A mathematical model to examine the heat transport features in Burgers fluid flow due to stretching cylinder
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A mathematical model to examine the heat transport features in Burgers fluid flow due to stretching cylinder Masood Khan1 · Zahoor Iqbal1 · Awais Ahmed1 Received: 1 April 2020 / Accepted: 1 September 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract In this article, a new mathematical modelling is presented for the flow of Burgers fluid induced by a stretching cylinder in the presence of magnetic field. Moreover, the mechanisms of heat and mass transport are also examined by using the law of conservation of energy with Fourier’s and Fick’s laws for thermal and solutal energy, respectively. The ordinary differential equations (ODEs) are attained from partial differential equations by making the use of dimensionless similarity transformations. The homotopic approach is being adopted to solve the developed ODEs. The influences of different physical parameters on velocity, thermal and concentration profiles are pondered through graphs and physical behavior of these parameters is enlightened with the realistic verdicts. The basic physical intimation of pertained results is that the (temperature ) and solutal curves of Burgers liquid(show ( for ) the enhancing trend for larger scales of relaxation time parameter 𝛽1 and ) material parameter of Burgers fluid 𝛽2 while, opposing behavior is being observed for retardation time parameter 𝛽3 . Moreover, it is assessed that the concentration rate and solutal boundary layer thickness decline with an intensification in Lewis number (Le). Also, it is noted that the temperature distribution enhances/declines with higher values of heat source and sink parameter, respectively. Keywords Burgers fluid · Mathematical model · Stretching cylinder · MHD · Heat source/sink List of symbols u, w Velocity components r, z Cylindrical coordinates 𝜆1 Fluid relaxation time 𝜆2 The material parameter of Burgers fluid 𝜆3 Fluid retardation time 𝐒 Extra stress tensor 𝐣 Mass flux 𝐪 Heat flux Cw Concentration at surface C∞ Ambient concentration wz Stretching cylinder velocity k Thermal conductivity p Fluid pressure f Dimensionless velocity function 𝛼 Thermal diffusivity cp Specific heat at constant pressure cf The specific heat * Zahoor Iqbal [email protected] 1
Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
M Magnetic field 𝛽2 Burgers fluid parameter 𝛿 Heat source/sink parameter Pr Prandtl number T Fluid temperature C Fluid concentration 𝐉1 Current density Q0 Heat source/sink A1 First Rivilin–Ericksen tensor Le Lewis number Tw Surface temperature T∞ Ambient temperature DB The diffusion coefficient 𝜌 Fluid density 𝜂 Dimensionless similarity variable 𝜇0 Zero shear viscosity 𝜈 Kinematic viscosity 𝜃 Dimensionless temperature 𝜙 Dimensionless concentration function 𝜌f The density of liquid 𝛽1 Fluid relaxation parameter 𝛽3 Fluid retardation parameter
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Introduction Basically, Burgers fluid is a non-Newtonian fluid. NonNewtonian substances have significant importance and lot of physical applicatio
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