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Energetic and entropic analyses of double-diffusive, forced convection heat and mass transfer in microreactors assisted with nanofluid

  • David G. P. Guthrie
  • Mohsen Torabi
  • Nader Karimi
Article
  • 5 Downloads

Abstract

This paper investigates the energetic and entropic characteristics of a microchannel with thick walls. A first-order, catalytic chemical reaction is imposed on the inner surfaces of the microchannel walls, and local thermal non-equilibrium approach is employed to analyse heat transfer within the porous section of the microchannel. Further, endo-/exothermic physicochemical processes are incorporated into the fluid phase and solid structure of the microchannel. Two models describing the fluid–porous interface conditions known as Models A and B are incorporated. It is shown that for both interface models, and with the considered parametric values, the optimum thickness of the porous insert to achieve the maximum Nu is around 0.6. However, when PEC is considered, this optimum thickness may vary between 0 and 0.5. It is further shown that depending on the specification of the microreactor, either Model A or B may result in the prediction of the minimum total entropy generation rate. It is also demonstrated that by altering the endothermicity of the microreactor it is possible to find an optimal value, which minimizes the total rate of entropy generation.

Keywords

Microreactor Catalytic reactions Porous material Entropy generation Local thermal non-equilibrium Performance evaluation criterion 

List of symbols

\(a_{\text{sf}}\)

Interfacial area per unit volume of porous media (m−1)

\(Bi\)

Biot number

\(C_{1} ,C_{2}\)

Concentration of the chemical products per unit volume \(\left( {{\text{kg}}\,{\text{m}}^{ - 3} } \right)\)

\(c_{{{\text{p}},{\text{nf}}}}\)

Specific heat of the fluid phase of the porous medium \(\left( {{\text{J}}\,{\text{kg}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

\(D_{1} , D_{2}\)

Diffusion coefficient \(\left( {{\text{m}}^{2} \,{\text{s}}^{ - 1} } \right)\)

\(Da\)

Darcy number

\(D_{{{\text{T}}_{1} }} , D_{{{\text{T}}_{2} }}\)

Thermodiffusion coefficient \(\left( {{\text{m}}^{2} \,{\text{s}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

\(h_{1}\)

Half-thickness of the microchannel \(( {\text{m)}}\)

\(h_{0}\)

Height of the inner boundary of the upper wall \(( {\text{m)}}\)

\(h_{\text{p}}\)

Half-thickness of the porous insert \(({\text{m}})\)

\(h_{\text{sf}}\)

Internal heat convection coefficient \(\left( {{\text{W}}\,{\text{m}}^{ - 2} \,{\text{K}}^{ - 1} } \right)\)

k

Solid-to-fluid effective thermal conductivity ratio

k1

Thermal conductivity of solid walls \(\left( {{\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

\(k_{{1{\text{s}}}}\)

Ratio of the porous solid phase to solid wall thermal conductivities

\(k_{{{\text{e}},{\text{f}}}}\)

Effective thermal conductivity of the fluid phase of the porous medium \(\left( {{\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

\(k_{{{\text{e}},{\text{s}}}}\)

Effective thermal conductivity of the solid phase of the porous medium \(\left( {{\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

kf

Thermal conductivity of the base fluid \(\left( {{\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

knf

Thermal conductivity of the nanofluid \(\left( {{\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

kp

Thermal conductivity of the nanoparticles \(\left( {{\text{W}}\,{\text{m}}^{ - 1} \,{\text{K}}^{ - 1} } \right)\)

\(k_{\text{d}}\)

Reaction kinetic constant \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)

Nu

Nusselt number

\(N_{\text{s}}\)

Dimensionless local entropy generation rate

\(N_{\text{t}}\)

Dimensionless total entropy generation rate

p

Pressure (Pa)

\(Q_{1}\)

Dimensionless volumetric internal heat generation rate for the solid walls

\(\dot{q}_{1}\)

Volumetric internal heat generation rate for the solid wall \(\left( {{\text{W}}\,{\text{m}}^{ - 3} } \right)\)

\(S_{\text{s}}\)

Volumetric internal heat generation rate for the solid phase of the porous medium \(\left( {{\text{W}}\,{\text{m}}^{ - 3} } \right)\)

\(S_{\text{nf}}\)

Volumetric internal heat generation rate for the nanofluid phase \(\left( {{\text{W}}\,{\text{m}}^{ - 3} } \right)\)

\(S^{{{\prime \prime }\prime }}\)

Local entropy generation rate \(\left( {{\text{W}}\,{\text{K}}^{ - 1} \,{\text{m}}^{ - 3} } \right)\)

\(Sr_{1} , Sr_{2}\)

Soret number

\(T_{1}\)

Temperature of the walls \(( {\text{K)}}\)

\(T_{{{\text{nf}}_{1} }} , T_{{{\text{nf}}_{2} }}\)

Temperature of the nanofluid \(( {\text{K)}}\)

\(T_{\text{s}}\)

Temperature of the solid phase of the porous medium \(( {\text{K)}}\)

\(\bar{U}\)

Average dimensionless velocity

\(u_{\text{p}}\)

Velocity of the nanofluid in porous medium \(\left( {{\text{m}}\,{\text{s}}^{ - 1} } \right)\)

\(U_{\text{p}} , U_{\text{nf}}\)

Dimensionless velocity

\(Y_{0}\)

Dimensionless height of the inner boundary of the upper wall

Y1

Dimensionless half-thickness of the microchannel

\(Y_{\text{p}}\)

Dimensionless half-thickness of the porous insert

Greek symbols

\(\lambda\)

Damköhler number

ϵ

Porosity

\(\theta_{1}\)

Dimensionless temperature of the solid walls

\(\theta_{\text{nf}}\)

Dimensionless temperature of the nanofluid phase

\(\theta_{\text{m}}\)

Dimensionless average temperature of the nanofluid phase

\(\theta_{\text{s}}\)

Dimensionless temperature of the solid phase of the porous medium

\(\kappa\)

Permeability \(\left( {{\text{m}}^{2} } \right)\)

\(\mu_{{{\text{e}},{\text{nf}}}}\)

Dynamic viscosity of porous medium \(\left( {{\text{kg}}\,{\text{s}}^{ - 1} \,{\text{m}}^{ - 1} } \right)\)

\(\mu_{\text{f}}\)

Dynamic viscosity of the base fluid \(\left( {{\text{kg}}\,{\text{s}}^{ - 1} \,{\text{m}}^{ - 1} } \right)\)

\(\mu_{\text{nf}}\)

Dynamic viscosity of the nanofluid \(\left( {{\text{kg}}\,{\text{s}}^{ - 1} \,{\text{m}}^{ - 1} } \right)\)

\(\omega_{\text{s}}\)

Dimensionless volumetric internal heat generation rate for the solid phase of the porous medium

\(\omega_{\text{nf}}\)

Dimensionless volumetric internal heat generation rate for the nanofluid phase

\(\rho_{\text{nf}}\)

Density of the nanofluid phase \(\left( {{\text{kg}}\,{\text{m}}^{ - 3} } \right)\)

\(\varPhi_{1}, \varPhi_{2}\)

Dimensionless concentration

\(\psi_{1}, \psi_{2}\)

Dimensionless parameters associated with concentration used in entropy generation equation

\(\tau\)

Dimensionless parameters associated with temperature used in entropy generation equation

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.School of EngineeringUniversity of GlasgowGlasgowUK
  2. 2.School of EngineeringUniversity of CaliforniaMercedUSA
  3. 3.Civil and Mechanical Engineering DepartmentUniversity of Missouri-Kansas CityKansas CityUSA

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