Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip

Inspired by simulating duct thermal processing of novel functional polymers, a novel mathematical model is developed for buoyancy‐driven heat transfer in non‐Newtonian Williamson fluid flow in a vertical parallel plate duct containing a permeable medium, under mutually orthogonal electrical and magnetic fields. The momentum equation features electrical and magnetic body force terms, and the Darcy–Brinkman–Forchheimer mode is used for non‐Darcy effects. The energy balance equation includes thermal buoyancy (natural convection body force) and a modified viscous dissipation term. The conservation equations with associated boundary conditions are reframed into a system of coupled non‐linear ordinary differential equations via appropriate similarity transformations. The emerging dimensionless boundary value problem is then solved with a differential transform method (DTM). Validation of DTM solutions with the bvp4c MATLAB collocation solver is included. The influence of key parameters on velocity, temperature and average Nusselt number, are computed and illustrated graphically. With elevation in Weissenberg (non‐Newtonian) number, velocity and temperature are reduced. Velocity is suppressed with increasing non‐Darcian parameter (Forchheimer effect) whereas it is enhanced with increment in buoyancy convection parameter. With increasing Forchheimer, Darcy number and Hartmann number, the average Nusselt number is boosted whereas it is decreased with higher values of buoyancy convection parameter, Brinkman number and Weissenberg number. A strong reduction in temperature is computed with increment in ratio of Joule electrical heating to heat conduction parameter. DTM is shown to be an exceptionally accurate and versatile approach for simulating non‐Newtonian electromagnetohydrodynamic transport in ducts.

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“…In view of the proposed assumptions, the continuity, momentum and the energy equations in vectorial form are defined as [61][62][63]:…”

Section: Mathematical Model For Electromagnetic Non-newtonian Thermal...mentioning

confidence: 99%

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

et al. 2022

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“…Their results show that the dipole-dipole interaction of ions contributes to the reduction of interfacial energy by adding the EDL effect. There have also been recent studies in the field that address similar issues [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52].…”

Section: Introductionmentioning

confidence: 99%

The Effect of Nanoparticle Shape and Microchannel Geometry on Fluid Flow and Heat Transfer in a Porous Microchannel

2020

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Microchannels are widely used in electrical and medical industries to improve the heat transfer of the cooling devices. In this paper, the fluid flow and heat transfer of water–Al2O3 nanofluids (NF) were numerically investigated considering the nanoparticle shape and different cross-sections of a porous microchannel. Spherical, cubic, and cylindrical shapes of the nanoparticle as well as circular, square, and triangular cross-sections of the microchannel were considered in the simulation. The finite volume method and the SIMPLE algorithm have been employed to solve the conservation equations numerically, and the k-ε turbulence model has been used to simulate the turbulence fluid flow. The models were simulated at Reynolds number ranging from 3000 to 9000, the nanoparticle volume fraction ranging from 1 to 3, and a porosity coefficient of 0.7. The results indicate that the average Nusselt number (Nuave) increases and the friction coefficient decreases with an increment in the Re for all cases. In addition, the rate of heat transfer in microchannels with triangular and circular cross-sections is reduced with growing Re values and concentration. The spherical nanoparticle leads to maximum heat transfer in the circular and triangular cross-sections. The heat transfer growth for these two cases are about 102.5% and 162.7%, respectively, which were obtained at a Reynolds number and concentration of 9000 and 3%, respectively. However, in the square cross-section, the maximum heat transfer increment was obtained using cylindrical nanoparticles, and it is equal to 80.2%.

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“…Ji Lang both theoretically and experimentally investigated the transient squeezing flow in a highly porous film [8]. Similarly, a large amount of literature is available in relation to long porous sliders (LPSs) [1,6,[9][10][11][12][13] and circular porous sliders (CPSs) [2,[14][15][16][17][18]. Awati investigated the lubrication of a long porous slider by using the homotopy analysis method (HAM) [10].…”

Section: Introductionmentioning

confidence: 99%

“…In a separate study, Khan studied the effects of Reynolds numbers by using different analytical methods [11,12]. Naeem studied the influence of Reynolds numbers (R) on long [13] and circular porous sliders [18]. Ghoreishi studied the circular slider [14].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Hydro-Magnetic Flow Arising in a Long Porous Slider and a Circular Porous Slider with Velocity Slip

et al. 2019

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The current research explores the injection of a viscous fluid through a moving flat plate with a transverse uniform magneto-hydrodynamic (MHD) flow field to reduce sliding drag. Two cases of velocity slip between the slider and the ground are studied: a long slider and a circular slider. Solving the porous slider problem is applicable to fluid-cushioned porous sliders, which are useful in reducing the frictional resistance of moving bodies. By using a similarity transformation, three dimensional Navier–Stokes equations are converted into coupled nonlinear ordinary differential equations. The resulting nonlinear boundary value problem was solved analytically using the homotopy analysis method (HAM). The HAM provided a fast convergent series solution, showing that this method is efficient, accurate, and has many advantages over the other existing methods. Solutions were obtained for the different values of Reynolds numbers (R), velocity slip, and magnetic fields. It was found that surface slip and Reynolds number had substantial influence on the lift and drag of the long and the circular sliders. Moreover, the effects of the applied magnetic field on the velocity components, load-carrying capacity, and friction force are discussed in detail with the aid of graphs and tables.

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Integral Transform Method to Solve the Problem of Porous Slider without Velocity Slip

Cited by 15 publications

References 15 publications

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

Numerical study of natural convection dissipative electro‐magnetic non‐Newtonian flow through a non‐Darcy channel

The Effect of Nanoparticle Shape and Microchannel Geometry on Fluid Flow and Heat Transfer in a Porous Microchannel

Three-Dimensional Hydro-Magnetic Flow Arising in a Long Porous Slider and a Circular Porous Slider with Velocity Slip

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