# Effect of volumetric flow rate on convection and radiation heat fluxes

Say we have two hot objects of the same material but of different width and same thickness.

The objects are moving horizontally, have initially the same temperature and are cooled by a gas blown from jets placed above and below them to reduce their temperature. The position of jets is fixed and they are directed normal to the surface of the objects. Their speeds are 0.58 m/sec and 1.85 m/sec.

Each object will look this way and it will have jets below and above it

What is the effect of volumetric flow rate of each object on convection and radiation heat fluxes? Each object is moving with a different velocity, and have different dimensions so one of them will have a minimum volumetric flow rate and another will have a maximum volumetric flow rate.

I will mention some definitions:

Volumetric flow rate is a term in physics that describes how much matter – in terms of physical dimensions, not mass – moves through space per a unit of time. It is calculated this way: Q = V*A , where Q is the volumetric flow rate, V is the flow velocity and A is the cross sectional area.

Heat transfer for Convection is q = hAdT , where q is the heat transfer, h is the convective coefficient, A is the area of the object surface, and dT is the difference in temperature between the object and its surrounding environment.

Heat transfer for Radiation is q = ƐσΑ*(T^4 - Tc^4) , where Ɛ is the emisivity, σ is stefan's constant, A is the area, T is temperature of object, and Tc is temperature of surroundings.

• When you say the objects are moving, do you mean the gas is still and the object moves? For convection one typically thinks in terms of a fluid moving across a stationary surface. – Bob D Aug 12 '19 at 14:28
• The two object are moving horizontally and at the same time there are jets above them blowing cooler gas on them to cool them down. They are cooled by convection because the objects are hot enough to heat the gas above them and in turn creates convective currents as heated gaz goes up and cooler gas go down. They are also cooled by radiance – user65035 Aug 13 '19 at 5:59
• @hellothere Is the position of the jet fixed? Is the jet directed at an angle or normal to the surface? What is the speed of objects compared to the speed of sound in air?Draw at least rough geometry of the problem. – Alex Trounev Aug 13 '19 at 6:20
• @AlexTrounev Thank you. I have edited the question and I will make a drawing now – user65035 Aug 13 '19 at 6:33

Using the equations you have provided Radiation is not affected by the travel of an object through its surroundings and convection is only affected if the convection coefficient changes due to that movement.

As you have stated that the coolant gas is directed normal to the surface of the object the effect of the convection current should not be affected by the lateral movement. For the purpose of this question I am assuming that any additional convection effect of that lateral movement can be ignored.

From the question you understand that both radiation and convection work at the surface. You have not given any information about the relative shapes of the objects and without this it is not possible to answer, however as you asked about how volumetric flow affects the rate of heat exchange we will state that for the purposes of this question the two objecs are geometrically similar. That is the proportions of their dimensions are the same, and so the surface area to volume ratio will be smaller for larger objects. Given the assumption that the objects are geometrically simalar, if we define a value k to be the scaling factor then the cross sectional area (and therefore volumetric flow) is proportional to $$k^2$$. The surface area to volume ration is proportional to $$1/k$$ (from $$k^2/k^3$$).

The amount of heat held by each, assuming a uniform heat density, is proportional to the volume of the object.

Both convection and radiation are proportional to the surface area of the object, (which you have defined in your question).

So at the initial instant when the two objects are intially at the same temperature the difference in heat loss will be proportional to the surface area of the object - so the object with the largest area will lose more heat.

Given my earlier assumption that the objects are geometrically similar then this means the larger object loses heat faster (but as the amout of heat held is proportional to its volume it holds more heat).

The heat loss in both results in a reduction of temperature - as the heat loss is proportional to the area and the amount of heat held by the object is proportional to the volume, the heat density of the larger object reduces more slowly than the heat density of the smaller object. So it loses temperature more slowly.

In the following instant the difference in temperature of the two objects will not be the same, and for both radiation and convection this will affect the amount of heat lost.

When we are calculating heat lost over time, the amount of time the objects are exposed to the cooling environment will affect the total heat loss, so an object that travels more slowly through the cooling chamber will be subject to the cooling for longer. However this is actual velocity, not volumetric flow.

So for objects of geometrically simlar shapes (but with different volumes) the surface area to volume ratio will affect the heat loss, and the amount of time they are exposed to the cooling chamber will affect the (total) heat loss.