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Transient conjugated heat transfer in thick walled pipes with axially periodic surface temperature in downstream region

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Abstract

Thermal entrance region transient conjugate heat transfer is investigated involving fluid axial heat conduction for laminar pipe flows. Constant outer wall temperature boundary condition is assumed in the upstream region of a thick walled, two regional pipe. In the downstream region, the outer wall temperature is considered changing spatially in a periodical manner. The problem is solved numerically by a finite difference method. A parametric analysis is conducted in order to determine the effects of Peclet number, wall thickness ratio, wall-to-fluid thermal conductivity ratio, wall-to-fluid thermal diffusivity ratio and axial frequency on heat transfer characteristics. It is seen that, the results are highly dependent on the parameter values and the most effective ones are the Peclet number and the wall thickness ratio. It is observed that heat is transferred towards upstream due to the axial conduction in the wall and in the fluid and with increasing values for high axial frequency.

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Abbreviations

a :

constant of discretization equation (Eq. 5)

B :

dimensionless frequency

c p :

specific heat at constant pressure, (kJ/kg·K)

d :

thickness of the pipe wall, (m)

F :

Factor

Fo :

Fourier number

Gz :

Graetz number

h :

the distance between nodes (Eq. 9), (m)

k :

thermal conductivity, (W/m·K)

n :

total number of the nodes

p :

order of computational method

Pe :

Peclet number

q :

heat flux, (W/m2·K)

r :

radial coordinate, ratio of the distance between nodes or grid refinement ratio (Eq. 9)

Re :

Reynolds number

t :

time, (s)

T :

temperature, (K)

T o :

initial temperature of the system, (K)

u :

axial velocity, (m/s)

x :

axial coordinate, (m)

α :

thermal diffusivity, (m2/s)

β :

frequency, (Hz)

δr :

radial position difference, (m)

δx :

axial position difference, (m)

Δr :

radial step size, (m)

Δt :

time step increment, (s)

ΔT :

amplitude of periodic temperature variation, (K)

Δx :

axial step size, (m)

ε :

relative error

φ :

global variable for the RMS calculation

ρ :

density, (kg/m3)

b :

bulk

c :

coarse

f :

fluid, fine

i :

inner wall

i, j:

at nodal point i, j

m:

mean

max:

maximum

o:

outer wall

s :

safety

w :

wall

wf :

ratio of wall to fluid

wi :

wall to fluid interface

* :

dimensionless quantity

0 :

at previous time step

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Authors and Affiliations

  1. Ilgın Vocational School, Selcuk University, Konya, Turkey

    Ali Ateş

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Ateş, A. Transient conjugated heat transfer in thick walled pipes with axially periodic surface temperature in downstream region. Sādhanā 44, 82 (2019). https://doi.org/10.1007/s12046-019-1079-z

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