# Discuss the trend in detail. Plot theoretical temperature on the same plot , compare both and discuss.

through the liquid at the object’s surface. An energy balance shows that the convection heat loss is verification of a decrease in the internal energy of the object
τρddTcTThAq−=−=∞)(
and with initial condition at 0 the equation can be solved as 0TT= =τ
τρ−∞∞=−−cVhAeTTTT0
which is the lumped capacity model in equation form. The results of the experimental analysis should indicate that the difference between the object and liquid temperature 67
decay exponentially to zero as the time reaches infinity. The time constant is dependent on the lumped thermal capacitance and resistance of the object to convection heat transfer. The verification of the Biot number must first be established to determine the validity of using the lumped capacitance model. This dimensionless number
()kAVh
must be less than 0.1 for the lumped capacity model to apply. The thermal conductivity (k) is assumed constant, and all other quantities can be determined either directly from the experiment or through analysis of the experimental results.
Useful data:
Diameter of sphere= 45 mm
Material of sphere: stainless steel
Experimental set up :
special instrument for lumped system.

Figure # ( 1 ) : Experimental Set up. 68
Experimental procedure
• Switch on the heater of water bath.
• Set the temperature of water bath around 60-80 oc.
• Open the data acquisition software.
• After the water temperature stabilizes at set temperature put the steel ball in water bath and start recording the temperature using software.
• After temperature reached steady state stop taking data.
• Cooling in room temperature. Take the steel ball out and again start recording temperature data until next 40-50 minute. This will be the case of cooling at ambient temperature.

Report requirements
1. Start with general energy balance to develop lumped capacity model equation for unsteady state heat transfer for sphere (This can be done in theory part)
2. Case 1 (heating the shape in constant temperature bath): plot the temperature of shape with time. Find the temperature of shape at t=1 minute. Using the lumped capacity equation and this temperature value at given time, calculate heat transfer coefficient of hot water inside bath. compare this value with the expected value of h.
3. Calculate Biot number by using calculated value of h and known values of thermal conductivity & diameter of sphere. comment on the value with respect to the validity of lumped capacity model.
4. Case 2: Cooling of hot sphere at room temperature: search for the value of convective heat transfer coefficient h for the case you studied (table 4-1 in your heat transfer text book could be helpful). Calculate Biot number for the case you studied. Comment on the value.
5. Draw temperature profile with time (cooling). Discuss the trend in detail. Plot theoretical temperature on the same plot , compare both and discuss. Find the value of h for air for which theoretical and experimental plot exactly matches. compare this value with the one you found in literature.

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