Heat and Mass Transfer of Upper Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Horizontal Melting Surface

Affiliation(s)

^{1}
Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.

^{2}
School of Science and Technology, National Open University of Nigeria, Lagos, Nigeria.

Abstract

The objective of this article is to present the dynamics of an Upper Convected Maxwell (UCM) fluid flow with heat and mass transfer over a melting surface. The influence of melting heat transfer, thermal and solutal stratification are properly accounted for by modifying the classical boundary conditions of temperature and concentration respectively. It is assumed that the ratio of inertia forces to viscous forces is high enough for boundary layer approximation to be valid. The corresponding influence of exponential space dependent internal heat source on viscosity and thermal conductivity of UCM is properly considered. The dynamic viscosity and thermal conductivity of UCM are temperature dependent. Classical temperature dependent viscosity and thermal conductivity models were modified to suit the case of both melting heat transfer and thermal stratification. The governing non-linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations and completed the solution numerically using the Runge-Kutta method along with shooting technique. For accurate and correct analysis of the effect of variable viscosity on fluid flow in which (*T*_{w} or *T*_{m}) < *T*_{∞} , the mathematical models of variable viscosity and thermal conductivity must be modified.

The objective of this article is to present the dynamics of an Upper Convected Maxwell (UCM) fluid flow with heat and mass transfer over a melting surface. The influence of melting heat transfer, thermal and solutal stratification are properly accounted for by modifying the classical boundary conditions of temperature and concentration respectively. It is assumed that the ratio of inertia forces to viscous forces is high enough for boundary layer approximation to be valid. The corresponding influence of exponential space dependent internal heat source on viscosity and thermal conductivity of UCM is properly considered. The dynamic viscosity and thermal conductivity of UCM are temperature dependent. Classical temperature dependent viscosity and thermal conductivity models were modified to suit the case of both melting heat transfer and thermal stratification. The governing non-linear partial differential equations describing the problem are reduced to a system of nonlinear ordinary differential equations using similarity transformations and completed the solution numerically using the Runge-Kutta method along with shooting technique. For accurate and correct analysis of the effect of variable viscosity on fluid flow in which (

Cite this paper

Adegbie, K. , Omowaye, A. , Disu, A. and Animasaun, I. (2015) Heat and Mass Transfer of Upper Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Horizontal Melting Surface.*Applied Mathematics*, **6**, 1362-1379. doi: 10.4236/am.2015.68129.

Adegbie, K. , Omowaye, A. , Disu, A. and Animasaun, I. (2015) Heat and Mass Transfer of Upper Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Horizontal Melting Surface.

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