# Why heat transfer happens only via conduction in this case?

Why heat transfer between a heated flat plate and a fluid happens via conduction only and not convection, when the fluid is present below it?

Consider a plate under which a fluid is present and it extends to infinity in the vertical direction. Let's assume that the fluid and the plate were initially at the same temperature (say $$25^o C$$) . If I took any fluid particle as shown in the figure below, the buoyant force will be balanced by the weight of the particle, so that the particle does not move. This will be true for any fluid particle.

Now let us say that the temperature of the plate is increased gradually. As the temperature increases, the fluid starts to gain thermal energy and its temperature starts rising. Let after a while, the temperature of the fluid particle that we considered is $$30^o$$C.

The weight of the particle now will be = $$\rho_{30} Vg$$

The Buoyant Force on the particle will be = $$\rho_{25}Vg$$

For calculating the buoyant force I took the density as $$\rho_{25}$$ because the average temperature of the fluid would still be approaching 25 even though the fluid started to heat, and I can think of the fluid particle to be submerged inside the fluid whose temperature was 25 and density was $$\rho_{25}$$

since $$\rho_{25} > \rho_{30}$$ we conclude that there will be some net upward force acting on this fluid particle, which will try to move this fluid particle in the upward direction. Now this will be the case for all the fluid particles that we take in the fluid. So I will have a situation like this -

I'm told that in this case the heat transfer will take place via conduction and no bulk fluid motion occurs. However, can't it be the case that since on all fluid particles some force acts in the upward direction, the fluid particles which are present somewhat below start to overtake the particles that are present above them to make convection happen?

In a nutshell I wanted to know why the particles don't move even though there is a force on them? Why the heat transfer doesn't happen via convection?

• The hottest fluid is at the top. Lower temperature fluid can't replace it so no convection. But fluids do conduct heat... Apr 21 at 12:24
• Are you considering accepting some answers to your other questions? Apr 21 at 12:28
• @SolarMike I guess that's also one way of putting my question that why hotter fluid particles remain above colder ones? Apr 21 at 12:36
• Do a search on Youtube for Feynmann's lectures on ideal gases and thermodynamics... I wasn't re-phrasing your question, I was trying to get you to improve your understanding. Hot fluid sits on top of cold Search "stratification", but water does not always play well. Apr 21 at 12:39

Hot fluid rises.

So, if the heating element is at the top of a tank, the hot fluid can't rise more that the top of the tank which means it cannot cause convective flow.

This is why a kettle is heated from the bottom so that the heat transfer mechanism is convective flow allowing the colder water to sink to the heating element.

Consider a solar water heating tank, which can be heated by Solar energy and a gas boiler when there is little sun. The solar coil is placed at the base of the tank so any warm water ie heat from the sun can be added to the tank, remember the coldest part of the tank is the bottom. The boiler coil is placed at the height where it can heat a sufficient amount of water to cover the needs, while leaving a volume of water for the solar system to work into.

So, the tank works on stratification where any heated water rises to the level where it meets water of the same temperature. Also, hot water is removed from the tank for showers and, perhaps, heating (underfloor is good as it uses relatively low temperature water to heat), so heating water can be taken from below the top of the tank.

The solar tank we fitted (1280 litres, 2m high, approx 1m in dia) can have water at 95 deg C at the top and water at 6 deg C at the bottom. This shows water is not a good conductor of heat.

Did an experiment in physics class at school where an ice cube was weighted to sit a the bottom of a 4" test tube, while the open end was heated in a bunsen and the water boiled. So water at 0 deg C and 100 deg C only 4" apart, conduction anyone...

• Thanks for the answer. So can I model this situation as if I were to have a room filled with balls and on each ball a vertical force was acting then none of the balls would move? When I first studied this concept I thought about it the same way (this room analogy) and was quite convinced then, until today that I thought - "but a ball at the bottom of the room can slide past other balls to make its way up". What are your thoughts on this? Apr 21 at 14:22