted by H) can be defined as follows:

# 2) Correlations for Predicting Heat-Transfer Coefficients

# Engineering practice makes use of dimensionless numbers for correlating heat transfer coefficients with the physical circumstances of heat transfer and the physical properties and flow conditions of the fluids involved.

The four dimensionless numbers used in heat transfer studies are:

For forced convection; the correlation is

# 3) Models for Convection Heat Transfer

# Some of the models that have been used to predict temperature distributions and velocity profiles in heated and cooled can liquid products.

The models may be classified as follows:

²Energy Balance Model

This is the simplest of the models.

By equating the overall rate of heat transfer into the

can with the rate of accumulation of heat inside the can, an energy balance equation can be established.

This equation shows that the rate of heating is an exponential function, which depends on the overall heat-transfer coefficient U (or the internal heat-transfer coefficient hint when steam is used as the heating medium with metallic cans), the surface area A, the mass of the contents and their specific heat, as well as the temperature of the heating medium and the initial temperature of the contents T0.

²Effective Thermal Diffusivity Model

This model makes use of the unsteady state

conduction model solutions and an apparent or effective thermal diffusivity.

This depended on the ratio of solids to liquid in the

container.

²Transport Equation Model

This is the most rigorous approach to determining the temperature distributions and the velocity profiles in containers filled with liquids.

The form of the equations depends on the geometry of the container; care should be taken to use the most appropriate coordinate system.

The equations which have to be solved in relation to the container boundaries are the equation of continuity:

# Radiation Heating

# Thermal radiation has a wavelength from 0.8 to 400μm and requires no medium to transmit its energy.

The transfer of energy by radiation involves three processes:

1)the conversion of the thermal energy of a hot source

into electromagnetic waves

2) the passage of the waves from the hot source to the cold receiver

3) the absorption and reconversion of the electromagnetic waves into thermal energy.

The quantity of energy radiated from the surface per unit time is the emissive power E of the surface.

For a perfect radiator, known as a black body, the emissive power is proportional to the fourth power of the temperature T :

The main application for radiation theory is in

relation to can sterilization using gaseous flames. The cooling of cans to the atmosphere also involves loss of heat by radiation as well as convection.

A more complex heat-transfer model for canned foods heated in a flame sterilizer was developed.

6. Radiation exchange only occurs between the flame and the can, and from the can to the surroundings.

7. The temperature of the flame is the adiabatic temperature calculated on the dissociation of the combustion species.

8. The dissociated species do not combine on the can surface.

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