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Conjugate heat transfer study comprising the effect of thermal conductivity and irreversibility in a pipe filled with metallic foams

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Abstract

A parametric study is proposed in this paper to examine heat dissipation rate and entropy generation of a forced convection in a horizontal pipe which is filled with high porous metallic foams. The study quantifies the effect of thermal conductivity and pore density on entropy generation when the pipe is fully filled with copper, aluminium and nickel metallic foams of 0.6 m length in the fluid flow direction. To predict fluid flow and heat transfer features through these metallic foams the Darcy-extended Forchheimer (DEF) flow and the local thermal non-equilibrium (LTNE) models are employed. The characteristics of laminar, transition and turbulent in the non-foam region of the pipe are captured by considering the appropriate flow models. To affirm the methodology adopted in this work, the results of the present numerical solutions are validated with the available experimental results reported in the literature. Colburn j factor and thermal performance factor are the important factors that decide the performance and efficiency of any heat exchange device. Hence, these parameters are critically evaluated and are observed to increase with increasing pore densities of the metal foams and decrease with increasing flow rates of the fluid. Furthermore, the numerical analysis is extended to obtain the results of wall temperature, Nusselt number, heat transfer enhancement ratio, frictional irreversibility and Bejan number.

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Abbreviations

A:

Area of the pipe (m2)

u:

Velocity of fluid (m/s)

L:

Length of the pipe (m)

Lf :

Length of the metal foam (m)

T:

Temperature (°C) or (°K)

asf :

Interfacial surface area (m−1)

C:

Form drag coefficient (m−1)

Cp :

Specific heat of fluid (J/kg K)

dp :

Pore diameter (m)

df :

Fiber diameter (m)

f:

Friction coefficient

h:

Heat transfer coefficient (W/m2°C)

hsf :

Interfacial heat transfer coefficient (W/m2°C)

K:

Permeability (m2)

Pr:

Prandtl number

Re:

Reynolds number based on hydraulic diameter

q”:

heat flux (W/m2)

\( {\operatorname{Re}}_{{\mathrm{d}}_{\mathrm{f}}} \) :

Reynolds number based on fiber diameter

D:

Diameter of the pipe (m)

Dh :

Hydraulic diameter of the pipe (m)

λ:

Thermal conductivity (W/m°C)

P:

Perimeter of the pipe (m)

\( \overline{\mathrm{Nu}} \) :

Average Nusselt number filled foam pipe

\( \overline{{\mathrm{Nu}}_{\Phi}} \) :

Average Nusselt number of empty pipe

NuER :

Heat transfer enhancement ratio

ɛ:

Porosity

λ:

Thermal conductivity (W/m°C)

μ:

Dynamic viscosity of the fluid (Ns/m2)

ν:

Kinematic viscosity (m2/s)

ρ:

Density of the fluid (kg/m3)

i:

Each data points/Local data points

ER :

Enhancement ratio

w:

Wall

f:

Fluid

eff:

Effective

s:

Solid

se:

Solid effective

fe:

Fluid effective

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Karnataka, Surathkal, 575025, India

    Prakash H. Jadhav, Gnanasekaran Nagarajan & D. Arumuga Perumal

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Correspondence to Gnanasekaran Nagarajan.

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Jadhav, P.H., Nagarajan, G. & Perumal, D.A. Conjugate heat transfer study comprising the effect of thermal conductivity and irreversibility in a pipe filled with metallic foams. Heat Mass Transfer 57, 911–930 (2021). https://doi.org/10.1007/s00231-020-03000-x

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