Quantum mechanics

Pure mathematics

Heat transfer

Homotopy

Differential equation

Thermal conductivity

Prandtl number

Thermodynamics

Boundary layer

Physics

Joule heating

Mathematics

Homotopy analysis method

Schmidt number

Mathematical analysis

Ordinary differential equation

Partial differential equation

Mechanics

Scientific Reports

This consideration highlights the belongings of momentum, entropy generation, species and thermal dissemination on boundary layer flow (BLF) of Casson liquid over a linearly elongating surface considering radiation and Joule heating effects significant. Transportation of thermal and species are offered by using the temperature-dependent models of thermal conductivity and mass diffusion coefficient. Arising problem appear in the form of nonlinear partial differential equations (NPDEs) against the conservation laws of mass, momentum, thermal and species transportation. Appropriate renovation transfigures the demonstrated problem into ordinary differential equations. Numerical solutions of renovated boundary layer ordinary differential equations (ODEs) are attained by a proficient and reliable technique namely optimal homotopy analysis method (OHAM). A graphical and tabular interpretation is given for convergence of analytic solutions through error table and flow behavior of convoluted physical parameters on calculated solutions are presented and explicated in this examination. Reliability and effectiveness of the anticipated algorithm is established by comparing the results of present contemplation as a limiting case of available work, and it is found to be in excellent settlement. Decline in fluid velocity and enhancement in thermal and species transportation is recorded against the fluctuating values of Hartman number. Also reverse comportment of Prandtl number and radiation parameter is portrayed. Moreover, it is conveyed that supplementing values of the magnetic parameter condenses the fluid velocity and upsurges the thermal and concentration distributions. Negative impact of elevating Joule heating phenomenon is noted on the molecular stability of the system via Brinkman number $$\left( {Br} \right).$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mfenced><mml:mrow><mml:mi>Br</mml:mi></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math> Furthermore, the system’s stability at a molecular level is controlled by diminishing values of radiation $$\left( R \right),$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mfenced><mml:mi>R</mml:mi></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math> temperature difference $$\left( { \in_{1} } \right),$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mfenced><mml:msub><mml:mo>∈</mml:mo><mml:mn>1</mml:mn></mml:msub></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math> concentration difference $$\left( { \in_{2} } \right),$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mfenced><mml:msub><mml:mo>∈</mml:mo><mml:mn>2</mml:mn></mml:msub></mml:mfenced><mml:mo>,</mml:mo></mml:mrow></mml:math> diffusion parameters $$\left( { \in_{3} } \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced><mml:msub><mml:mo>∈</mml:mo><mml:mn>3</mml:mn></mml:msub></mml:mfenced></mml:math> and Brinkman number $$\left( {Br} \right).$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mfenced><mml:mrow><mml:mi>Br</mml:mi></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:math>

Entropy generation in MHD Casson fluid flow with variable heat conductance and thermal conductivity over non-linear bi-directional stretching surface