Handbook of air conditioning and refrigeration / Shan K

3.4 CHAPTER THREE
Convective Heat Transfer
kA,kB,kC � thermal conductivity of layers A, B, and C, respectively, of composite wall,
Btu/h�ft�°F (W/m�°C)
Eliminating T2 and T3, we have
T1 � T4 qk �
(3.3)
LA /(k A A) � LB /(k B A) � LC /(k C A)
For a multilayer composite wall of n layers in perfect thermal contact, the rate of conduction heat
transfer is given as
T1 � Tn�1 qk �
(3.4)
L1/(k 1 A) � L2 /(k 2 A) � � � � � Ln /(k n A)
Subscript n indicates the nth layer of the composite wall.
In Eq. (3.2), conduction heat transfer of any of the layers can be written as
R* � L
k A �T
qk � �T �
L R*
k A
where R* � thermal resistance, h�°F/Btu (°C/W). In Eq. (3.5), an analogy can be seen between
heat flow and Ohm’s law for an electric circuit. Here the temperature difference �T � T 1 � T 2 indicates
thermal potential, analogous to electric potential. Thermal resistance R* is analogous to electric
resistance, and heat flow q k is analogous to electric current.
The total conductive thermal resistance of a composite wall of n layers R T,h�°F/Btu (°C/W),
can be calculated as
R* T � R* 1 � R* 2 � � � � � R* n
where R* 1 , R* 2 , � � � R* n � thermal resistances of layers 1, 2, ���, n layer of the composite wall,
h�°F/Btu (°C/W). The thermal circuit of a composite wall of three layers is shown in the lower
part of Fig. 3.1.
Convective heat transfer occurs when a fluid comes in contact with a surface at a different temperature,
such as the heat transfer taking place between the airstream in a duct and the duct wall.
Convective heat transfer can be divided into two types: forced convection and natural or free
convection. When a fluid is forced to move along the surface by an outside motive force, heat is
transferred by forced convection. When the motion of the fluid is caused by the density difference
of the two streams in the fluid as a product of contacting a surface at a different temperature, the
result is called natural or free convection.
The rate of convective heat transfer q c, Btu/h (W), can be expressed in the form of Newton’s
law of cooling as
(3.5)
(3.6)
q c � h cA(T s � T �) (3.7)
where h c � average convective heat-transfer coefficient, Btu/h�ft 2 �°F (W/m 2 �°C)
T s � surface temperature, °F (°C)
T � � temperature of fluid away from surface, °F (°C)
In Eq. (3.7), the convective heat-transfer coefficient h c is usually determined empirically. It is
related to a dimensionless group of fluid properties, such as the correlation of flat-plate forced