Heat conduction in a cooling fan

Input(s)

z: Distance from Start of Fan (cm)

L: Length of Fan (cm)(\mathrm{cm})

B: Breadth of Fan (cm)(\mathrm{cm})

h\mathrm{h}: Heat Transfer Coefficient (J/sm2 K)\left(\mathrm{J} / \mathrm{s} \mathrm{m}^{2} \mathrm{~K}\right)

k: Thermal Conductivity (W/cm K)

TwT_{w}: Temperature of Wall (K)

TaT_{a}: Ambient Temperature of Air (K)

Output(s)

ξ\xi: Dimensionless Distance (dimensionless)

N: Dimensionless Heat Transfer Coefficient (dimensionless)

Θ\Theta: Dimensionless Temperature (dimensionless)

T: Temperature at Distance Z\mathrm{Z} from Wall at the Fan (K)(\mathrm{K})

Formula(s)

ξ=zLN=(h( L2)k B)0.5Θ=cosh(N(1ξ))cosh(N)T=Ta+Θ( TwTa)\begin{gathered} \xi=\frac{\mathrm{z}}{\mathrm{L}} \\ \mathrm{N}=\left(\frac{\mathrm{h} *\left(\mathrm{~L}^{2}\right)}{\mathrm{k} * \mathrm{~B}}\right)^{0.5} \\ \Theta=\frac{\cosh (\mathrm{N} *(1-\xi))}{\cosh (\mathrm{N})} \\ \mathrm{T}=\mathrm{T}_{\mathrm{a}}+\Theta *\left(\mathrm{~T}_{\mathrm{w}}-\mathrm{T}_{\mathrm{a}}\right) \end{gathered}

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley & Sons, Chapter: 10, Pages: 308, 309.


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