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Physical assessments on variable thermal conductivity and heat generation/absorption in cross magneto-flow model

  • Faisal SultanEmail author
  • Waqar Azeem Khan
  • Muhammad Shahzad
  • Mehboob AliEmail author
  • Zakir Hussain
Article

Abstract

The present work focused here is a mixed convective MHD flow of cross fluid in the presence of heat generation/absorption and variable thermal conductivity over a bidirectional stretchable sheet. To elaborate the mechanism of heat transfer is analyzed in view of non-Fourier heat flux based upon Cattaneo–Christov theory. The influence of a simple isothermal model of homogeneous–heterogeneous reactions is further used for solute concentration. As a result, the relevant Buongiorno fluid model is utilized in mathematical modeling and then it is simplified through lubrication technique. By using appropriate transformations, the raised PDEs initially converted to ODEs. Convergent solutions of ODEs are obtained by the implementation of the numerical procedure bvp4c technique. However, the velocity, temperature and concentration profiles have been sketched by distinct physical flow parameter. Drag coefficients and heat transport are also computed numerically. Our results reveal that temperature profile has an inverse relation between the relaxation parameter and variable thermal conductivity.

Keywords

Cross fluid model Cattaneo–Christov heat flux Variable thermal conductivity Heat generation/absorption Homogeneous–heterogeneous reactions 

List of symbols

\(T_{\infty }\)

Ambient temperature of fluid

\(p,q\)

Concentrations of chemical species \(P,Q\)

\(D_{\text{P}} ,\;D_{\text{Q}}\)

Diffusion coefficient of species \(P\) and \(Q\)

\(B_{0}^{2}\)

Magnetic field strength

\(n\)

Power-law index

\(k_{\text{m}} ,\;K_{\text{s}}\)

Rate coefficient of homogeneous/heterogeneous reactions

\(x,y,z\)

Space coordinates

\(U_{\text{w}} \left( {x,t} \right),\;V_{\text{w}} \left( {y,t} \right)\)

Stretching velocities

\(T\)

Temperature of fluid

\(K\left( T \right)\)

Variable thermal conductivity

\(u,v,w\)

Velocity components

\(f,g\)

Dimensionless velocities

\(C_{\text{fx}}\)

Skin friction

Sc

Schmidt number

M

Magnetic parameter

\(\Pr\)

Prandtl number

\(K\)

Strength coefficient homogenous reaction

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

Local Reynolds number

\({\text{We}}_{1} ,\;{\text{We}}_{2}\)

Weissenberg numbers

\({\text{Nu}}_{\text{x}}\)

Local Nusselt number

Greek alphabets

\(h_{\text{f}}\)

Heat transfer coefficient

\(\left( {\rho c} \right)_{\text{f}}\)

Heat capacity of fluid

\(\nu\)

Kinematics viscosity

\(\varepsilon_{1}\)

Ratio of diffusion coefficient

\(\sigma^{*}\)

Stefan–Boltzmann constant

\(k\)

Thermal conductivity

\(k_{\text{T}}\)

Thermal conductivity time of the heat discussion

\(\varGamma\)

Time material constant

\(\alpha\)

The ratio of stretching rates parameter

\(\gamma_{1}\)

Biot number

\(c_{\text{p}}\)

Specific heat at constant pressure

\(\phi\)

Dimensionless concentration

\(\lambda_{\text{T}}\)

Relaxation time of heat flux

\(\rho\)

Density

\(\varepsilon\)

Variable thermal conductivity parameter

\(\gamma\)

Thermal relaxation parameter

\(\theta\)

Dimensionless temperature

\(\lambda\)

Heat generation/absorption

\(\eta\)

Dimensionless variable

Notes

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Department of MathematicsHazara UniversityMansehraPakistan
  2. 2.School of Mathematics and StatisticsBeijing Institute of TechnologyBeijingChina
  3. 3.Departement of MathematicsCOMSATS Institute of Information TechnologyAbbottabadPakistan

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