LAPLACE TRANSFORM ANALYSIS OF UNSTEADY MAGNETOHYDRODYNAMIC AL₂O₃–CU/WATER HYBRID NANOFLUID FLOW OVER A STRETCHING SHEET
Keywords:
Laplace Transform, MHD, Hybrid Nanofluid, Al₂O₃–Cu/Water, Stretching Sheet, Transient FlowAbstract
Nanofluids and, more recently, hybrid nanofluids have emerged as powerful working media for advanced thermal systems where high heat transfer performance is required while still maintaining acceptable pumping power and flow controllability. In this study, the unsteady magnetohydrodynamic (MHD) boundary-layer flow and heat transfer of an Al₂O₃–Cu/water hybrid nanofluid over a linearly stretching sheet is investigated. The sheet velocity varies linearly with the streamwise coordinate and decays with time, and a uniform transverse magnetic field is imposed.
The governing unsteady boundary-layer equations for momentum and energy are derived under standard boundary-layer assumptions, including the incorporation of effective density, viscosity, heat capacity, thermal conductivity, and electrical conductivity for the hybrid nanofluid. After introducing an appropriate similarity variable in the wall-normal direction and dimensionless fields for velocity and temperature, the problem is reduced to a pair of unsteady diffusion-type equations with a reaction term in the momentum equation due to the applied magnetic field.
To obtain analytical insight into the transient behavior, the Laplace transform with respect to time is applied to the dimensionless equations. The transformed problems are linear ordinary differential equations in the similarity variable, which are solved explicitly. The inverse Laplace transform is then evaluated, yielding closed-form expressions for the dimensionless velocity and temperature profiles in terms of the complementary error function.
From the analytical expressions, symbolic formulas are derived for the wall shear stress and wall heat flux, and hence for the skin-friction coefficient and local Nusselt number. The influence of the magnetic parameter, Prandtl number, nanoparticle volume fractions, and time on the flow and temperature fields is discussed qualitatively using these expressions.
