Numerical study of a one and two-dimensional heat flow using finite volume

Patel, Manoj R.; Pandya, Jigisha U.

doi:10.1016/j.matpr.2021.04.413

Cited by 4 publications

(3 citation statements)

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“…This results in a set of algebraic equations. By solving this with the appropriate solver, we may acquire the Hermite wavelet's unknown coefficients, which yields numerical solutions for Equations ( 8) and (12).…”

Section: Process Of Integration Of Matrixmentioning

confidence: 99%

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Application of Hermite wavelet method for heat transfer in a porous media

Vinod

Raghunatha

2022

Heat Trans

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In this article, the flow and heat transfer for non‐Newtonian viscoelastic fluid in an axisymmetric channel with a porous wall is investigated. Convective boundary conditions have been used in the problem formulation. We obtain coupled, highly nonlinear ordinary differential equations from the fundamental governing equations via appropriate similarity variables. The solution for velocity and temperature are computed by applying the Hermite wavelet method (HWM). The comparison between the results from the HWM, differential transform method, and numerical method are well in agreement which proves the capacity of HWM for solving such problems. The effects of Reynolds number and Prandtl number on the velocity and temperature are illustrated through graphs and tables for different values of an independent variable.

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Section: Process Of Integration Of Matrixmentioning

confidence: 99%

“…Lin et al 11 applied the deep collocation method for heat transfer through porous media and also verified the finite element method. Patel and Jigisha 12 studied the unsteady state of one‐dimension and the steady state of two‐dimensional heat flow using the finite volume method.…”

Section: Introductionmentioning

confidence: 99%

Application of Hermite wavelet method for heat transfer in a porous media

Vinod

Raghunatha

2022

Heat Trans

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“…On the other hand, the examination of nanofluids within porous media has the potential to enhance the attributes of convection heat transfer. This is due to the presence of porosity structures in diverse applications such as oil flow filtration, cooling of turbine blades, thermal insulation, and various types of heat exchangers that necessitate cooling or heating systems [27,28]. A porous media is typically distinguished by its porosity, such as intergranular or intercrystalline porosity.…”

Section: Introductionmentioning

confidence: 99%

Exploring the effects of TiO2${\rm TiO}_2$–Ag/water hybrid nanofluid on MHD flow over a permeable exponentially stretching–shrinking sheet with radiative heat transfer and slip conditions

Patel,

Pandya,

Patel

2024

Z Angew Math Mech

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The objective of this article is to study the importance of velocity and thermal slip in the exponentially stretching or shrinking sheet with the megnetohydrodynamic (MHD) hybrid nanofluid flow along with magnetic field, radiative, heat generation effects. This study has practical importance in enhancing heat transfer efficiency, improving energy conversion and optimizing thermal management systems. The findings can also contribute to the development of sustainable energy systems and aid in assessing the stability and safety of nanofluid applications. The governing partial differential equations are transformed into nonlinear ordinary differential equations using similarity transformation. The ODEs are solved using bvp4c solver in MATLAB. The dual solutions are achieved for specific range of the stretching or shrinking parameter and mass suction parameter. The first solution is physically significant after considering stability analysis. The hybrid nanofluid has numerous real‐life and industrial applications, such as microelectronics, manufacturing, naval structures, nuclear system cooling, biomedical, and drug reduction. The skin‐friction increases but Nusselt number decreases over the stretching sheet whereas the opposite effect shows over shrinking sheet for the both solution with the increasing velocity slip parameter. On the other hand, The Nusselt number decreases over the shrinking or stretching sheet for both solutions with the increasing in the thermal slip parameter. The skin friction increases over shrinking sheet but decreases over stretching sheet for the first solution with increasing silver volume fraction parameter and porosity parameter (). Enhancing magnetic field parameter leads to the skin friction increases over the shrinking sheet but decreases over stretching sheet but Nusselt number shows opposite trend. The Nusselt number decreases over shrinking sheet but increases over stretching sheet for the first solution with increasing porosity parameter (). The Nusselt number decreases over shrinking or stretching sheet as the increases heat generation () and variable thermal conductivity parameter () but Nusselt number shows opposite trend as the increases radiative parameter ().

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