Heat transfer means heat energy is transferred from a region of higher temperature to a region of lower temperature. It is transferred by three mechanisms: conduction, convection, and radiation. It is unusual for the transfer to take place by one mechanism only.

#### 3 Types of Heat Transfer Process

**Conduction:** It is the most widely studied mechanism of heat transfer and the most significant one in solids. The flow of heat depends on the transfer of vibrational energy from one molecule to another and, in the case of metals, the movement of free electrons with the occurrence of no appreciable displacement of matter. Radiation is rare in solids, but examples are found among glasses and plastics. Convection, by definition, is not possible in these conditions. Conduction in the bulk of fluids is normally overshadowed by convection, but it assumes great importance at fluid boundaries.

**Convection:** The motion of fluids transfers heat between them by convection. In natural convection, the movement is caused by buoyancy forces induced by variations in the density of the fluid, caused by differences in temperature. In forced convection, movement is created by an external energy source, such as a pump.

**Radiation:** All bodies with a temperature above absolute zero radiate heat in the form of electromagnetic waves. Radiation may be transmitted, reflected, or absorbed by matter, the fraction absorbed being transformed into heat. Radiation is of importance at extremes of temperature and in circumstances in which the other modes of heat transmission are suppressed. Although heat losses can, in some cases, equal the losses by natural convection, the mechanism is, from the standpoint of pharmaceutical processing, least important and needs only brief consideration.

Heat transfer in many systems occurs as a steady-state process, and the temperature at any point in the system will not vary with time. In other important processes, temperatures in the system do vary with time. The latter, which is common among the small-scale, batch-operated processes of the pharmaceutical and fine chemicals industry, is known as unsteady heat transfer and, since warming or cooling occurs, the thermal capacity, that is, the size and specific heat, of the system becomes important. Unsteady heat transfer is a complex phenomenon that is difficult to analyze from the first principles at a fundamental level.

#### Heat Transfer between Fluids

The transfer of heat from one fluid to another across a solid boundary is of great importance in pharmaceutical processing. The system, which frequently varies in nature from one process to another, can be divided into constituent parts, and each part is characterized in its resistance to the transfer of heat. The whole system may be considered in terms of the following equation:

#### Heat Transfer through a Wall

Heat transfer by conduction through walls follows the basic relation given by Fourier’s equation in which the rate of heat flow, Q, is proportional to the temperature gradient, dT/dx, and to the area normal to the heat flow, A.

As the distance, x, increases, the temperature, T, decreases. Hence, measuring in the x direction, the temperature gradient, dT/dx, is algebraically negative. The proportionality constant, k, is the thermal conductivity. Its numerical value depends on the material of which the body is made and on its temperature.

Values of thermal conductivity, k, for a number of materials are given in below table –

Steady non-directional heat transfer through a plane wall of thickness x and area A. Assuming that the thermal conductivity does not change with temperature, the temperature gradient will be linear and equal to (T1-T2)/x, where T1 is the temperature of the hot face and T2 is the temperature of the cool face. Equation then becomes -

Where, x/k is the thermal resistance. Thus, for a given heat flow, a large temperature drop must be created if the wall or layer has a high thermal resistance.

#### Heat Transfer in Pipes and Tubes

Pipes and tubes are common barriers over which heat exchange takes place. Conduction is complicated in this case by the changing area over which heat is transferred.

If above equation is to be retained, some value of A must be derived from the length of the pipe, l, and the internal and external radii, r1 and r2, respectively. When the pipe is thin walled and the ratio r2/r1 is less than approximately 1.5, the heat transfer area can be based on an arithmetic mean of the two radii. Above equation then becomes –

#### Heat Exchange between a Fluid and a Solid

Conduction and convection contribute to the transfer of heat from a fluid to a boundary. A film transmitting heat only by conduction may be postulated to evaluate the rate of heat transfer at a boundary. This fictitious film presents the same resistance to heat transfer as the complex turbulent and laminar regions near the wall. If, on the hot side of the wall, the fictitious layer had a thickness x1, the equation of heat transfer to the wall would be –

Where k is the thermal conductivity of the fluid. A similar equation will apply to heat transfer at the cold side of the wall. The thickness of the layer is determined by the same factors that control the extent of the laminar sublayer. In general, it is not known and the equation above may be rewritten as –

Where h1 is the heat transfer coefficient for the film under discussion. It corresponds to the ratio k/x1 and has units J/m2•sec•K. This is a convenient, numerical expression of the flow of heat by conduction and convection at a boundary.

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