, Volume 46, Issue 5, pp 1127–1143 | Cite as

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

  • M. M. RahmanEmail author


This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.


Convective flow Heat transfer Similar solution Slip flow Variable thermal conductivity Variable viscosity 




constant appears in (9)


surface convection parameter


magnetic induction [Wb m−2]




local skin-friction coefficient




specific heat at constant pressure [kJ kg−1 K−1]


dimensionless stream function


Hartmann number


convective heat transfer coefficient [W m−2 K−1]


slip length [m]


local Knudsen number based on slip length


local Knudsen number based on mean free path


local Nusselt number


variable Prandtl number


ambient Prandtl number


local Reynolds number


constant appears in (9)


temperature at the surface of the plate [K]


temperature of the fluid within the boundary layer [K]


temperature of the ambient fluid [K]


free stream velocity [m s−1]


the x- and y-components of the velocity field [m s−1]


distance along and normal to the plate [m]



fluid density [kg m−3]


thermal conductivity parameter


dynamic viscosity [Pa s]


dynamic viscosity at ambient temperature [Pa s]


kinematic viscosity [m2 s−1]


slip parameter


tangential momentum accommodation coefficient


magnetic permeability [N A−2]


mean free path [m]


stream function [m2 s−1]


similarity variable


dimensionless temperature


variable viscosity parameter


thermal conductivity [W m−1 K−1]


thermal conductivity at ambient temperature [W m−1 K−1]


constant appears in (8)



surface condition; ambient condition


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics, College of ScienceSultan Qaboos UniversityMuscatSultanate of Oman

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