Acta Mechanica Sinica

, Volume 27, Issue 3, pp 389–398

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

  • Joaquín Zueco
  • O. Anwar Bég
  • L. M. López-Ochoa
Research Paper

DOI: 10.1007/s10409-011-0461-9

Cite this article as:
Zueco, J., Anwar Bég, O. & López-Ochoa, L.M. Acta Mech Sin (2011) 27: 389. doi:10.1007/s10409-011-0461-9

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.

Keywords

Thermophoresis MHD Network simulation model Heat and mass transfer Hartmann number 

Nomenclature

B

Magnetic field strength

Cw

Wall species concentration

cp

Specific heat capacity of the fluid

C

Concentration at the free stream

C1, C2, C3

Empirical constants

Cc

Cunningham coefficient

Cm

Momentum exchange coefficient

Cs

Temperature creeping coefficient

Ct

Temperature jump coefficient

D

Species (mass) diffusivity

Ec

Eckert number

f

Dimensionless stream function

f0

Dimensionless wall transpiration velocity

g

Acceleration due to gravity

Ha

Hartmann number

j

Electrical current (in the network model)

k

Thermophoretic coefficient

kf

Thermal conductivity of the fluid

kv

Thermophoretic diffusivity

Kn

Knudsen number

l

Mean free path of the particles

Lc

Characteristic length of the flow field

N

Number of cells

Pr

Prandtl number

Qo

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

Vo

Transpiration velocity at the wall

VT

Thermophoretic velocity

x

Axial coordinate

y

Coordinate normal to the plate

Greek symbols

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

λp

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

Δt

Time-step

Δη

Spatial discretization

ϕ

Non-dimensional concentration

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Joaquín Zueco
    • 1
  • O. Anwar Bég
    • 2
  • L. M. López-Ochoa
    • 3
  1. 1.Thermal Engineering and Fluids DepartmentTechnical University of Cartagena, ETSII Campus Muralla del MarCartagenaSpain
  2. 2.Aerospace Engineering, Department of Engineering and MathematicsSheffield Hallam UniversitySheffieldUK
  3. 3.Mechanical Engineering DepartamentUniversity of RiojaLogroño (La Rioja), 20Spain