Abstract
This work shows an approximate analytical solution for the heat transfer problem of transient laminar forced convection valid for the thermal entrance region of a parallel plate duct, with walls interacting with an ambient medium outside the duct. The inlet temperature varies periodically with time and duct wall thermal capacity is considered finite. Periodic solutions, obtained by using Laplace transform, are presented for the duct wall temperature, fluid bulk temperature and wall heat flux as a function of the axial position and of the involved parameters.
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Abbreviations
- A :
-
amplitude
- a*:
-
dimensionless parameter defined by equation (3)
- b*:
-
dimensionless parameter defined by equation (9b)
- c p :
-
fluid specific heat at constant pressure
- c w :
-
wall specific heat
- c*:
-
defined by equation (9a)
- h :
-
heat transfer coefficient
- i :
-
\(\sqrt { - 1}\)
- Im:
-
imaginary part of
- k :
-
thermal conductivity of fluid
- L :
-
half-spacing between plates
- l :
-
wall thickness
- Nu0 :
-
outside Nusselt number
- n :
-
number of terms in the series
- Re:
-
real part of
- s :
-
Laplace transform parameter
- T(x, z, t):
-
fluid temperature
- T 0 :
-
cycle mean temperature
- T ∞ :
-
reference temperature
- t :
-
time
- U :
-
mean velocity
- u :
-
flow velocity
- W(r):
-
function related to error function
- X :
-
dimensionless normal coordinate
- x :
-
normal coordinate
- Z :
-
dimensionless axial coordinate
- z :
-
axial coordinate
- α :
-
thermal diffusivity of fluid
- ΔT 0 :
-
amplitude of inlet oscillations
- θ(X, Z, τ):
-
dimensionless temperature
- ρ :
-
fluid mass density
- ρ w :
-
wall density
- τ:
-
dimensionless time
- ψ(Z):
-
dimensionless periodic part of
- Ω:
-
dimensionless frequency of oscillations
- ω:
-
frequency of oscillations
- b :
-
bulk temperature
- h :
-
heat flux
- w :
-
wall temperature
- ∼:
-
Laplace transform of
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Santos, W.F.N., Travelho, J.S. Transient conjugated forced convection in a parallel plate duct with convection from the ambient and periodic variation of inlet temperature. Appl. Sci. Res. 51, 625–638 (1993). https://doi.org/10.1007/BF00868004
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DOI: https://doi.org/10.1007/BF00868004