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Viscous Dissipation and Joule Heating Effects in Non-Fourier MHD Squeezing Flow, Heat and Mass Transfer Between Riga Plates with Thermal Radiation: Variational Parameter Method Solutions

  • Research Article - Mechanical Engineering
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Abstract

A Riga plate is an electromagnetic actuator which comprises permanent magnets and alternating electrodes placed on a plane surface. The present article investigates the influence of viscous and Joule heating (Ohmic dissipation) in the magnetohydrodynamic squeezing flow, heat and mass transfer between two Riga plates. A non-Fourier (Cattaneo–Christov) heat flux model is employed which generalizes the classical Fourier law to incorporate thermal relaxation time. Via suitable transformations, the governing partial differential conservation equations and boundary conditions are non-dimensionalized. The resulting nonlinear ordinary differential boundary value problem is well posed and is solved analytically by the variational parameter method (VPM). Validation of the solutions is included for the special case of non-dissipative flow. Extensive graphical illustrations are presented for the effects of squeeze parameter, magnetic field parameter, modified Hartmann number, radiative parameter, thermal Biot number, concentration Biot number, Eckert number, length parameter, Schmidt number and chemical reaction parameter on the velocity, temperature and concentration distributions. Additionally, the influence of selected parameters on reduced skin friction, Nusselt number and Sherwood number are tabulated. An error analysis is also included for the VPM solutions. Detailed interpretation of the results is provided. The study is relevant to smart lubrication systems in biomechanical engineering and sensor design.

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Abbreviations

\( a \) :

Dimensional constant

\( b \) :

Width of magnets and electrodes

\( B \) :

Dimensionless constant

\( B_{0} \) :

Applied magnetic field

\( B_{i1} \) :

Biot number for temperature

\( B_{i2} \) :

Biot number for concentration

\( C \) :

Concentration of fluid

\( C_{{{\text{f}}1}} \) :

Concentration of upper plate

\( C_{\text{f}} \) :

Skin friction coefficient

\( C_{\text{h}} \) :

Ambient temperature

\( C_{\text{p}} \) :

Specific heat capacity

\( D_{\text{B}} \) :

Brownian diffusion coefficient

\( Ec \) :

Eckert number

\( h_{1} \) :

Convective heat transfer coefficient

\( h_{2} \) :

Convective mass transfer coefficient

\( j_{0} \) :

Applied current density

\( k \) :

Thermal conductivity

\( K_{\text{c}} \) :

Dimensionless chemical reaction parameter

\( M^{2} \) :

Hartmann magnetic body force parameter

\( M_{0} \) :

Magnetization

\( m^{ * } \) :

Coefficient of mean absorption

\( Nux \) :

Local Nusselt number

\( p \) :

Pressure

\( Pr \) :

Prandtl number

\( q_{\text{r}} \) :

Radiative heat flux (W/m2)

\( \text{R} \) :

Radiation parameter

\( {Re}_{x} \) :

Local Reynolds number

\( Sc \) :

Bioconvection Schmidt number

\( Shx \) :

Local Sherwood number

\( t \) :

Time (s)

\( T \) :

Temperature (K)

\( T_{{{\text{f}}1}} \) :

Temperatures of upper plate

\( u \) :

Velocity component in x-direction (m/s)

\( U_{\text{w}} \) :

Stretching velocity

\( v \) :

Velocity component in y-direction (m/s)

\( v_{\text{f}} \) :

Fluid velocity

\( Z \) :

Modified Hartmann number

\( \beta \) :

Squeezing parameter

\( \beta {}_{\text{e}} \) :

Thermal relaxation time

\( \eta \) :

Dimensionless variable

\( \rho \) :

Fluid density (kg/m3)

\( \sigma \) :

Electric conductivity

\( \sigma^{ * } \) :

Stefan–Boltzmann constant

\( \mu \) :

Dynamic viscosity of squeeze film

\( \gamma \) :

Characteristic constant parameter

\( \delta \) :

Length parameter

\( \varOmega_{\text{E}} \) :

Temperature difference

\( \lambda_{\text{E}} \) :

Thermal relaxation parameter

\( \pi \) :

Component of deformation

\( \psi \) :

Stream function

\( \theta \) :

Dimensional less temperature

\( \phi \) :

Dimensionless concentration

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This research has not received any specific grants from any sources.

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This research did not receive any specific grant from funding agencies in the public, commercial or not-for profit sectors.

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Authors and Affiliations

  1. Department of Mathematics, Vaagdevi College of Engineering, Warangal, Telangana State, India

    Md. Shamshuddin

  2. Department of Mathematics, Siksha O Anusandhan Deemed to be University, Bhubaneswar, India

    S. R. Mishra

  3. Department of Aeronautical and Mechanical Engineering, University of Salford, Manchester, UK

    O. Anwar Bég & A. Kadir

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  1. Md. Shamshuddin
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  3. O. Anwar Bég
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Shamshuddin, M., Mishra, S.R., Bég, O.A. et al. Viscous Dissipation and Joule Heating Effects in Non-Fourier MHD Squeezing Flow, Heat and Mass Transfer Between Riga Plates with Thermal Radiation: Variational Parameter Method Solutions. Arab J Sci Eng 44, 8053–8066 (2019). https://doi.org/10.1007/s13369-019-04019-x

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