In Depth Notes on Free Convection

Definition of Free Convection

  • Free Convection (Natural Convection): Fluid movement occurs due to density changes from heating/cooling rather than being forced by external means (like a pump or fan).

Distinction from Forced Convection

  • Forced Convection: Fluid is actively moved over a heat surface via an external force (e.g., a fan).
  • Free Convection: Fluid is moved by buoyancy effects induced by temperature differences within the fluid.

Ingredients Required for Free Convection

  • External Force Field: Such as gravity, which acts on the fluid.
  • Temperature Gradient: A difference in temperature within the fluid, leading to density variations.
  • Temperature Dependent Density: Density must vary with temperature to create buoyancy forces.

Role of Temperature Gradient

  • A temperature gradient alone is insufficient for free convection; it needs to result in a density gradient.
  • Buoyancy: The force that results from density differences in varying temperatures, causing bulk motion of fluid.

Buoyancy and Free Convection

  • Buoyancy effects generate the forces that drive free convection, countering gravitational force:
    • Buoyant Force
    • Gravitational Force

Real-Life Effects of Free Convection

  • Common phenomena include:
    • Heated wires overheat leading to convection currents.
    • Heated discharge from devices such as room heaters.

Applications in Industry

  • Examples include:
    • Glass Window Design: Considering thickness, layers, and safety.
    • Cooking Ovens: Convection dynamics within the hot cavity vs ambient kitchen air.

Free Convection on a Vertical Heated Plate

  • In a stationary fluid around a heated plate:
    • Fluid velocity at the plate is zero ($u = 0$).
    • Temperature varies: Surface temperature ($Tw$) is higher than ambient temperature ($T$), leading to convection.
  • Important forces in play include:
    • Body Force: Resulting from buoyancy that drives convection.
    • Viscous, Inertial, and Pressure Forces: Affect fluid motion.

Density and Temperature Relationship

  • Defined by the coefficient of volumetric expansion $eta$:
    • $Density ext{ (Ideal Gas)} = pg eta (T - T)$, where $T$ is the absolute temperature.

Non-Dimensionalizing Free Convection Equations

  • Application of non-dimensional terms like the Grashof Number:
    • $Gr = rac{g eta (Tw - Ta) L^3}{
      u^2}$ (where $g$ is acceleration due to gravity).

Significance of Grashof Number

  • Grashof Number ($Gr$): A non-dimensional number indicating the strength of buoyancy forces relative to viscous forces.
  • High $Gr$ signifies substantial free convection effects, analogous to how Reynolds number indicates flow regimes in forced convection.

Nusselt Number for Free Convection

  • Nusselt number ($Nu$) defined under specific conditions for vertical plates, indicating the convective heat transfer relative to conduction.
  • Analyzing local and average Nusselt numbers provides insight into thermal performance.

Different Convection Regimes

  • Free Convection dominates when $Gr ext{ > } 1$.
  • Forced Convection dominates when $Gr ext{ << } 1$.
  • Mixed Convection occurs at $Gr ext{ ~ } 1$.

Empirical Correlations for Free Convection

  • Correlations used for heat transfer calculations often take the form of empirical equations considering Grashof and Prandtl numbers combined into Rayleigh number ($Ra$).

Specific Empirical Correlations

  • For vertical plates and various conditions (constant wall temperature or heat flux) specific forms for $Nu$ and $Gr$ are detailed to predict thermal performance.
  • Generally, properties are evaluated at the film temperature through calculation.

Flow Visualization in Free Convection

  • Flow patterns represented through isotherms and streamlines help visualize the heated fluid dynamics, studied using reference materials like "An Album of Fluid Motion" by Milton Van Dyke.

Important References

  • Essential reading for understanding these concepts includes:
    • Class Notes from Prof. P. Srinivasan, BITS Pilani.
    • Heat Transfer Textbooks by: Holman & Bhattacharya, Incropera & DeWitt.
    • Relevant visual aids from Milton Van Dyke's collection.