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saurabhjain

A vertical plate and a horizontal plate are suspended in an open room. Both are heated to the same temperature. Which one will cool first? Why?

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I believe vertical plate will cool down first. It's free convection mechanism that drags the cold air up along the wall due to pressure difference (hot air in the border area has lower density). Horizontal plate resists the flow in vertical direction, and thus convective heat transfer coefficient is lower in that case.

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horizontal plate is placed at what height with respect to vertical plate

at the bottom...middle....at the top which is not clear in the question

so cooling depends on the position

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The horizontal plate should cool faster since it's top surface is in contact with atmospheric air which is applied vertically to surface of the plate to dissipate heat faster.

The answer is only a logical response and not intricate engineering solution.

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Assuming both plates are suspended in free air, the vertical unit will cool significantly faster.

The convection of the air as a result of heat emanating from the plate will be significantly greater than the horizontal.

Effectively, the convection will increase as the warming air travels up the plate faster as it warms more due to the proximity of the sink allowing cold air to replace from the bottom. 

On the horizontal plate, the air mass above gets 'in the way' of the convective effects due to the effective horizontal area involved...basically, it has to be pushed out of the way by the less dense, warmer air.

On the vertically suspended plate, the horizontal equivalent area involved in the convection is significantly lower resulting in significantly reduced air mass effects to slow the convection..this is further aided by the convected air being continually heated as it rises up the plate drawing more energy from the plate.

 

 

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Doh! Basic error...I didn't read the question properly...

 

...The room of course!

 

The room cools quickest as that is the only way to break the equilibrium of the temperatures (Room/plates which are both "heated to the same temperature" allowing a differential on the plates forcing them to cool.  This may be a semantic answer, but a relevant one.

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