Heat Transfer Analysis for Viscous Fluid Flow with the Newtonian Heating and Effect of Magnetic Force in a Rotating Regime

In this article, an unsteady free convection flow of MHD viscous fluid over a vertical rotating plate with Newtonian heating and heat generation is analyzed. The dimensionless governing equations for temperature and velocity fields are solved using the Laplace transform technique. Analytical solutions are obtained for the temperature and components of velocity fields. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are presented graphically.

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A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

Canadian Journal of Physics ◽

10.1139/cjp-2018-0602 ◽

2020 ◽

Vol 98 (1) ◽

pp. 89-101 ◽

Cited By ~ 4

Author(s):

Nauman Raza ◽

Muhammad Asad Ullah

Keyword(s):

Exact Solutions ◽

Fractional Derivatives ◽

Numerical Solutions ◽

Maxwell Fluid ◽

Heat Transfer Analysis ◽

Flow Parameters ◽

Fluid Parameter ◽

Laplace Transform Technique ◽

The Laplace Transform ◽

Temperature And Velocity Fields

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

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Dufour Effect on Transient MHD Double Convection Flow of Fractionalized Second-Grade Fluid with Caputo–Fabrizio Derivative

Complexity ◽

10.1155/2021/7625031 ◽

2021 ◽

Vol 2021 ◽

pp. 1-21

Author(s):

Imran Siddique ◽

Sehrish Ayaz ◽

Fahd Jarad

Keyword(s):

Fluid Flow ◽

Thermal Flux ◽

Numerical Algorithms ◽

Velocity Fields ◽

Second Grade ◽

Convection Flow ◽

Dufour Effect ◽

The Laplace Transform ◽

Fractional Mass ◽

Temperature And Velocity Fields

This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo–Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters α and β on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.

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Slip effects on unsteady free convective heat and mass transfer flow with Newtonian heating

Thermal Science ◽

10.2298/tsci131119142a ◽

2016 ◽

Vol 20 (6) ◽

pp. 1939-1852 ◽

Cited By ~ 4

Author(s):

Abid Hussanan ◽

Ilyas Khan ◽

Mohd Salleh ◽

Sharidan Shafie

Keyword(s):

Vertical Plate ◽

Fluid Velocity ◽

Convection Flow ◽

Newtonian Heating ◽

Governing Equations ◽

Free Convection Flow ◽

Slip Effects ◽

Laplace Transform Technique ◽

The Laplace Transform ◽

Transfer Flow

This article investigates the effects of slip condition on free convection flow of viscous incompressible fluid past an oscillating vertical plate with Newtonian heating and constant mass diffusion. The governing equations together with imposed initial and boundary conditions are solved using the Laplace transform technique. The results for velocity, temperature and concentration are obtained and plotted for the embedded parameters. The results for skin friction, Nusselt number and Sherwood number are computed in table. It is investigated that the presence of slip parameter reduces the fluid velocity.

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Heat Transfer Analysis For Oscillating Flow of Magnetized Fluid By Using The Modified Prabhakar-Like Fractional Derivatives

10.21203/rs.3.rs-1086428/v1 ◽

2021 ◽

Author(s):

Ali Raza ◽

Sami Ullah Khan ◽

M. Ijaz Khan ◽

Essam Roshdy El-Zahar

Keyword(s):

Heat Transfer ◽

Fractional Derivatives ◽

Velocity Fields ◽

Heat Transfer Analysis ◽

Solution Approach ◽

Flow Parameters ◽

And Behavior ◽

Temperature And Velocity Fields ◽

Oscillating Plate ◽

With Memory

Abstract In this analysis, an unsteady and incompressible flow of magnetized fluid in presence of heat transfer has been presented with fractional simulations. The oscillating plate with periodically variation has induced the flow. The model is formulated in terms of partial differential equations (PDE’s). The traditional PDEs cannot analyze and examine the physical behavior of flow parameters with memory effects. On this end, the solution approach is followed with the efficient mathematical fractional technique namely Prabhakar fractional derivative. The non-dimensional leading equations are transformed into the fractional model and then solved with the help of the Laplace transformation scheme. The effects and behavior of significant physical and fractional parameters are analyzed graphically and numerically. As a result, we have concluded that the temperature and velocity profiles decrease with the enhancement of fractional parameters. Furthermore, with time both (temperature and velocity fields)decreasing away from the plate and asymptotically increases along y-direction, which also satisfies the corresponding conditions.

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EFFECTS OF NEWTONIAN HEATING AND MASS DIFFUSION ON MHD FREE CONVECTION FLOW OVER VERTICAL PLATE WITH SHEAR STRESS AT THE WALL

Jurnal Teknologi ◽

10.11113/jt.v78.7816 ◽

2016 ◽

Vol 78 (3-2) ◽

Author(s):

Arshad Khan ◽

Ilyas Khan ◽

Sharidan Shafie

Keyword(s):

Shear Stress ◽

Free Convection ◽

Vertical Plate ◽

Mass Diffusion ◽

Convection Flow ◽

Newtonian Heating ◽

Free Convection Flow ◽

Laplace Transform Technique ◽

Set Up ◽

Energy Equations

Effects of Newtonian heating and mass diffusion on magnetohydrodynamic free convection flow over a vertical plate that applies arbitrary shear stress to the fluid is studied. The fluid is considered electrically conducting and passing through a porous medium. The influence of thermal radiation in the energy equations is also considered. General solutions of the problem are obtained in closed form using the Laplace transform technique. They satisfy the governing equations, initial and boundary conditions and can set up a huge number of exact solutions correlatives to various fluid motions. The effects of various parameters on velocity profiles are shown graphically and discussed in details

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Influence of Thermal Radiation on Unsteady MHD Free Convection Flow of Jeffrey Fluid over a Vertical Plate with Ramped Wall Temperature

Mathematical Problems in Engineering ◽

10.1155/2016/6257071 ◽

2016 ◽

Vol 2016 ◽

pp. 1-12 ◽

Cited By ~ 7

Author(s):

Nor Athirah Mohd Zin ◽

Ilyas Khan ◽

Sharidan Shafie

Keyword(s):

Free Convection ◽

Thermal Radiation ◽

Wall Temperature ◽

Vertical Plate ◽

Convection Flow ◽

Jeffrey Fluid ◽

Dimensionless Time ◽

Free Convection Flow ◽

Laplace Transform Technique ◽

The Laplace Transform

Influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature is studied. The Laplace transform technique is used to obtain the analytical solutions. Expressions for skin friction and Nusselt number are also obtained. Results of velocity and temperature distributions are shown graphically for embedded parameters such as Jeffrey fluid parameterλ, Prandtl numberPr, Grashof numberGr, Hartmann numberHa, radiation parameterRd, and dimensionless timeτ. It is observed that the amplitude of velocity and temperature profile for isothermal are always higher than ramped wall temperature.

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Unsteady Free Convection Flow between Two Vertical Parallel Plates with Newtonian Heating

MATEMATIKA ◽

10.11113/matematika.v35.n2.1104 ◽

2019 ◽

Vol 35 (2) ◽

pp. 117-127

Author(s):

Fasihah Zulkiflee ◽

Ahmad Qushairi Mohamad ◽

Sharidan Shafie ◽

Arshad Khan

Keyword(s):

Nusselt Number ◽

Free Convection ◽

Skin Friction ◽

Approximate Solutions ◽

Convection Flow ◽

Parallel Plates ◽

Newtonian Heating ◽

Free Convection Flow ◽

Laplace Transform Technique ◽

Incompressible Viscous Fluids

Free convection flow in a boundary layer region is a motion that results from the interaction of gravity with density differences within a fluid. These differences occur due to temperature or concentration gradients or due to their composition. Studies pertaining free convection flows of incompressible viscous fluids have received much attention in recent years both theoretically (exact or approximate solutions) and experimentally. The situation where the heat be transported to the convective fluid via a bounding surface having finite heat capacity is known as Newtonian heating (or conjugate convective flows). In this paper, the unsteady free convection flow of an incompressible viscous fluid between two parallel plates with Newtonian heating is studied. Appropriate non-dimensional variables are used to reduce the dimensional governing equations along with imposed initial and boundary conditions into dimensionless forms. The exact solutionsfor velocity and temperature are obtained using the Laplace transform technique. The corresponding expressions for skin friction and Nusselt number are also calculated. The graphical results are displayed to illustrate the influence of various embedded parameters such as Newtonian heating parameter and Grashof number. The results show that the effect of Newtonian heating parameter increases the Nusselt number but reduces the skin friction.

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A new approach for the generalized fractional Casson fluid model with Newtonian heating described by the modified Riemann-Liouville fractional operator

10.22541/au.162437480.00269038/v1 ◽

2021 ◽

Author(s):

RADHAKRISHNAN BHEEMAN ◽

Tamilarasi Mathivanan

Keyword(s):

Fluid Model ◽

Vertical Direction ◽

Casson Fluid ◽

Newtonian Heating ◽

New Approach ◽

Laplace Transform Technique ◽

Casson Fluid Model ◽

The Laplace Transform ◽

Liouville Fractional Derivative ◽

Oscillating Plate

This research is about the transfer of heat of a generalized fractional Casson fluid on an unsteady boundary layer which is passing through an infinite oscillating plate, in vertical direction combined with the Newtonian heating. The results are obtained by using modified Riemann-Liouville fractional derivative. The present fluid model, starts with the governing equations which are then converted to a system of partial differential equations(linear) by using some suitable non-dimensional variables. Using the method of integral balance and the Laplace transform technique, an analytical solution is obtained. The velocity and temperature expressions are derived and the effects of modelling parameters re shown in tables and graphs to validate the obtained theoretical results.

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General Solutions for Magnetohydrodynamic Natural Convection Flow with Radiative Heat Transfer and Slip Condition over a Moving Plate

Zeitschrift für Naturforschung A ◽

10.5560/zna.2013-0041 ◽

2013 ◽

Vol 68 (10-11) ◽

pp. 659-667 ◽

Cited By ~ 15

Author(s):

Constantin Fetecau ◽

Dumitru Vieru ◽

Corina Fetecau ◽

Shahraz Akhter

Keyword(s):

Natural Convection ◽

Radiative Heat ◽

Fluid Motion ◽

Slip Condition ◽

Convection Flow ◽

Natural Convection Flow ◽

Moving Plate ◽

General Solutions ◽

Special Cases ◽

Laplace Transform Technique

General solutions for the magnetohydrodynamic (MHD) natural convection flow of an incompressible viscous fluid over a moving plate are established when thermal radiation, porous effects, and slip condition are taken into consideration. These solutions, obtained in closed-form by Laplace transform technique, depend on the slip coefficient and the three essential parameters Gr, Preff, and Keff. They satisfy all imposed initial and boundary conditions and can generate a large class of exact solutions corresponding to different fluid motions with technical relevance. For illustration, two special cases are considered and some interesting results from the literature are recovered as limiting cases. The influence of pertinent parameters on the fluid motion is graphically underlined.

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Exact Solutions of Heat and Mass Transfer with MHD Flow in a Porous Medium under Time Dependent Shear Stress and Temperature

Abstract and Applied Analysis ◽

10.1155/2015/975201 ◽

2015 ◽

Vol 2015 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

Arshad Khan ◽

Ilyas Khan ◽

Farhad Ali ◽

Asma Khalid ◽

Sharidan Shafie

Keyword(s):

Mass Transfer ◽

Porous Medium ◽

Shear Stress ◽

Heat And Mass Transfer ◽

Fluid Motion ◽

Mhd Flow ◽

Convection Flow ◽

Closed Form Solutions ◽

Special Cases ◽

Laplace Transform Technique

This paper aims to study the influence of thermal radiation on unsteady magnetohyrdodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow.

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