# Heat Transfer - Fluids/ Thermo Equation

I have an equation derived for a simple crossflow heat exchanger

the final equation is listed on the attachment its very simple

there are 2 variables in the equation that I do not know what they are

a C and a roe??

Simply tell me what c and roe are its a specific heat and a density I belive ???

https://brainmass.com/engineering/mechanical-engineering/heat-transfer-fluids-thermo-equation-237943

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Yes. C = Specific heat of the material (Here, copper) at constant volume and

Rho = Mass density of the material (Here, copper)

Here is how the derivation goes, starting from equation (4.4):

m C (dT/dt) + h A t = h A (Ta) [I am using A as the surface area of the rod and Ta for ambient temperature]

Mass of the copper rod = Mass density * Volume = (Rho) * [(pi D^2 /4) * L]

Suraface area of the rod = pi D L

Plugging these in place of m and A in the equation, we get

(Rho) * [(pi D^2 /4) * L] * C * (dT/dt) + h * (pi D L) = h (pi D L) (Ta)

Divide both sides of the equation by (Rho) * [(pi D^2 /4) * L] * C to get

(dT/dt) + [{h * (pi D L)}/{(Rho) * (pi D^2 /4) * L * C}] = {h (pi D L) (Ta)}/{(Rho) * (pi D^2 /4) * L * C}

On simplification, this gives

dT/dt + [{4h}/{(Rho) D C}] = [{4h}/{(Rho) D C}] (Ta)

On solving this differential equation, we get the equation given in (4.8).

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