Question

A hot plate transfers heat with a heat flux of 8000 W/m² into the ambient air at 25°C. if the surface of the hot plate is maintained at 125°C, calculate the heat transfer coefficient for the convection between the plate and the air:

1. 75 W/m² - K
2. 80 W/m² - K
3. 70 W/m² - K
4.

60 W/m² - K

Answer 1

Correct Answer - Option 2 : 80 W/m² - K

Concept:

Newtons Law of cooling:

The law states that the rate heat of transfer by convection between a solid body and the surrounding fluid is directly proportional to the temperature difference between them and is also directly proportional to the area of contact or area of exposure between them.

Q = hA(T_w - T_∞)

Where T_w = Hot plate temperature, T_∞ = Temperature of air, h = Convective heat transfer coefficient, A = Area of contact

Now, \(\frac{{\rm{Q}}}{{\rm{A}}} = \;{\rm{\dot q}} = {\rm{h}}\left( {{{\rm{T}}_{\rm{w}}} - {{\rm{T}}_\infty }} \right)\)

Where q̇ = Heat flux

∴ \({\rm{h}} = \frac{{{\rm{\dot Q}}}}{{\left( {{{\rm{T}}_{\rm{w}}}{\rm{\;}} - {\rm{\;}}{{\rm{T}}_\infty }} \right)}}\) ...(i)

Calculation:

Given:

Q̇ = 8000 W/m2, T_w = 125°C, T∞ = 25°C

Substituting all the values in equation (i)

\({\rm{h}} = \frac{{8000}}{{\left( {125{\rm{\;}} - {\rm{\;}}25} \right)}}\)

h = 80 W/m2-K