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HEAT TRANSFER MECHANISM OF WILLIAMSON HYBRID NANOFLUID FLOW ACROSS A NONLINEARLY EXTENDING SURFACE WITH RADIATION EFFECTS

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Sunita JSunita JSunita JSunita J 1, Suresh Biradar , Suresh Biradar, Suresh Biradar, Suresh Biradar, Suresh Biradar , Suresh Biradar , Suresh Biradar , Suresh Biradar 1* and Samrat SP and Samrat SPand Samrat SP and Samrat SP and Samrat SPand Samrat SP and Samrat SP2
» doi: 10.48047/ecb/2023.12.9.DOI:10.48047/ecb/2023.12.9.DOI:10.48047/ecb/2023.12.9. 44

Abstract

In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD In this study, we examined the radiative MHD WilliamsonWilliamson Williamson WilliamsonWilliamson hybrid nanofluidhybrid nanofluidhybrid nanofluid hybrid nanofluid hybrid nanofluid hybrid nanofluid flow over an flow over an flow over an flow over an flow over an flow over an uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed uneven stretching surface with the nonlinear heat source. The hybrid nanofluid is composed of MoS of MoS 2 and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit and Ag suspended in ethylene glycol. The similarity variables are used to transmit PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R PDE’s to ODE’s and resolved by adopting R -K method with the K method with the K method with the K method with the shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, shooting technique. Further, the stimulus stimulus stimulus of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, of physical parameters on dimensionless quantities like momentum, thermal, wall wall wall friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that friction and Nusselt number are discussed thru plots tables. Results reveal that decreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo decreasing velocity and rising temperature are fodecreasing velocity and rising temperature are fo und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic und by considering larger magnetic properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductance properties. The volume fraction tends to develop conductanceproperties. The volume fraction tends to develop conductance of the hybrid nanofluid of the hybrid nanofluidof the hybrid nanofluid of the hybrid nanofluidof the hybrid nanofluidof the hybrid nanofluidof the hybrid nanofluid of the hybrid nanofluid of the hybrid nanofluid . The . The . The hybrid nanofluid shows a higher flow and heat hybrid nanofluid shows a higher flow and heat hybrid nanofluid shows a higher flow and heat hybrid nanofluid shows a higher flow and heat hybrid

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