1. Convective Heat Transfer

<aside> 💡 Convection Heat Transfer is the energy transfer between a surface and a fluid moving over that surface

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$$ q_h = h(T_s-T_\infty) $$

• $h$ - Convective Heat Transfer Coefficient

Convective Heat Transfer Coefficient mostly depends on:

1. Fluid Thermal Conductivity
2. Fluid Velocity Field
   • Which depends on geometry, flow patterns, etc.

Quantifying h - Nusselt Formulation

Modelling Convective Heat Transfer as conduction through the fluid.

$$ h(T_s-T_\infty) = -k\frac{\partial T}{\partial y} $$

To non-dimensionalise this:

$$ T^* = \frac{T-T_\infty}{T_s-T_\infty} \\ y^* = \frac{y}{L} $$

Therefore:

$$ h(T_s-T_\infty) = -k\frac{\partial T}{\partial y}

-k\frac{(T_s-T_\infty)}{L}\frac{\partial T^}{\partial y^} \\ h = -\frac{k}{L}\frac{\partial T^}{\partial y^} \\ \frac{hL}{k}\thicksim \frac{\partial T^}{\partial y^} \\ \therefore Nu = \frac{hL}{k} $$

• $Nu$ - Nusselt Number, non-dimensional number
• $h$ - Convective Heat Transfer Coefficient
• $L$ - Length scale
• $k$ - Fluid Thermal Conductivity

Nusselt Number ($Nu$) is a non-dimensional number that represents the fluid temperature gradient at the surface

$$ Nu = \frac{\partial T^}{\partial y^}\vert_{y^*=0} $$

$Nu$ depends on Prandtl Number ($Pr$) and Reynolds Number ($Re$)