# Melting heat transfer in steady laminar flow over a moving surface

- First Online:

- Received:
- Accepted:

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

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## 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

*C*_{f}Skin friction coefficient

*c*_{p}Specific heat at constant pressure

*c*_{s}Solid surface heat capacity

*f*Dimensionless stream function

*k*Thermal conductivity

*M*Melting parameter

*Nu*_{x}Local Nusselt number

*Pr*Prandtl number

*q*_{w}Surface heat flux

*Re*_{x}Local Reynolds number

*T*Fluid temperature

*T*_{0}Solid surface temperature

*T*_{m}Melting surface temperature

*T*_{∞}Free stream temperature

*u*,*v*Velocity components along the

*x*and*y*directions, respectively*U*_{w}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

*τ*_{w}Wall shear stress

*ψ*Stream function

### Subscripts

*w*At the wall

- ∞
In the free stream

### Superscript

- ′
Differentiation with respect to

*η*