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The hybrid method, a new method for accurate heat transfer predictions in channels with axially variable heat flux

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Abstract

A new computation method is presented for the accurate determination of temperature fields and heat transfer characteristics for steady forced convection flow in coolant channels with an arbitrary prescribed wall heat flux. The essential feature of this method is that the fluid region is discretized in the section normal to the flow direction. Energy balances set up for each of the elements yield a system of linear first order differential equations with as a sole independent variable an axial distance parameter. This system of equations is solved analytically using a matrix method. The method is illustrated for the case of laminar flow in flat and circular ducts.

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Abbreviations

a :

thermal diffusivity, λ c/ρc p.

[A]:

symmetric tridiagonal matrix of dimensionless transport coefficients, eqs. (19–21)

c p :

specific heat

D :

dimensionless transport coefficient, eq. (16)

d e :

equivalent hydraulic diameter

d e·t :

equivalent thermal diameter

G i :

elementary mass flow rate in an element i

G t :

total mass flow rate

GR i :

reduced elementary mass flow rate, eq. (15)

H :

fluid enthalpy

ΔH :

total fluid enthalpy rise over length of channel

HR i :

dimensionless fluid enthalpy, eq. (10)

L :

heated channel length

N :

number of fluid elements in discretization procedure

Nu :

local Nusselt number, αd e/λ, dimensionless

Pe :

Peclet number, d e u b/a, dimensionless

Q :

heat flow per unit of length

QR i :

dimensionless heat generation term, eq. (17)

q′ :

heat generation per unit of length

q″ :

local heat flux

s i·j :

lateral extent of boundary between adjacent fluid elements i and j

T :

temperature

u :

axial velocity

[VE]:

eigenvector matrix

x :

axial distance coordinate

X :

dimensionless axial distance x/L

y :

wall distance

y 0 :

distance between wall and symmetry line

Δy i :

width of grid element

α :

heat transfer coefficient, eq. (47)

β i·j :

local transport coefficient, eq. (4)

γ i :

eigenvalue, dimensionless

λ :

thermal conductivity of fluid

ρ :

fluid density

av:

averaged over heated channel length

b:

bulk

c:

channel centre, or adiabatic wall

i :

number of fluid element

in:

inlet

w:

wall

x :

axial position

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Authors and Affiliations

  1. Technology Div. Joint Research Centre, EURATOM, Ispra (Va.), Italy

    R. Nijsing & W. Eifler

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  1. R. Nijsing
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  2. W. Eifler
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Nijsing, R., Eifler, W. The hybrid method, a new method for accurate heat transfer predictions in channels with axially variable heat flux. Appl. Sci. Res. 28, 401–418 (1973). https://doi.org/10.1007/BF00413080

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  • DOI: https://doi.org/10.1007/BF00413080

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