TY  - JOUR
AU  - Shah, Faisal
PY  - 2025
DA  - 2025/08/03
TI  - Numerical Study of Nonlinear Third-Grade Nanofluid with Generalized Heat and Mass Flux in Mixed Convective Flow
JO  - ICCK Journal of Applied Mathematics
T2  - ICCK Journal of Applied Mathematics
JF  - ICCK Journal of Applied Mathematics
VL  - 1
IS  - 2
SP  - 52
EP  - 61
DO  - 10.62762/JAM.2025.671250
UR  - https://www.icck.org/article/abs/JAM.2025.671250
KW  - modified fourier and fick's law
KW  - third-grade nano-fluid
KW  - MHD
KW  - viscous dissipation
AB  - This paper investigates the bio-convective behavior of a third-grade non-Newtonian nanofluid over a stretching sheet. While the influence of Newtonian fluid flow based on classical Fourier and Fick’s laws has been widely discussed in previous studies, this work focuses on a novel third-grade nanofluid model incorporating various physical effects. Notably, the classical Fourier law is replaced by the Cattaneo–Christov (CC) theory for both heat and mass fluxes, capturing relaxation phenomena in the presence of bioconvective effects. Heat and mass transport are modeled using the CC framework, and nanoscale mechanisms are described via the Buongiorno nanofluid model. The influences of thermophoresis and Brownian motion are analyzed alongside dissipative and radiative effects. The Optimal Homotopy Asymptotic Method (OHAM) is employed to solve the resulting nonlinear equations. Graphical representations of key parameters are presented. Results reveal that the velocity profile increases with higher values of material parameters but decreases with an increase in the Reynolds number. The temperature decreases with higher Prandtl number but increases with greater radiation parameter. The concentration profile is found to decline with increasing Schmidt number.
SN  - 3068-5656
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 

@article{Shah2025Numerical,
  author = {Faisal Shah},
  title = {Numerical Study of Nonlinear Third-Grade Nanofluid with Generalized Heat and Mass Flux in Mixed Convective Flow},
  journal = {ICCK Journal of Applied Mathematics},
  year = {2025},
  volume = {1},
  number = {2},
  pages = {52-61},
  doi = {10.62762/JAM.2025.671250},
  url = {https://www.icck.org/article/abs/JAM.2025.671250},
  abstract = {This paper investigates the bio-convective behavior of a third-grade non-Newtonian nanofluid over a stretching sheet. While the influence of Newtonian fluid flow based on classical Fourier and Fick’s laws has been widely discussed in previous studies, this work focuses on a novel third-grade nanofluid model incorporating various physical effects. Notably, the classical Fourier law is replaced by the Cattaneo–Christov (CC) theory for both heat and mass fluxes, capturing relaxation phenomena in the presence of bioconvective effects. Heat and mass transport are modeled using the CC framework, and nanoscale mechanisms are described via the Buongiorno nanofluid model. The influences of thermophoresis and Brownian motion are analyzed alongside dissipative and radiative effects. The Optimal Homotopy Asymptotic Method (OHAM) is employed to solve the resulting nonlinear equations. Graphical representations of key parameters are presented. Results reveal that the velocity profile increases with higher values of material parameters but decreases with an increase in the Reynolds number. The temperature decreases with higher Prandtl number but increases with greater radiation parameter. The concentration profile is found to decline with increasing Schmidt number.},
  keywords = {modified fourier and fick's law, third-grade nano-fluid, MHD, viscous dissipation},
  issn = {3068-5656},
  publisher = {Institute of Central Computation and Knowledge}
}