Explore BrainMass

Explore BrainMass

    Heat Transfer - Fluids/ Thermo Equation

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 ???

    © BrainMass Inc. brainmass.com December 24, 2021, 8:00 pm ad1c9bdddf
    https://brainmass.com/engineering/mechanical-engineering/heat-transfer-fluids-thermo-equation-237943

    Attachments

    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).

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 8:00 pm ad1c9bdddf>
    https://brainmass.com/engineering/mechanical-engineering/heat-transfer-fluids-thermo-equation-237943

    ADVERTISEMENT