## Related questions with answers

Consider a thin 16-cm-long and 20-cm-wide horizontal plate suspended in air at $20^\circ C.$ The plate is equipped with electric resistance heating elements with a rating of 20 W. Now the heater is turned on and the plate temperature rises. Determine the temperature of the plate when steady operating conditions are reached. The plate has an emissivity of 0.90 and the surrounding surfaces are at $17^\circ C.$ As an initial guess, assume a surface temperature of $50^\circ C.$ Is this a good assumption?

Solution

VerifiedWe are given following data:

$L=0.16\text{ m}$

$t=0.20\text{ m}$

$\dot Q=20\text{ W}$

$T_{C}=20\text{ C}=293\text{ K}$

$T_{sur}=17\text{ C}=290\text{ K}$

$T_{SC}=50\text{ C}=323\text{ K}$

$\epsilon=0.9$

Film temperature is equal to:

$T_f=\dfrac{T_{SC}+T_C}{2}=\dfrac{50+20}{2}=35\text{ C}=308\text{ K}$

From properties of air table A-15 we can find values we need:

$\begin{align*} \beta&=\dfrac{1}{308}\text{ K}^{-1}=0.00325\text{ K}^{-1}\\ \rho&=1.145\frac{\text{ kg}}{\text{ m}^3}\\ k&=0.02625\frac{\text{ W}}{\text{ m K}}\\ P_r&=0.7268\\ \mu&=1.895\cdot 10^{-5}\text{ Pa s}\\ \end{align*}$

Before we can calculate Grashof number, we have to determine characteristic length:

$L_c=\dfrac{L\cdot t}{2(L+t)}=\dfrac{0.16\cdot 0.2}{2\dot (0.2+0.16)}=0.044\text{ m}$

Calculating Grashof number:

$\begin{align*} G_r&=\dfrac{g\cdot \beta\cdot (T_{SC}-T_C)\cdot L_c^3}{\left(\dfrac{\mu}{\rho}\right)^2}=\dfrac{9.81\cdot 0.00325\cdot (50-20)\cdot 0.044^3}{\left(\dfrac{1.895\cdot 10^{-5}}{1.145}\right)^2}\\\\ &=3\cdot 10^{5} \end{align*}$

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Heat and Mass Transfer: Fundamentals and Applications

5th Edition•ISBN: 9780073398181Yunus A. Cengel#### Fundamentals of Electric Circuits

6th Edition•ISBN: 9780078028229Charles Alexander, Matthew Sadiku#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (4 more)Randall D. Knight#### Advanced Engineering Mathematics

10th Edition•ISBN: 9780470458365 (3 more)Erwin Kreyszig## More related questions

1/4

1/7