Entropy generation for peristaltic flow of gold-blood nanofluid driven by electrokinetic force in a microchannel

Abstract

The physiology system loses its thermal energy in the form of blood perfusion to the neighbour cells. Such lost energy causes severe hypothermia, sudden death in heart surgeries, anaemia and high or low blood pressure. Therefore, physicians and biomedical engineers are increasingly interested in examining entropy generation to quantify biological systems’ energy loss. Further, entropy generation is employed as the thermodynamic state to approach the cancer cells during the chemotherapy treatment. Because of these applications, the current mathematical model illustrates the entropy generation of gold-blood pseudoplastic nanofluid flow in a microchannel with electrokinetic force and electro-conductive heating. The dimensional form of momentum and thermal equations are transformed into the dimensionless form using long-wavelength and small Reynolds number approximations. HPM computations have been executed to solve the influences of various parameters such as radiation, Weissenberg number, Helmholtz–Smoluchowski velocity, Joule heating parameter, Hartmann number and electroosmotic parameter on velocity, temperature, pressure drop, streamlines, and heat transfer rate and are portrayed through graphs. The results elucidate that the Hartmann number diminishes the blood pseudoplastic velocity in the channel centre. The gold-blood temperature expresses the decreasing nature by elevating the electro-osmosis parameter. The streamlines are dissipated from the channel centre due to the negative value of the Helmholtz–Smoluchowski parameter.

Appendix

$$\begin{aligned}&A1 = \frac{{{\mu _{nf}}}}{{{\mu _f}}},\,A2 = - \frac{1}{2}\frac{F}{{{h^3}}},\,A3 = \frac{3}{2}\frac{F}{h},\,A4 = \left( {\frac{{{k_{nf}}}}{{{k_f}}} + R_d} \right) ,\\&A5 = \frac{{{\sigma _{nf}}}}{{{\sigma _f}}},\,A6 = 6\, A1\, \left( {1 - \beta } \right) \left( {n - 1} \right) W{e^a}A2,\,\\&A7 = - 6\, A5\, M{^2}A2,\, \\&A8 = \frac{{{m^3}{U_{HS}}}}{{\cosh \left( {mh} \right) }},\, A9 = A{2^3}A8\, a,\,\\&A10 = A9mah + 5A9\, mh + 6\, mA8\, A{2^3}h,\\&A11 = 3\, A9a + 15\, A9 + 18\, A8\, A{2^3},\,\\&A12 = \frac{{\left( {\, A10 + A11} \right) }}{{\left( {4\, {a^2} + 20\, a + 24} \right) {m^4}hA{2^3}A1}},\\&A13 = \frac{{\left( {\, A10 - A11} \right) }}{{\left( {4\, {a^2} + 20\, a + 24} \right) {m^4}hA{2^3}A1}},\\&A14 = A9mah + 3A9\, mh,\,A15 = A9a + 3\, A9,\,\\&A16 = \frac{{\left( {\, A14 - A15} \right) }}{{4aA1\, A{2^3}{m^4}\left( {a + 3} \right) {h^3}}},\\&A17 = \frac{{\left( {\, A14 + A15} \right) }}{{4\, aA1\, A{2^3}{m^4}\left( {a + 3} \right) {h^3}}},\\&A18 = A{2^3}A7\, {a^2}{h^5}{m^4},\,A19 = A7\, {h^5}A{2^3}a{m^4},\,\\&A20 = 30\, A6\, {6^a}{\left( {A2\, h} \right) ^{a + 3}}{m^4},\\&A21 = \frac{{\left( {A18 + 3\, A19 + A20} \right) }}{{60\, aA1\, A{2^3}{m^4}\left( {a + 3} \right) {h^3}}},\\&A22 = \frac{{\left( {A18 + 5\, A19 + 6\, A7\, {h^5}A{2^3}{m^4} + 2\, A20} \right) }}{{\left( {120\, {a^2} + 600\, a + 720} \right) {m^4}hA{2^3}A1}}, \\&A23 = \frac{{A6\, {6^a}{{\left( {A2\, \eta } \right) }^{a + 3}}}}{{A1A{2^3}a\left( {a + 2} \right) \left( {a + 3} \right) }},\\&A24 = \frac{{36\, \, A1\, A{2^2}BrW{e^a}{6^a}\left( {n - 1} \right) \left( {\beta \, - 1} \right) }}{{A4\, a\left( {{a^2} + 7\, a + 12} \right) }},\\&A25 = \frac{{3A{2^2}A5\, Br\, M{^2}}}{{10A4}},\\&A26 = \frac{{A2\, A3\, A5\, Br\, M{^2}}}{{2A4}} + \, \frac{{3Br\, A1\, A{2^2}}}{{A4}},\\&A27 = \frac{{A{3^2}A5\, Br\, M{^2}}}{{2A4}},\,\\&A28 = 3A{2^2}A5\, Br\, M{^2}{h^4},\,A29 = 5A2\, A3\, A5\, Br\, M{^2}{h^2},\,\\&A30 = 30A1\, A{2^2}Br\, {a^3}{h^2},\\&A31 = 5\, A{3^2}A5\, Br\, M{^2},\,\\&A32 = A28 + A29 + A30 + A31. \end{aligned}$$