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Generalised Lie similarity transformations for the unsteady flow and heat transfer under the influence of internal heating and thermal radiation

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Abstract

Lie similarity transformations for unsteady flow in a thin film under the influence of internal heating and thermal radiation have been deduced earlier. These transformations have been employed to reduce the partial differential equations of the fluid flow and heat transfer to ordinary differential equations. Fluid velocity and temperature profiles were presented by constructing homotopic solutions for the obtained system of equations. Here we apply a general linear combination of all the Lie point symmetries associated with the equations describing the flow and heat transfer with internal heating and thermal radiation, to construct the general Lie similarity transformations. By applying these transformations to the flow, we map them to ordinary differential equations. The reduced system of differential equations contains the arbitrary constants used to construct the generalised Lie similarity transformations through the linear combination of all the Lie symmetries of the flow equations. Further, we determine analytic solutions using the homotopy analysis method for the reduced system of equations. We show that the presence of arbitrary constants in the reduced system of differential equations enables control of the deduced homotopic analytic solutions, i.e., these constants serve as control parameters. We illustrate the effects of these control parameters on the temperature profiles graphically.

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong Technology and Business University, Yantai, 264005, China

    Shuguang Li

  2. School of Mechanical and Manufacturing Engineering (SMME), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan

    M Safdar, M Bilal & S Ahmed

  3. College of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), Islamabad, 44000, Pakistan

    S Taj

  4. Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, 44000, Pakistan

    M Ijaz Khan

  5. Department of Mechanical Engineering, Lebanese American University, Kraytem, Beirut, 1102-2801, Lebanon

    M Ijaz Khan

  6. Department of Mathematics, COMSATS University Islamabad, Attock, 43600, Pakistan

    Maimona Rafiq

  7. Faculty of Chemical Engineering, New Uzbekistan University, Tashkent, Uzbekistan

    Sherzod Shukhratovich Abdullaev

  8. Department of Science and Innovation, Tashkent State Pedagogical University Named After Nizami, Bunyodkor Street 27, Tashkent, Uzbekistan

    Sherzod Shukhratovich Abdullaev

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  1. Shuguang Li
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  2. M Safdar
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  3. S Taj
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  4. M Bilal
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  5. S Ahmed
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  6. M Ijaz Khan
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  7. Maimona Rafiq
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  8. Sherzod Shukhratovich Abdullaev
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Correspondence to Maimona Rafiq.

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Li, S., Safdar, M., Taj, S. et al. Generalised Lie similarity transformations for the unsteady flow and heat transfer under the influence of internal heating and thermal radiation. Pramana - J Phys 97, 203 (2023). https://doi.org/10.1007/s12043-023-02672-4

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  • DOI: https://doi.org/10.1007/s12043-023-02672-4

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