Brinkman number formula |
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\( Br \;=\; \dfrac{ \mu \cdot U^2 }{ k \cdot \Delta T }\) (Brinkman Number) \( \mu \;=\; \dfrac{ Br \cdot k \cdot \Delta T }{ U^2 }\) \( U \;=\; \sqrt{ \dfrac{ Br \cdot k \cdot \Delta T }{ \mu } }\) \( k \;=\; \dfrac{ \mu \cdot U^2 }{ Br \cdot \Delta T }\) \( \Delta T \;=\; \dfrac{ \mu \cdot U^2 }{ Br \cdot k }\) |
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| Symbol | English | Metric |
| \( Br \) = Brinkman Number | \( dimensionless \) | \( dimensionless \) |
| \( \mu \) (Greek symbol mu) = Fuid Dynamic Viscosity | \(lbf-sec\;/\;ft^2\) | \(Pa-s \) |
| \( U \) = Characteristic Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
| \( k \) = Fluid Thermal Conductivity | \(Btu-ft\;/\;hr-ft^2-F\) | \(W\;/\;m-K\) |
| \( \Delta T \) = System Characteristic Temperature | \(F\) | \(K\) |
Brinkman Number, abbreviated as Br, a dimensionless number, used in fluid dynamics and heat transfer to characterize the relative importance of viscous heating to heat conduction in a fluid flow. It’s commonly used in non-Newtonian fluid mechanics, microfluidics, and engineering applications where viscous effects play a critical role in temperature distribution.
Brinkman Number Interpretation
- Low Brinkman Number (MA << 1) - Indicates that viscous heating dominates over heat conduction, which can be significant in high-viscosity fluids or high-speed flows (polymer processing or lubrication)
- .High Brinkman Number (Br >> 1) - Suggests that heat conduction dominates, and viscous heating effects are negligible (in low-viscosity fluids like water under typical conditions).
- The numerator (\( \mu \cdot U^2 \)) represents the heat generated due to viscous dissipation (friction within the fluid).
- The denominator (\(k \cdot \Delta T\)) represents the heat conducted away from the system.
