Meccanica

, Volume 43, Issue 1, pp 37–46 | Cite as

Unsteady conjugate problem of a dissipative fluid in a horizontal channel with a periodic variation temperature

Article

Abstract

The unsteady two-dimensional transient heat transfer problem referring to a fully laminar flow developing in a parallel-plane channel exposed to a periodic variation surface temperature with distance is numerically studied. The effects of channel thickness, Péclet number, wall-to-fluid conductivity ratio, thermal diffusivity ratio, angular frequency and the viscous dissipation parameter are determined in the solutions. The non-linear equations are discretized by means an implicit finite difference scheme and the electric analogy to the resulting system is applied to convert these equations into a network-electrical model that was solved using a computer code (electric circuits simulator). In this scheme, only spatial discretization is necessary, while time remains as a real continuous variable, and its programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The network simulation method, which satisfies the conservation law for the heat flux variable and the uniqueness law for temperature, also permits the direct visualization of the local and/or integrated transport variables at any point or section of the medium.

Keywords

Transient heat conduction Conjugate problem Viscous dissipation Network method Heat transfer 

Abbreviations

A

Ratio of diffusivities, α s/α f

B

Dimensionless angular frequency

Br

Brinkman number

ce

Specific heat

C

Capacitor

k

Thermal conductivity

G

Control-voltage current-source

L0

Half distance between the channel walls

L1

Thickness of the pipe

N

Number of cells

Nu

Nusselt number

Pe

Péclet number

q

Heat flux

R

Resistor

t

Time

T

Temperature

u

Velocity

U

Dimensionless velocity

x

Axial co-ordinate

y

Vertical co-ordinate

Greek symbols

α

Diffusivity

β

Angular frequency

ΔT

Oscillation amplitude temperature

ΔX

Axial thickness of the cell

ΔY

Vertical thickness of the cell

Γ

Dimensionless geometric parameter

θ

Dimensionless temperature

μ

Dynamic viscosity

ρ

Density

τ

Dimensionless time

Subscripts

f

Associated to fluid

i, j

Associated with i,j nodal point

i, i−Δ, i

Associated to the centre, left and right position on the cell

m

Medium value

mea

Associated to measurement

s

Associated to solid

w

Solid-fluid interface

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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Engineering Thermal and FluidsUniversity Politechnique of CartagenaCartagenaSpain

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