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Energy storage in fluid saturated porous media subjected to oscillatory flow

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Abstract

Transient thermal effects in a porous medium subjected to oscillatory flow of hot and cold fluid are studied. The governing equations of thermal non-equilibrium model have been numerically solved by a finite difference scheme. The amplitude of temperature fluctuation, a parameter relating to the energy storage, is seen to vary significantly with distance and time. The storage of energy is largely governed by fluid to solid phase thermal storage capacity ratio. Effects arising from changes in bed parameters are discussed.

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Abbreviations

A IF :

specific area of the porous insert (m−1)

A f :

non-dimensional value of A if : A IF× R

Bi :

Biot number (h R(ks)−1)

C p :

specific heat (J(kg K)−1)

d p :

particle diameter (m)

E :

energy (J)

h sf :

heat transfer coefficient at the particle surface (Wm−2 K−1)

K :

thermal conductivity (W (m K)−1)

K :

weighted ratio of thermal storage capacities of the fluid and solid phase, \( \frac{{\left( {1 - \varepsilon } \right)\left( {\rho c_{\text{p}} } \right)_{\text{s}} }}{{\left( \varepsilon \right)\left( {\rho c_{\text{p}} } \right)_{\text{f}} }} = \frac{1 - \varepsilon }{\varepsilon \beta } \)

(k eff,f ) r :

effective thermal conductivity of the fluid in r-direction (W (m K)−1)

(k eff,f ) z /k f :

dispersion coefficient of fluid in z-direction

L :

length of porous domain scaled by R

N :

cycle number

Nu :

Nusselt number, hR/k

Pe :

Peclet number, Re × Pr

Q :

interphase heat transfer

Pr :

Prandtl number (μCp/k)

R :

non-dimensional radial coordinate

Re :

Reynolds number (ρUR/μ)

REV:

representative elementary volume

T :

time, non-dimensionalized by α f /R2

t p :

time period of oscillations (s)

R :

characteristic length scale, m also the pipe radius

T :

non-dimensional temperature: (T− T C )/ΔT

ΔT :

reference temperature difference (T H − T C )

U :

non-dimensional axial velocity scaled with U

U :

characteristic fluid velocity equal to the average velocity in the tube (ms−1)

α:

thermal diffusivity (m2 s−1)

β:

thermal capacity ratio between the fluid and the solid phases

ε:

porosity of the medium

λ:

thermal conductivity ratio between the fluid and the solid phases

μ:

dynamic viscosity of the fluid (kg (m s)−1)

ν:

kinematic viscosity of the fluid (m2 s−1)

ρ:

material density (kg m−3)

ω:

frequency of oscillations, 2π/t p (rad/s)

ωt:

phase angle (radians)

A:

ambient conditions

C:

cold water temperature (K)

D:

particle diameter

F:

fluid phase

H:

hot water temperature (K)

M:

porous medium

ND:

non-dimensional quantity

S:

solid phase

P:

time-period

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Authors and Affiliations

  1. Mechanical Engineering Department, University College of Engineering, Punjabi University, Patiala, 147002, India

    Chanpreet Singh

  2. Lala Lajpat Rai Institute of Engineering and Technology, Moga, 142001, India

    R. G. Tathgir

  3. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, 208016, India

    K. Muralidhar

Authors
  1. Chanpreet Singh
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  2. R. G. Tathgir
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  3. K. Muralidhar
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Correspondence to Chanpreet Singh.

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Singh, C., Tathgir, R.G. & Muralidhar, K. Energy storage in fluid saturated porous media subjected to oscillatory flow. Heat Mass Transfer 45, 427–441 (2009). https://doi.org/10.1007/s00231-008-0435-z

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  • DOI: https://doi.org/10.1007/s00231-008-0435-z

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