Heat transfer principles between different fluids are similar, even though different
heat transfer rates vary between each other. There are fundamental relationships
between various dimensionless groups that make possible generalizations of the
heat transfer rate between an object and a fluid (Gates 1980). Dimensional analysis
is the method used for deducing dimensionless groups. Equations relating to convective transfer coefficients, hx, can be as follows (e.g., Mimoso 1987; Fox and
McDonald 1985):
h x ¼ f ðj 1 ; j 2 ; j 3 ; . . .. . .; j n Þ
ð 6:27Þ
where the coefficients, j i , are representative of independent factors.
The previous equation can be written as
h x
f ðj 1 ; j 2 ; ::; j n Þ
¼ 1
ð6:28Þ
or:
FðJ 1 ; J 2 ; . . .. . .:; J k Þ ¼ 0
ð6:29Þ
where J 1 , J 2 ,…….,J k (k < n) are sets of independent variables that form groups or
dimensionless numbers. The dimensionless formulations for forced and natural
convection are different, giving compact expressions, valid for any of the independent variables, provided that the quantitative similarity relationships between
these variables are maintained throughout (e.g., Fox and McDonald 1985; Mimoso
1987).
6.2.2 Forced Convection
6.2.2.1 Dimensionless Parameters
Forced convection relates to heat transfer caused by fluid in motion induced by an
external effect. The heat transfer coefficient by forced convection, h c , is a function
of a variable relating to the object, e.g., the characteristic dimension D on a flat plate
(abscissa in Fig. 6.4) or cylinder, or dimensionless variables, linking several object
variables, for example, the ratio between length and width of a flat surface. A set of
five variables related to the fluid are (Gates 1980): flow velocity V a , thermal conductivity k, density q, dynamic viscosity l, and kinematic m, and the specific heat at
constant pressure c p . The three dimensionless groups derived from these variables
are the Nusselt Nu, Reynolds Re, and Prandtl Pr, numbers.
Experimental data can be grouped into dimensionless groups, such as the
Nusselt number, defined as
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6 Heat and Mass Transfer Processes
heat transfer rates vary between each other. There are fundamental relationships
between various dimensionless groups that make possible generalizations of the
heat transfer rate between an object and a fluid (Gates 1980). Dimensional analysis
is the method used for deducing dimensionless groups. Equations relating to convective transfer coefficients, hx, can be as follows (e.g., Mimoso 1987; Fox and
McDonald 1985):
h x ¼ f ðj 1 ; j 2 ; j 3 ; . . .. . .; j n Þ
ð 6:27Þ
where the coefficients, j i , are representative of independent factors.
The previous equation can be written as
h x
f ðj 1 ; j 2 ; ::; j n Þ
¼ 1
ð6:28Þ
or:
FðJ 1 ; J 2 ; . . .. . .:; J k Þ ¼ 0
ð6:29Þ
where J 1 , J 2 ,…….,J k (k < n) are sets of independent variables that form groups or
dimensionless numbers. The dimensionless formulations for forced and natural
convection are different, giving compact expressions, valid for any of the independent variables, provided that the quantitative similarity relationships between
these variables are maintained throughout (e.g., Fox and McDonald 1985; Mimoso
1987).
6.2.2 Forced Convection
6.2.2.1 Dimensionless Parameters
Forced convection relates to heat transfer caused by fluid in motion induced by an
external effect. The heat transfer coefficient by forced convection, h c , is a function
of a variable relating to the object, e.g., the characteristic dimension D on a flat plate
(abscissa in Fig. 6.4) or cylinder, or dimensionless variables, linking several object
variables, for example, the ratio between length and width of a flat surface. A set of
five variables related to the fluid are (Gates 1980): flow velocity V a , thermal conductivity k, density q, dynamic viscosity l, and kinematic m, and the specific heat at
constant pressure c p . The three dimensionless groups derived from these variables
are the Nusselt Nu, Reynolds Re, and Prandtl Pr, numbers.
Experimental data can be grouped into dimensionless groups, such as the
Nusselt number, defined as
172
6 Heat and Mass Transfer Processes