Heat and Mass Transfer

, Volume 46, Issue 4, pp 463–468

Melting heat transfer in steady laminar flow over a moving surface

  • Anuar Ishak
  • Roslinda Nazar
  • Norfifah Bachok
  • Ioan Pop
Original

DOI: 10.1007/s00231-010-0592-8

Cite this article as:
Ishak, A., Nazar, R., Bachok, N. et al. Heat Mass Transfer (2010) 46: 463. doi:10.1007/s00231-010-0592-8

Abstract

The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel to a constant free stream is studied in this paper. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, moving parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. It is found that the problem admits dual solutions.

List of symbols

Cf

Skin friction coefficient

cp

Specific heat at constant pressure

cs

Solid surface heat capacity

f

Dimensionless stream function

k

Thermal conductivity

M

Melting parameter

Nux

Local Nusselt number

Pr

Prandtl number

qw

Surface heat flux

Rex

Local Reynolds number

T

Fluid temperature

T0

Solid surface temperature

Tm

Melting surface temperature

T

Free stream temperature

u, v

Velocity components along the x and y directions, respectively

Uw

Moving surface velocity

U

Free stream velocity

x, y

Cartesian coordinates along the plate and normal to it, respectively

Greek symbols

α

Thermal diffusivity

ε

Moving parameter

η

Similarity variable

θ

Dimensionless temperature

λ

Fluid latent heat

μ

Dynamic viscosity

ν

Kinematic viscosity

ρ

Fluid density

τw

Wall shear stress

ψ

Stream function

Subscripts

w

At the wall

In the free stream

Superscript

Differentiation with respect to η

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Anuar Ishak
    • 1
  • Roslinda Nazar
    • 1
  • Norfifah Bachok
    • 2
  • Ioan Pop
    • 3
  1. 1.School of Mathematical SciencesUniversiti Kebangsaan MalaysiaUKM BangiMalaysia
  2. 2.Department of Mathematics, Faculty of ScienceUniversiti Putra MalaysiaUPM SerdangMalaysia
  3. 3.Faculty of MathematicsUniversity of ClujClujRomania