Modes of Heat Transfer: Conduction, Convection and Radiation

Heat Transfer

The heat transfer is defined as the transmission of heat energy from one region to another region as a result of temperature gradient. In actual practice, the heat transfer always takes place from the region of high temperature to the region of low temperature.

Modes of Heat Transfer

The transfer of heat energy from one region to another region takes place by the following three modes −

• Conduction

• Convection

• Radiation

In a majority of real situations, heat transfer occurs as a result of a combination of these modes of heat transfer.

Conduction

When the heat transfers from one part of the substance to another part without the movement in the molecules of the substance, it is called the conduction mode of heat transfer.

In this mode, the rate of heat transfer, i.e., the rate of conduction of heat along the substance depends upon the temperature gradient.

Mathematically, for a cubic body with parallel faces with

$$\mathrm{\mathrm{Thickness\:=}\:\mathit{t}\:\mathrm{meters}}$$

$$\mathrm{\mathrm{Cross\: sectional \:area}\:=\:\mathit{A}\:\mathrm{m^{\mathrm{2}}}}$$

$$\mathrm{\mathrm{Temperature\: of\: two \:faces}\:=\:\mathit{T_{\mathrm{1}}}_{}^{\circ }\textrm{C}\:\mathrm{and}\:\mathit{T_{\mathrm{2}}}_{}^{\circ }\textrm{C}}$$

$$\mathrm{\mathrm{Time\: for\: which\: heat\: transfer\: takes\: palce}\:=\:\mathit{T}\:\mathrm{hours}}$$

Then, the amount of heat passed through this cubic body is given by,

$$\mathrm{\mathit{H}\:=\:\frac{\mathit{kA}}{\mathit{t}}\mathrm{\left( \mathit{T_{\mathrm{1}}-\mathit{T_{\mathrm{2}}}} \right )}\mathit{T}}$$

Where, H is measured in Mega Joules (MJ) and k is the coefficient of the thermal conductivity for the substance and it is measured in $\mathrm{MJ/m^{\mathrm{3}}/_{}^{\circ }\textrm{C}/hr}$.

Examples of heat transfer through the conduction mode are refractory heating, the heating of insulating material, etc.

Convection

When the transfer of heat takes place from one part to another part of the substance or fluid due to the actual motion of the molecules, it is called the convection mode of heat transfer. In this method, the rate of heat transfer depends mainly upon the difference in the fluid density at different temperature.

The transfer of heat energy from immersion water heater to water is an example of convection mode of heat transfer. The amount of heat absorbed by water from the heater through convection partly depends upon the temperature of the heating element and partly upon the position of the heater.

Mathematically, the heat dissipation in convection mode of heat transfer is given by the following expression −

$$\mathrm{\mathit{H}\:=\:\mathit{a}\times \mathrm{\left ( \mathit{T_{\mathrm{1}}}-\mathit{T_{\mathrm{2}}} \right )^{\mathit{b}}}\:\mathrm{W/m^{\mathrm{2}}}}$$

Where,

• 'a' and 'b' are the constants whose values depend upon the heating surface.

• $\mathit{T_{\mathrm{1}}}$ and $\mathit{T_{\mathrm{2}}}$ are the temperatures of heating element and the fluid / substance in °C.

Radiation

When the heat transfer takes place from the source of heat to the substance to be heated without direct contact between them, it is called the radiation mode of heat transfer. The heat transfer through the radiation depends upon the surface. The transfer of heat in case of solar heater is an example of radiation mode of heat transfer.

Mathematically, the rate of heat dissipation through radiation is given by Stefan's law, that is

$$\mathrm{\mathit{H}\:=\:\mathrm{\left ( 5.72\:\times \:10^{\mathrm{4}} \right )}\:\times \:\mathit{ke}\mathrm{\left [ \mathrm{\left (\frac{\mathit{T_{\mathrm{1}}}}{1000}\right )^{\mathrm{4}}} -\mathrm{\left ( \frac{\mathit{T_{\mathrm{2}}}}{1000} \right )^{\mathrm{4}}}\right ]}\:\mathrm{W/m^{\mathrm{2}}}}$$

Where,

• σ = (5.72× 10⁴) is the Stefan's constant

• 'e' is the emissivity (it is 1 for ideal radiator)

• $\mathit{T_{\mathrm{1}}}$ is the temperature of source in Kelvin

• $\mathit{T_{\mathrm{2}}}$ is the temperature of the substance to be heated in Kelvin

• 'k' is the radiant coefficient (it is 1 for single element, 0.5-0.8 for black body, 0.9 for resistance heating element).

Also, from the expression of radiant heating it can be observed that the radiant heat is proportional to the difference of fourth power of temperature. Therefore, the radiant heating is very efficient heating at high temperature.