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ABSTRACT
In this article, numerical solutions are obtained to observe the influence of thermal radiation on Casson particulate suspension flow past a complex isothermal wavy surface. Rosseland diffusion approximation is employed to express the contribution of radiative heat flux over the Casson fluid model. Using coordinate transformations, the two-phase model is converted into a suitable form and then integrated numerically by employing implicit finite-difference method. The numerical results are discussed in detail in terms of shear stress, rate of heat transfer, streamlines, and isotherms. It is found that the rate of heat transfer increases extensively when radiation parameter and mass concentration parameter are penetrated into the mechanism.
Nomenclature
| ā1, ā2 | = | Dimensional amplitudes of complex wavy surface (m) |
| a1, a2 | = | Dimensionless amplitudes of complex wavy surface |
| cp | = | Specific heat at constant pressure for fluid-phase (J∕kgK) |
| cs | = | Specific heat at constant pressure for particle-phase (J∕kgK) |
| Dρ | = | Mass concentration parameter |
| eij | = | (i,j)-th component of the deformation rate (s−1) |
| g | = | Acceleration due to gravity (m∕s2) |
| Gr | = | Grashof number |
| L | = | Characteristic length associated with wavy surface surface (m) |
| Pr | = | Prandtl number |
| = | Dimensional pressure of carrier phase (N∕m2) | |
| = | Dimensional pressure of particle phase (N∕m2) | |
| p | = | Dimensionless pressure of the carrier phase |
| pp | = | Dimensionless pressure of the particle phase |
| py | = | Yield stress of fluid (N∕m2) |
| = | Radiation heat flux (W∕m2) | |
| Rd | = | Thermal Radiation parameter |
| T | = | Dimensional temperature of fluid-phase (K) |
| T∞ | = | Ambient fluid temperature (K) |
| Tp | = | Dimensional temperature of particle-phase (K) |
| = | Dimensional fluid-phase velocity components (m∕s) | |
| = | Dimensional particle-phase velocity components (m∕s) | |
| u,v | = | Dimensionless fluid-phase velocity components |
| = | Dimensionless particle-phase velocity components | |
| = | Dimensional cartesian coordinates (m) | |
| x,y | = | Dimensionless coordinate system |
| = | Greek symbols | |
| α | = | Thermal diffusivity (m2∕s) |
| αr | = | Rosseland mean absorption coefficient (1∕m) |
| αd | = | Dusty fluid parameter |
| β | = | Casson fluid parameter |
| βT | = | Volumetric expansion coefficient (1∕K) |
| γ | = | Ratio of cp to cs |
| κ | = | Thermal conductivity (W∕mK) |
| θ | = | Dimensionless fluid-phase temperature |
| θp | = | Dimensionless particle-phase temperature |
| θw | = | Surface temperature parameter |
| ρ | = | Density of fluid-phase (kg∕m3) |
| ρp | = | Density of particle-phase (kg∕m3) |
| μ | = | Dynamic viscosity of fluid (kg∕ms) |
| μβ | = | Dynamic viscosity of plastic (kg∕ms) |
| ν | = | Kinematic viscosity of fluid (m2∕s) |
| τm | = | Velocity relaxation time of the particles (s) |
| τT | = | Thermal relaxation time of the particles (s) |
| τw | = | Shear stress at the surface |
| Qw | = | Rate of heat transfer at the surface |
| π | = | Product of components of deformation rate |
| πc | = | Critical value of π |
| = | Dimensional surface profile function (m) | |
| σ(x) | = | Dimensionless surface profile function |
| σx | = | First derivative of the function σ w.r.t. x |
| σxx | = | Second derivative of the function σ w.r.t. x |
| σs | = | Scattering coefficient (1∕m) |
| σ* | = | Stephan-Boltzmann constant |
| = | Subscripts | |
| w | = | surface condition |
| ∞ | = | ambient condition |
| p | = | particle phase |
| = | Superscripts | |
| − | = | dimensional system |
Nomenclature
| ā1, ā2 | = | Dimensional amplitudes of complex wavy surface (m) |
| a1, a2 | = | Dimensionless amplitudes of complex wavy surface |
| cp | = | Specific heat at constant pressure for fluid-phase (J∕kgK) |
| cs | = | Specific heat at constant pressure for particle-phase (J∕kgK) |
| Dρ | = | Mass concentration parameter |
| eij | = | (i,j)-th component of the deformation rate (s−1) |
| g | = | Acceleration due to gravity (m∕s2) |
| Gr | = | Grashof number |
| L | = | Characteristic length associated with wavy surface surface (m) |
| Pr | = | Prandtl number |
| = | Dimensional pressure of carrier phase (N∕m2) | |
| = | Dimensional pressure of particle phase (N∕m2) | |
| p | = | Dimensionless pressure of the carrier phase |
| pp | = | Dimensionless pressure of the particle phase |
| py | = | Yield stress of fluid (N∕m2) |
| = | Radiation heat flux (W∕m2) | |
| Rd | = | Thermal Radiation parameter |
| T | = | Dimensional temperature of fluid-phase (K) |
| T∞ | = | Ambient fluid temperature (K) |
| Tp | = | Dimensional temperature of particle-phase (K) |
| = | Dimensional fluid-phase velocity components (m∕s) | |
| = | Dimensional particle-phase velocity components (m∕s) | |
| u,v | = | Dimensionless fluid-phase velocity components |
| = | Dimensionless particle-phase velocity components | |
| = | Dimensional cartesian coordinates (m) | |
| x,y | = | Dimensionless coordinate system |
| = | Greek symbols | |
| α | = | Thermal diffusivity (m2∕s) |
| αr | = | Rosseland mean absorption coefficient (1∕m) |
| αd | = | Dusty fluid parameter |
| β | = | Casson fluid parameter |
| βT | = | Volumetric expansion coefficient (1∕K) |
| γ | = | Ratio of cp to cs |
| κ | = | Thermal conductivity (W∕mK) |
| θ | = | Dimensionless fluid-phase temperature |
| θp | = | Dimensionless particle-phase temperature |
| θw | = | Surface temperature parameter |
| ρ | = | Density of fluid-phase (kg∕m3) |
| ρp | = | Density of particle-phase (kg∕m3) |
| μ | = | Dynamic viscosity of fluid (kg∕ms) |
| μβ | = | Dynamic viscosity of plastic (kg∕ms) |
| ν | = | Kinematic viscosity of fluid (m2∕s) |
| τm | = | Velocity relaxation time of the particles (s) |
| τT | = | Thermal relaxation time of the particles (s) |
| τw | = | Shear stress at the surface |
| Qw | = | Rate of heat transfer at the surface |
| π | = | Product of components of deformation rate |
| πc | = | Critical value of π |
| = | Dimensional surface profile function (m) | |
| σ(x) | = | Dimensionless surface profile function |
| σx | = | First derivative of the function σ w.r.t. x |
| σxx | = | Second derivative of the function σ w.r.t. x |
| σs | = | Scattering coefficient (1∕m) |
| σ* | = | Stephan-Boltzmann constant |
| = | Subscripts | |
| w | = | surface condition |
| ∞ | = | ambient condition |
| p | = | particle phase |
| = | Superscripts | |
| − | = | dimensional system |