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

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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.

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Abbreviations

\(T_{\infty }\) :

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

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

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

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Authors and Affiliations

  1. Department of Mathematics, Hazara University, Mansehra, 21300, Pakistan

    Faisal Sultan, Muhammad Shahzad & Mehboob Ali

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Waqar Azeem Khan

  3. Departement of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

    Zakir Hussain

Authors
  1. Faisal Sultan
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  2. Waqar Azeem Khan
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  3. Muhammad Shahzad
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  5. Zakir Hussain
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Correspondence to Faisal Sultan or Mehboob Ali.

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Sultan, F., Khan, W.A., Shahzad, M. et al. Physical assessments on variable thermal conductivity and heat generation/absorption in cross magneto-flow model. J Therm Anal Calorim 140, 1069–1078 (2020). https://doi.org/10.1007/s10973-019-08957-4

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