Introduction
In the previous lesson, we looked at ‘Thermal Conduction’, which is the transfer of heat energy through a body by means of high energy particles colliding and imparting kinetic energy on their neighbouring lower energy particles.
In this lesson we shall be considering ‘Convection’, the process in which heat flows from a solid to its surrounding fluid environment. Heat energy is transferred from the solid to the fluid at the boundary and then is removed from the boundary area via mass transfer (i.e. the motion of the fluid).
The rate of heat transfer is contingent both on the condition at the boundary (e.g.: the roughness or shape) and on the properties of the fluid itself (e.g.: density, viscosity or velocity).
Commonly these fluid properties are mathematically captured by the Convective Heat Transfer Coefficient (h).
Newton’s Law of Cooling
A simple model of convection is given by Newton’s Law of Cooling which states that the heat flux between two mediums is proportional to difference in temperature - the constant of proportionality in this case being the Convective Heat Transfer Coefficient (h):
eq.(10)
Where Tfl is the ambient fluid temperature and T0 is the solid surface temperature.
Remembering that flux is the rate of heat transfer by unit area (f = q/A) and assuming that the heat transfer across a given surface of area ‘A’ is constant, this relationship can also be described in terms of the rate of heat transfer (q):
Typical Values of the Coefficient of Convection
Eq. (10) tells us that systems with a large value of ‘h’ (Coefficient of Convection) result in a larger rate of heat transfer for a given temperature differential than those with a low value of ‘h’. As this coefficient captures many properties of the boundary relationship, it is often impractical to state typical values of ‘h’ for a standardised system.
The coefficient can also be manually increased by modifying the conditions of the fluid surroundings, for example by increasing ventilation and using a fan to increase the airflow over a hot surface. In practice ‘h’ is often measured experimentally for a given cooling system. However, for the purposes of these lessons, some typical values for ‘h’ are provided below:
Description |
Coefficient of Convection (W/m2 K) |
Free convection, vertical surface in air |
1 – 20 |
Forced Convection, low speed air over surface |
10 – 500 |
Forced Convection, mod speed air over surface |
300 – 1000 |
Forced Convection, water flowing in a pipe |
1000 - 10000 |
Table 3: Typical values of ‘h’
Example 4
A house has a glass window through which heat is lost to the outside world. The following system conditions apply:
Window Dimensions - width: 2 m, height: 1 m, thickness ‘d’: 4 mm.
Thermal Conductivity of Glass ‘k’: 0.8 W/m K.
The convective heat transfer coefficients are 5 W/m2 K for the internal surface and 150 W/m2 K for the external surface.
Internal ambient temperature ‘Tin’ is 20 °C and external ‘Tout’ is 10 °C.
Assume the walls are perfectly insulated and no heat energy is stored or generated within the window pane.
- What is the rate of heat loss through the window?
- What are the temperatures (‘T1’ and ‘T2’) on the inside and outside surfaces of the window respectively?
What is the rate of heat loss through the window?
To answer this question, we must consider the various stages of heat transfer through the window:
- Heat transfer from the internal ambient air to the window pane (Convection).
- Heat transfer through the window pane (Conduction).
- Heat transfer through the window pane (Conduction).
A key consideration is that in the absence of heat storage/generation, these three rates of heat transfer are equal.
Rearranging the three equations on the previous slide in terms of temperatures, we get:
Adding these equations we can eliminate the unknown temperatures on the window pane surfaces (T1 and T2):
Solving for the rate of heat transfer ‘q’ gives:
What are the temperatures (‘T1’ and ‘T2’) on the inside and outside surfaces of the window respectively?
To answer this question, we can use the same formulae previously considered:
Example 5
Consider the wall adjacent to the window. In this case, the wall is made of 400 mm thick breeze block and has a Thermal Conductivity of ‘k’: 0.2 W/m K.
Assume that the environmental conditions are as per Example 4:
hin: 5 W/m2 K |
Tin: 20 °C |
hout: 150 W/m2 K |
Tout: 10 °C |
- What is the rate of heat loss through the breeze block wall?
- What are the temperatures (‘T1’ and ‘T2’) on the inside and outside surfaces of the wall?
a) What is the rate of heat loss through the breeze block wall?
b) What are the temperatures (‘T1’ and ‘T2’) on the inside and outside surfaces of the wall?
Comparing Examples 4 and 5, it is clear that the rate of heat loss through the wall is less than the rate of heat loss through the pane of glass. Double glazing acts by encapsulating an airgap within the window between two panes of glass to raise the thermal resistivity of the window.
References
Annaratone D. (2010) Steady Conduction (pp 13-27). In: Engineering Heat Transfer. Springer, Berlin, Heidelberg. 30 October 2009. Available as an EBOOK in the UHI library.