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Analytical Solution of Exothermic Reactions Model with Constant Heat Source and Porous Medium

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Abstract

The objective of this article is to present a modified analytical scheme, namely homotopy analysis transform method (HATM), to investigate the exothermic reactions model in the presence of constant heat source and porous medium. The heat flow patterns profiles are required for the heat transfer in each type of the thermal insulation. The driving force model to analyze the temperature gradient is studied. The governing equation of the model is restricted into an energy balance equation that gives the value of temperature in conduction state in the presence of constant heat source. By employing the HATM iterative process, we study the behavior of independent variable for the convergence series solution in admissible range. The HATM technique manipulates and controls the series solution, which quickly converges to the exact solution in large admissible domain in efficient way. The solution procedure and explanation show the flexible efficiency of HATM in comparison with other existing methods for handling different kinds of nonlinear differential equations occurring in fluid mechanics.

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Authors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, 303905, India

    Ram Prakash Sharma

  2. Department of Mathematics, IIT Roorkee, Roorkee, 247667, India

    Madhu Jain

  3. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, 302004, India

    Devendra Kumar

Authors
  1. Ram Prakash Sharma
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  2. Madhu Jain
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  3. Devendra Kumar
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Correspondence to Ram Prakash Sharma.

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Sharma, R.P., Jain, M. & Kumar, D. Analytical Solution of Exothermic Reactions Model with Constant Heat Source and Porous Medium. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90, 239–243 (2020). https://doi.org/10.1007/s40010-018-0562-y

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  • DOI: https://doi.org/10.1007/s40010-018-0562-y

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