Repository
Author-submitted research and ten original WLM expository articles are hosted here as PDFs with permanent URLs. Indexed open-access research links to its official full text — the record stays here, the copyright stays with the source. Every entry is moderated before it appears.
Dual solutions for MHD slip flow of Cu-Al₂O₃/water hybrid nanofluid over a permeable radially stretching/shrinking disk with thermal stratification and thermal radiation
Axisymmetric MHD flow and heat transfer of a Cu–Al₂O₃/water hybrid nanofluid over a permeable radially stretching/shrinking disk with thermal stratification, thermal radiation, velocity slip, Joule heating and wall mass suction; the reduced ODE system is solved with bvp4c and dual (first/second branch) solutions are computed and analysed for the shrinking regime.
MHD boundary-layer flow over a stretching sheet: formulation, similarity reduction and an exact solution
From Navier–Stokes with the Lorentz force to f‴+ff″−f′²−Mf′=0 and the closed-form solution f(η)=(1−e^(−βη))/β — the benchmark for modern nanofluid numerics.
The Reynolds number and the transition to turbulence
Re derived by nondimensionalising Navier–Stokes, dynamic similarity, Reynolds' 1883 experiment and the pipe-flow regime thresholds.
The Hagen–Poiseuille law: a complete derivation
Force balance on a fluid cylinder → linear shear → parabolic profile → Q = πΔPR⁴/8μL, with the physics of the fourth-power law.
Bernoulli's equation: derivation, interpretation and limits
Euler's equation integrated along a streamline, the head form, and a catalogue of the equation's failure modes including cavitation.
The Blasius boundary layer: similarity structure and key values
Reduction of Prandtl's equations to f‴+½ff″=0, the value f″(0)=0.33206, and the δ, C_f and C_D laws it fixes.
Effective-property models for nanofluids and hybrid nanofluids
Tiwari–Das mixture/Brinkman/Maxwell correlations, the Buongiorno two-phase framework, and sequential hybrid property construction.
Similarity methods for boundary-layer equations
The similarity recipe as a systematic method: scaling, the stream-function ansatz, the cancellation test, and the Blasius, Falkner–Skan and stretching-sheet families.
The thermal boundary layer on a stretching sheet
Reduction of the energy equation to θ″+Pr fθ′=0, the Nusselt number, and the competing effects of Pr and the magnetic parameter.
The Casson model in boundary-layer flow
The yield-stress constitutive relation, the (1+1/β_c) modification of the momentum equation, and its qualitative effects on flow and heat transfer.
Numerical solution of boundary-value problems: shooting and collocation
Shooting with Newton iteration on the missing wall derivative, bvp4c collocation, dual solutions, and the validation discipline of credible numerics.
Numerical simulation of MHD boundary layer flow and heat transfer over a nonlinear stretching sheet in the porous medium with viscous dissipation using hybrid approach
MHD nanofluid flow with heat and mass transfer over a nonlinear stretching sheet in a porous medium; the PDEs reduce to coupled nonlinear ODEs solved by a finite-element/symbolic hybrid technique.
Dual solutions and stability analysis of a hybrid nanofluid over a stretching/shrinking sheet executing MHD flow
Unsteady MHD Cu–Al₂O₃/water hybrid nanofluid with thermal radiation; a shooting method reveals dual solution branches within specific parameter ranges.
The MHD Newtonian hybrid nanofluid flow and mass transfer analysis due to super-linear stretching sheet embedded in porous medium
Similarity reduction for a super-linearly stretching sheet in a porous medium; the concentration field becomes a confluent hypergeometric equation with a WKB asymptotic treatment.
Unsteady MHD flow of tangent hyperbolic ternary hybrid nanofluid in a Darcy–Forchheimer porous medium over a permeable stretching sheet with variable thermal conductivity
A ternary hybrid nanofluid with tangent-hyperbolic rheology; quantifies how variable conductivity, unsteadiness and permeability reshape velocity and temperature fields.
EMHD nanofluid flow with radiation and variable heat flux effects along a slandering stretching sheet
Electro-magnetohydrodynamic nanofluid flow over a variable-thickness sheet with radiation and variable heat flux — relevant to metallurgy and reactor design.
MHD Casson nanofluid boundary layer flow in presence of radiation and non-uniform heat source/sink
Casson nanofluid over a stretched magnetic surface in a porous medium: the Casson parameter raises temperature while lowering velocity, with full Nusselt and skin-friction data.
Numerical analysis of Casson nanofluid three-dimensional flow over a rotating frame exposed to a prescribed heat flux with viscous heating
3-D Casson nanofluid flow in a rotating frame under the Buongiorno model with viscous heating; rotation thins the momentum layer while Brownian and thermophoretic effects raise heat transfer.
Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating
Exact treatment of an unsteady Casson fluid past an oscillating vertical plate with Newtonian heating — a widely cited base solution in the non-Newtonian literature.
MHD flow and heat transfer of Casson nanofluid through a porous media over a stretching sheet
Keller-box solution of MHD Casson nanofluid (Ag–water, Cu–water) over a stretching surface in a porous medium, charting the governing parameters' effects.