Melting Heat Transfer in Steady Laminar Flow Over a Flat Plate

Epstein, Michael; Cho, D. H.

doi:10.1115/1.3450595

Cited by 180 publications

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“…The formulation of the second term in boundary Eq. (14) states that the heat conducted to the melting surface is equal to the heat of melting plus the sensible heat required to raise the solid temperature T * o to its melting temperature T m (for details, see Epstein and Cho (1976)). The increase of temperature may also leads to a local increase in the transport phenomena by reducing the viscosity across the momentum boundary layer and so the heat transfer rate at the wall may also be affected greatly.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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An upper-convected Maxwell (UCM) fluid flow over a melting surface situated in hot environment is studied. The influence of melting heat transfer and thermal stratification are properly accounted for by modifying the classical boundary condition of temperature to account for both. 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 exponentially space dependent internal heat generation 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 are 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 (RK4SM). The numerical procedure is validated by comparing the solutions of RK4SM with that of MATLAB based bvp4c. The results reveal that increase in stratification parameter corresponds to decrease in the heat energy entering into the fluid domain from freestream and this significantly reduces the overall temperature and temperature gradient of UCM fluid as it flows over a melting surface. The transverse velocity, longitudinal velocity and temperature of UCM are increasing function of temperature dependent viscous and thermal conductivity parameters. At a constant value of melting parameter, the local skin-friction coefficient and heat transfer rate increases with an increase in Deborah number.

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Section: Mathematical Formulationmentioning

confidence: 99%

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Omowaye

Animasaun

2016

JAFM

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“…From their investigation, they observed that melting at the interface results in a decrease in the Nusselt number. Epstein and Cho [29] discussed the laminar film condensation on a vertical surface. Much later, melting heat transfer in a nanofluid boundary layer on a stretching circular cylinder was examined by Gorla et al [30].…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

Ajayi

Omowaye

Animasaun

2017

Journal of Applied Mathematics

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The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in Re 1/2 is guaranteed with when magnitude of is large. Re 1/2 decreases with and .

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“…In the present formulation, transient effects in the solid have been neglected. This assumption is valid as long as the melting solid is large compared to its thermal boundary layer thickness [see Epstein and Cho (1976) (…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…Epstein and Cho (1976) studied the melting heat transfer from a flat plate in a steady laminar case, while Kazmierczak et al, (1986Kazmierczak et al, ( , 1987 analyzed melting from a vertical flat plate embedded in a porous medium in both free and forced convection processes. The heat transfer at the melting surface in the laminar boundary layer by using Karman-Pohlhausen method was discussed by Pozvonkov et al, (1970).…”

Section: Introductionmentioning

confidence: 99%

The Effect of Melting on Mixed Convection Heat and Mass Transfer in Non-Newtonian Nanofluid Saturateed in Porous Medium

RamReddy¹,

Kairi²

2015

Frontiers in Heat and Mass Transfer

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In this paper, we investigated the influence of melting on mixed convection heat and mass transfer from the vertical flat plate in a non-Newtonian nanofluid saturated porous medium. The wall and the ambient medium are maintained at constant, but different, levels of temperature and concentration. The Ostwald-de Waele power-law model is used to characterize the non-Newtonian nanofluid behavior. A similarity solution for the transformed governing equations is obtained. The numerical computation is carried out for various values of the non-dimensional physical parameters. The variation of temperature, concentration, heat and mass transfer coefficients with the power-law index, mixed convection parameter, melting parameter, Brownian motion parameter, thermophoresis parameter, buoyancy ratio and Lewis number are discussed in a wide range of values of these parameters.

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Melting Heat Transfer in Steady Laminar Flow Over a Flat Plate

Cited by 180 publications

References 0 publications

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Upper-Convected Maxwell Fluid Flow with Variable Thermo-Physical Properties over a Melting Surface Situated in Hot Environment Subject to Thermal Stratification

Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

The Effect of Melting on Mixed Convection Heat and Mass Transfer in Non-Newtonian Nanofluid Saturateed in Porous Medium

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