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Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

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Abstract

Network simulation method (NSM) is used to solve the laminar heat and mass transfer of an electrically-conducting, heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable, η. The resulting coupled, nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters, viz Prandtl number, thermophoretic coefficient (a function of Knudsen number), thermal conductivity parameter, wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication, aerosol filter precipitators, particle deposition on hydronautical blades, semiconductor wafer design, thermo-electronics and problems including nuclear reactor safety.

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Abbreviations

B :

Magnetic field strength

C w :

Wall species concentration

c p :

Specific heat capacity of the fluid

C ∞ :

Concentration at the free stream

C1, C2, C3:

Empirical constants

C c :

Cunningham coefficient

C m :

Momentum exchange coefficient

C s :

Temperature creeping coefficient

C t :

Temperature jump coefficient

D :

Species (mass) diffusivity

Ec :

Eckert number

f :

Dimensionless stream function

f 0 :

Dimensionless wall transpiration velocity

g :

Acceleration due to gravity

Ha :

Hartmann number

j :

Electrical current (in the network model)

k :

Thermophoretic coefficient

k f :

Thermal conductivity of the fluid

k v :

Thermophoretic diffusivity

Kn :

Knudsen number

l :

Mean free path of the particles

L c :

Characteristic length of the flow field

N :

Number of cells

Pr :

Prandtl number

Q o :

Heat source/sink parameter

Sc :

Schmidt number

T :

Fluid temperature

T ∞ :

Free stream temperature

u :

x-direction (axial) fluid velocity

u ∞ :

Free stream velocity

ν :

y-direction fluid velocity

V o :

Transpiration velocity at the wall

V T :

Thermophoretic velocity

x :

Axial coordinate

y :

Coordinate normal to the plate

α :

Thermophysical constant dependent on the fluid

β :

Thermal conductivity variation parameter

ν :

Kinematic fluid viscosity

ψ :

Dimensionless stream function parameter

ξ :

Dimensionless axial coordinate

η :

Dimensionless radial coordinate

θ :

Dimensionless temperature

λ p :

Thermal conductivity of the diffused particles

µ:

Dynamic viscosity of the fluid

ρ :

Density

σ :

Electrical conductivity

τ :

Dimensionless thermophoretic parameter

Δ :

Non-dimensional heat source/sink coefficient

Δ t :

Time-step

Δη :

Spatial discretization

ϕ :

Non-dimensional concentration

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Author information

Authors and Affiliations

  1. Thermal Engineering and Fluids Department, Technical University of Cartagena, ETSII Campus Muralla del Mar, Cartagena, 30202, Spain

    Joaquín Zueco

  2. Aerospace Engineering, Department of Engineering and Mathematics, Sheffield Hallam University, Sheaf Building, Sheffield, S1 1WB, UK

    O. Anwar Bég

  3. Mechanical Engineering Departament, University of Rioja, C/Luís de Ulloa, Logroño (La Rioja), 20, E-26004, Spain

    L. M. López-Ochoa

Authors
  1. Joaquín Zueco
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  2. O. Anwar Bég
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  3. L. M. López-Ochoa
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Correspondence to Joaquín Zueco.

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Zueco, J., Anwar Bég, O. & López-Ochoa, L.M. Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer. Acta Mech Sin 27, 389–398 (2011). https://doi.org/10.1007/s10409-011-0461-9

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  • DOI: https://doi.org/10.1007/s10409-011-0461-9

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