### Convective Heat Transfer Convection Equation and Calculator

**Heat Transfer Engineering
Thermodynamics
Convection of Known Surface Area Calculator**

**Convective heat transfer **, often referred to simply as **convection **, is the transfer of heat from one place to another by the movement of fluids . Convection is usually the dominant form of heat transfer in liquids and gases. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes of conduction (heat diffusion) and advection (heat transfer by bulk fluid flow).

The convective heat transfer coefficient (h), defines, in part, the heat transfer due to convection. The convective heat transfer coefficient is sometimes referred to as a film coefficient and represents the thermal resistance of a relatively stagnant layer of fluid between a heat transfer surface and the fluid medium. Common units used to measure the convective heat transfer coefficient are:

- 1 W/(m
^{2}K) = 0.85984 kcal/(h m^{2}° C) = 0.1761 Btu/(ft^{2}h ° F) - 1 kcal/(h m
^{2}° C) = 1.163 W/(m^{2}K) = 0.205 Btu/(ft^{2}h ° F) - Btu/hr - ft
^{2}- °F = 5.678 W/(m^{2}K) = 4.882 kcal/(h m^{2}° C)

Convection involves the transfer of heat by the motion and mixing of "macroscopic" portions of a fluid (that is, the flow of a fluid past a solid boundary). The term natural convection is used if this motion and mixing is caused by density variations resulting from temperature differences within the fluid. The term forced convection is used if this motion and mixing is caused by an outside force, such as a pump. The transfer of heat from a hot water radiator to a room is an example of heat transfer by natural convection. The transfer of heat from the surface of a heat exchanger to the bulk of a fluid being pumped through the heat exchanger is an example of forced convection.

Heat transfer by convection is more difficult to analyze than heat transfer by conduction because no single property of the heat transfer medium, such as thermal conductivity, can be defined to describe the mechanism. Heat transfer by convection varies from situation to situation (upon the fluid flow conditions), and it is frequently coupled with the mode of fluid flow. In practice, analysis of heat transfer by convection is treated empirically (by direct observation).

Convection heat transfer is treated empirically because of the factors that affect the stagnant film thickness:

- Fluid velocity
- Fluid viscosity
- Heat flux
- Surface roughness
- Type of flow (single-phase/two-phase)

Convection involves the transfer of heat between a surface at a given temperature (T_{1}) and fluid at a bulk temperature (T_{b}). The exact definition of the bulk temperature (T_{b}) varies depending on the details of the situation. For flow adjacent to a hot or cold surface, T_{b} is the temperature of the fluid "far" from the surface. For boiling or condensation, T_{b}is the saturation temperature of the fluid. For flow in a pipe, T_{b} is the average temperature measured at a particular crosssection of the pipe.

The basic relationship for heat transfer by convection has the same form as that for heat transfer by conduction:

*Q = h · A · ΔT*

where

Q = rate of heat transfer (Btu/hr)

h = convective heat transfer coefficient (Btu/hr-ft^{2} - °F)

A = surface area for heat transfer (ft^{2})

ΔT = temperature differnece (°F)

or

Q = h_{c} · A · (T_{s} - T_{a})

where

Q = heat transferred per unit time (W)

A = heat transfer area of the surface (m^{2})

h_{c} = convective heat transfer coefficient of the process (W/(m^{2} K) or W/(m^{2} ° C))

T_{s} = Temperature surface

T_{a} = Temperature air

The convective heat transfer coefficient (h) is dependent upon the physical properties of the fluid and the physical situation. Typically, the convective heat transfer coefficient for laminar flow is relatively low compared to the convective heat transfer coefficient for turbulent flow. This is due to turbulent flow having a thinner stagnant fluid film layer on the heat transfer surface. Values of h have been measured and tabulated for the commonly encountered fluids and flow situations occurring during heat transfer by convection.

Example calculations:

A 22 foot uninsulated steam line crosses a room. The outer diameter of the steam line is 18 in. and the outer surface temperature is 280^{o}F. The convective heat transfer coefficient for the air is 18 Btu/hr-ft ^{2} - ^{o}F.

Calculate the heat transfer rate from the pipe into the room if the room temperature is 72 ^{o}F.

Solution

*Q = h · A · ΔT*

Q = h ( 2 *· * π *· * r *· * L ) *ΔT*

*Q = ( 18 Btu / ( hr-ft ^{2}-°F) · 2 · ( 3.14157) · ( 0.75 ft) · ( 22 ft ) · ( 280°F - 72°F) *

*Q = 3.88 x 10 ^{5} Btu/hr *

Many applications involving convective heat transfer take place within pipes, tubes, or some similar cylindrical device. In such circumstances, the surface area of heat transfer normally given in the convection equation ( ) varies as heat passes through the cylinder. In addition, the temperature difference existing between the inside and the outside of the pipe, as well as the temperature differences along the pipe, necessitates the use of some average temperature value in order to analyze the problem. This average temperature difference is called the log mean temperature difference (LMTD), described earlier.

It is the temperature difference at one end of the heat exchanger minus the temperature difference at the other end of the heat exchanger, divided by the natural logarithm of the ratio of these two temperature differences. The above definition for LMTD involves two important assumptions: (1) the fluid specific heats do not vary significantly with temperature, and (2) the convection heat transfer coefficients are relatively constant throughout the heat exchanger.

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