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KAUSAR AHMAD KULLIYYAH OF PHARMACY Heat Transfer By Conduction 1 PHM3133 Dosage Design /11

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Contents 2 Practical heat transfer Heat transfer medium Heat transfer through multiple layers Heat transfer at boundary PHM3133 Dosage Design /11

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Practical Heat Transfer 3 1.You stir some hot soup with a silver spoon and notice that the spoon warms up. 2.You stand watching a bonfire, but can’t get too close because of the heat. 3.It is hard for central air-conditioning in an old house to cool the attic. PHM3133 Dosage Design /11

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Heat transfer medium Water ………………….…. Steam……………………. Oil………………..……… Thermal liquid………..…. Air……………………. Pebbles/Sand/Iron balls… ……. water-bath …….fluid energy mill …..oil-bath ……….???? …oven, spray drier …high temperature equipment PHM3133 Dosage Design /11 4

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Thermal conductivity, k 5 k = “thermal conductivity” good thermal conductors ---- high k [k] = J/s-m- C ( C or K) good thermal insulators … low k Exercise What is k for vacuum? Polystyrene cup? PHM3133 Dosage Design /11

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Values of k (J/s-m-K) 6 MaterialTemperature/ K kUses Copper 373 (100 C) 379? Graphite 323 (50 C) 138? Glass wool Piping insulation Water circulation Air 473 (200 C) fluid Steam energy mill PHM3133 Dosage Design /11

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Thermal conductivity of air PHM3133 Dosage Design /11 7 Temperature Thermal conductivity

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Rate of heat transfer 8 H = Q/t = rate of heat transfer, Unit: J/s H = k A (T H -T C )/L Q/t = k A T/ x T H Hot T C Cold L Area A PHM3133 Dosage Design /11

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Find the rate of heat transfer 9 Q/t = k A T/ xx T = T H -T C = 25 C Plug in…. Q/t = x 35 x 25/0.02 H=3500 J/s H=3500 Watts Inside: T H = 25 C Outside: T C = 0 C Wood: thickness x = 0.02 m area A = 35 m 2 k = J/s ● m ● C PHM3133 Dosage Design /11

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Heat transfer through multiple layers 10 Air is better than wool! And cheaper!! Therefore important for insulation.Hence…layered clothing! Low k For effective heat transfer, choose material with high thermal conductivity. TT PHM3133 Dosage Design /11 Δx = x1 + x2 + x3

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Examples: heat transfer through multiple layers 11 Heat transfer between fluids…..air heater Heat transfer through a wall ….pot on stove Heat transfer in pipes and tubes…. heat exchanger Heat exchange between a fluid and a solid boundary……fluidised bed PHM3133 Dosage Design /11

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Find the rate of heat transfer in multiple layers 12 Assume H1 H1 = H2H2 k 1 A(T 0 -T C )/x 1 = k 2 A(T H -T 0 )/x 2 solve for T0 T0 = temp at junction T 0 =2.27 C then solve for H 1 or H2H2 H=318 Watts x 2 = m A 1 = 35 m 2 k 1 = J/s-m-C Inside: T H = 25 C Outside: T C = 0 C PHM3133 Dosage Design /11 x 1 = 0.02 m A 1 = 35 m 2 k 1 = J/s-m-C

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Thermal Resistance 13 Q/t = k A T/ x H/A = T k/ x = T/R R = x/k [Joules/s ● m 2 ], R is the thermal resistance R “adds” for multiple layers Q/tA = T/ k x = T/(R 1 +R 2 +R ) R 1 = x 1 /k 1 etc PHM3133 Dosage Design /11

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Insulation 14 Insulation for piping is critical to ensure minimum heat loss Typical insulators are Glass wool/rock wool Aluminum sheets PHM3133 Dosage Design /11

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Heat exchange between a fluid and a solid boundary 15 At the boundary, heat transfer is influenced by conduction and convection: H = hA(T 1 – T 1, wall ), h is the film coefficient A T1T1 T1, wall PHM3133 Dosage Design /11

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Film coefficient, h (J/m 2 -s-K) 16 Fluidh Water (heat-exchanger) Gases Organic solvents Oils …….why? PHM3133 Dosage Design /11

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Overall heat transfer coefficient 17 Taking into account k and h, k, thermal conductivity and h,film coefficient Q = U AdT U is the overall heat transfer coefficient PHM3133 Dosage Design /11

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U values Overall heat transfer coefficient 18 Convection Sea-breeze….1 Radiation Else, heat from sun produces roasted human…… 2 Indirect i.e. through wall conduction House is our shelter…20 Contactive mechanism i.e. gaseous phase heat carrier passes directly through the solids bed200 PHM3133 Dosage Design /11

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Common heat transport fluids 19 from Perry’s Chemical Engineers’ Handbook 6th Ed. PHM3133 Dosage Design /11

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Heat transfer equipment: Fluidised bed dryer 20 Hence, drying of solids using fluidised bed technique is very popular! 0002?VNETCOOKIE=NO 0002?VNETCOOKIE=NO PHM3133 Dosage Design /11

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Relationship between Energy and Temperature 21 Temperature (K) Energy PHM3133 Dosage Design /11

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References 22 Aulton, M. E. (Ed.) (1988). Pharmaceutics – The Science of Dosage Form Design. Churchill Livingstone. PHM3133 Dosage Design /11

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