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Joule heating in mixed convective peristalsis of Sisko nanomaterial

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Abstract

No doubt the nanomaterial has superior thermophysical characteristics when compared with traditional fluid in numerous engineering and biological phenomena. Here, model is constructed for mixed convective peristaltic motion in the presence of Joule heating. Analysis has been organized for Sisko fluid. Brownian motion and thermophoresis are used to examine the nanomaterial effects. Velocity and thermal slip conditions are utilized. Zero mass flux condition is imposed. Small Reynolds number and large wavelength arguments are employed. Governing problem is nonlinear in terms of both differential equation and boundary conditions. Numerical solution to incoming nonlinear problem is computed. The solutions for velocity, temperature, concentration and pressure gradient are examined for the influential variables. It represents that concentration of nanomaterial rapidly enhances for higher N \(_{{\rm t}}\). Concentration of nanomaterial against Brinkman number is increased throughout the channel.

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Abbreviations

U, V (m s−1):

Components of velocity

μ f (kg m−1s−1):

Dynamic viscosity of water

ρ f (kg m−3):

Density of water

K f (kg m K−1s−3):

Thermal conductivity of water

B 0 (Am−1):

Magnetic field strength

G (m s−2):

Gravity

N b :

Non-dimensional Brownian motion parameter

M:

Non-dimensional Hartman number

G T :

Non-dimensional thermal Grashof number

ɵ:

Non-dimensional temperature

σ :

Non-dimensional velocity slip

dp/dx :

Non-dimensional pressure gradient

T (K):

Temperature of fluid

C p (m2 s−2 K−1):

Specific heat of fluid

P (Nm(Pa)):

Pressure

σ nf (kg−1 m−3 s3A2):

Electrical conductivity of nanofluid

σ 1 (kg−1 m  s2):

Velocity slip coefficient

C (Kg m−3):

Concentration of nanoparticles

N T :

Non-dimensional thermophoresis parameter

m:

Non-dimensional Hall number

G C :

Non-dimensional concentration of Grashof number

\(\varphi\) :

Non-dimensional concentration

γ :

Non-dimensional thermal slip

Br:

Non-dimensional Brinkman number

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Authors and Affiliations

  1. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan

    Bilal Ahmed & T. Hayat

  2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University 80203, Jeddah, 21589, Saudi Arabia

    T. Hayat & A. Alsaedi

  3. Department of Mathematics, COMSATS University, Islamabad, 44000, Pakistan

    F. M. Abbasi

Authors
  1. Bilal Ahmed
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  2. T. Hayat
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  3. A. Alsaedi
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  4. F. M. Abbasi
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Correspondence to Bilal Ahmed.

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Ahmed, B., Hayat, T., Alsaedi, A. et al. Joule heating in mixed convective peristalsis of Sisko nanomaterial. J Therm Anal Calorim 146, 1–10 (2021). https://doi.org/10.1007/s10973-020-09997-x

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