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Unsteady forced convection heat/mass transfer from a flat plate

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Abstract

Numerical methods are used to investigate the transient, forced convection heat/mass transfer from a finite flat plate to a steady stream of viscous, incompressible fluid. The temperature/concentration inside the plate is considered uniform. The heat/mass balance equations were solved in elliptic cylindrical coordinates by a finite difference implicit ADI method. These solutions span the parameter ranges 10≤ Re ≤ 400 and 0.1 ≤ Pr ≤ 10. The computations were focused on the influence of the product (aspect ratio) × (volume heat capacity ratio/Henry number) on the heat/mass transfer rate. The occurrence on the plate’s surface of heat/mass wake phenomena was also studied.

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Abbreviations

c P :

Heat capacity

C :

Concentration of the transferring species

D :

Diffusion coefficient of the transferring species in the fluid phase

L :

Plate length

Pr :

Fluid phase Prandtl (Schmidt) number, Pr = ν/α (D)

Re :

Reynolds number based on plate length, Re = U∞ L/ν

t :

Time

T :

Temperature

x :

Streamwise (horizontal) coordinate

X :

Non-dimensional streamwise coordinate, X = x/L

y :

Transverse (vertical) coordinate

Y :

Non-dimensional transverse coordinate, Y = y/L

Z :

Dimensionless temperature/concentration defined by the relations, \( Z_{{({\text{p}})}} = \frac{{T_{{({\text{p}})}} - T_{\infty } }} {{T_{{{\text{p}},0}} - T_{\infty } }}\quad {\text{or}}\quad Z_{{\text{p}}} = \frac{{C_{{\text{p}}} - C_{\infty } \,\Xi }} {{C_{{{\text{p}},0}} - C_{\infty } \,\Xi }},\quad \quad Z = \frac{{C - C_{\infty } }} {{C_{{{\text{p}},0}} /\Xi - C_{\infty } }} \)

α:

Thermal diffusivity of the fluid phase

ɛ:

Aspect ratio

η:

Elliptical cylindrical coordinate defined by Eq. 1

ν:

Kinematic viscosity of the fluid phase

ρ:

Density

τ:

Dimensionless time or Fourier number, τ = 4 t α (D)/ L2

ω:

Dimensionless vorticity

ξ:

Elliptical cylindrical coordinate defined by Eq. 1

ψ:

Dimensionless stream function

Ξ:

(ρ p c P , p )/(ρ c c P c ) or Henry number

c:

Refers to the continuous (fluid) phase

p :

Refers to plate

0:

Initial conditions

∞:

Large distance from the plate

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  1. Catedra Inginerie Chimica, Politehnica University Bucharest, Polizu 1, 78126, Bucharest, Romania

    Gh. Juncu

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Juncu, G. Unsteady forced convection heat/mass transfer from a flat plate. Heat Mass Transfer 41, 1095–1102 (2005). https://doi.org/10.1007/s00231-005-0641-x

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