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An improved analytical solution on viscous dissipation effect in extended Stokes' second problem in microchannel with
1Intel Microelectronics (M) Sdn. Bhd., Halaman Kampung Jawa, Kawasan Perindustrian Bayan Lepas, Post Code 11900, Pulau, Pinang, Malaysia.
Heliyon
|September 26, 2024
Summary
This study solves the thermal effects of fluid motion in microchannels caused by surface oscillation. It provides an exact analytical solution for temperature fields, crucial for understanding viscous dissipation in applications like artificial joints.
Area of Science:
- Fluid dynamics
- Heat transfer
- Microfluidics
Background:
- The extended Stokes' problem analyzes fluid motion induced by oscillating surfaces.
- Understanding the thermal effects of viscous dissipation in such flows is crucial for applications like artificial hip joints and mechanical bearings.
- Previous analytical solutions for the temperature field in unsteady flows with complex velocity fields were lacking.
Purpose of the Study:
- To derive the full exact analytical temperature field for the extended Stokes' problem with viscous dissipation.
- To investigate the thermal effects of fluid friction under symmetric isothermal boundary conditions in a microchannel.
- To provide a foundational solution for unsteady microchannel flows with thermal considerations.
Main Methods:
- Utilized partial differential equation analysis to solve the energy equation.
- Modeled one-dimensional, incompressible, laminar, Newtonian flow with constant properties.
- Obtained the temperature field as a function of Brinkman number, Prandtl number, and dimensionless angular frequency.
Main Results:
- An exact analytical solution for the temperature field was successfully obtained.
- The results were validated against a reported numerical solution within a specific range of variables.
- The findings extend the applicability of solutions beyond the limited condition of dimensionless angular frequency less than or equal to unity.
Conclusions:
- The derived analytical solution for the temperature field advances the understanding of thermal phenomena in oscillating microchannel flows.
- The study highlights the significance of viscous dissipation in temperature rise in microfluidic systems.
- The research introduces a new Stokes number, offering a more comprehensive parameter for analyzing such flows.
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