Journal Vol – 12 No -2, January 2018

NUMERICAL STUDY LAMINAR CONVECTION OVER A PLATE HEATED FROM BELOW BY CONVECTION

Authors:

Asish Mitra

DOI NO:

https://doi.org/10.26782/jmcms.2018.01.00001

Abstract:

In the present numerical study, laminar convection over a plate in a uniform free stream is investigated when the bottom surface of the plate is heated by convection from a hot fluid. It is found that the similarity solution is possible if the convective heat transfer associated with the hot fluid on the lower surface of the plate is proportional to x1/2. The numerical solutions thus obtained are analyzed for a range of values of the parameter characterizing the hot fluid convection process and for representative Prandtl numbers of 0.1, 0.72 and 10. The results of the present simulation are then compared with the reports published in literature and find a good agreement.

Keywords:

Boundary Layer,Convective Boundary Condition,Horizontal Plate,Matlab,Similarity Solution,

Refference:

1. Blasius, H., “Grenzschichten in Flussigkeiten mit kleiner reibung,” Z. Math
Phys., vol. 56, pp. 1–37, 1908.
2. Incropera F P et al., Fundamentals of Heat and Mass Transfer. 6th ed. New
York, John Wiley, 2007.
3. Kays W M, Crawford M E., Convective Heat and Mass Transfer. New York,
McGraw Hill, 1980, pp. 51–54.
4. Bejan A., Convective Heat Transfer. 3rd ed. New York, John Wiley, 2004, pp.
84.
5. Rogers David F., Laminar Flow Aanalysis. New York, Cambridge University
Press, 1992, pp. 13–139.
6. Shu J-J, Pop I., “On thermal boundary layers on a flat plate subjected to a
variable heat flux,” Int J Heat Fluid Flow, vol. 19, pp. 79-84, 1988.
7. Cortell R., “Numerical solutions of classical Blasius flat plate problem,” Appl
Math Comput, vol 170, pp. 706-710, 2005.
8. A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat
plate with a convective surface boundary condition,” Commun.Nonlinear Sci.
Numer. Simul., vol. 14, pp. 1064-1068, 2009.
9. L. Howarth, “On the solution of the laminar boundary layer equation,” Proc.
RSoc. Lond. A., vol. 164, pp. 547-579, 1938.

View Download

ON THE PEAK SHAPE METHOD OF THE DETERMINATION OF ACTIVATION ENERGY AND ORDER OF KINETICS IN THERMOLUMINESCENCE RECORDED WITH HYPERBOLIC HEATING PROFILE

Authors:

SK Azharuddin, S. Dorendrajit Singh, P. S. Majumdar

DOI NO:

https://doi.org/10.26782/jmcms.2018.01.00002

Abstract:

A set of expressions are presented for the determination of activation energy of thermoluminescence peaks recorded with hyperbolic heating profile. Along with conventional half intensity points the peak widths at signal levels equal to 2/3 and 4/5 of peak height are used to determine the activation energy. A method of determination of order of kinetics of the peak by using its symmetry factor is also proposed. The present method is applied both to numerically computed and experimental TL peaks and encouraging results have been obtained.

Keywords:

Thermoluminescence,activation energy,order of kinetics,hyperbolic heating profile,

Refference:

1. Chen R. and Mckeever S.W.S., Theory of thermoluminescence and related phenomena, World Scintific, Singapore (1997)

2. Chen R. and Pagonis V. , Thermally and optically stimulated luminescence, A simulation approach, Wiely and Sons LTD,Chichester,U.K. (2011)

3. Arnold W. And Sherwood H. , J PhysChem, 63,2 (1959)

4. Halperin A., Leibovitz M. And Schlesinger M., Rev. Sci. Instrum ,33,1168 (1962)

5. Stammers K. , J Phys E, 12, 637 (1979)

6. Kelly P.J. and Laubitz M. J. Can J Phys, 45, 311 (1967)

7. Bos. A. J. J. Vijverberg R.N.M, Piters T.M and Mckeever S.W.S. ,J Phys D, 25 1249 (1992)

8. Fleming R.J., Can J Phys , 46,1509 (1968)

9. Balarin M, Phys Stat Sol(a), 31,K 111 (1975R)

10. Chen R. and Krish Y., Analysis of thermally stimulated process, Pargamon Oxford(1981)

11. Das B.C. Mukherjee B. N., Differential Calculus, U. N. Dhar and Sons, Kolkata,India (2012)

12. Randal J. T. And Wilkins M. H. F., ProcPhysSoc A, 184, 390 (1945)

13. Garlick G. F. J. And Gibson A.F. , Procphyssoc, 40, 579 (1948)

14. Sanyal D.C. and Das K.,introduction to numerical analysis,U.N.Dhar and sons Kolkata,India(2012)

15. Spigel M. R., Steptens L. J., Theory and Problems of statistics, 3rd edition, Tata McGraw Hill publication company, New Delhi, India (2000)

View Download

AN INVENTORY MODEL FOR DETERIORATING ITEM WITH ALLOWABLE DELAY IN PAYMENT

Authors:

Md Abdul Hakim

DOI NO:

https://doi.org/10.26782/jmcms.2018.01.00003

Abstract:

In this paper, we have developed an inventory model for deteriorating item with permissible delay in payment. Demand function dependent on the selling price and frequency of advertisement cost. Partially backlogged shortages are allowed and backlogged rate dependent on the duration of waiting time up to arrival of next lot. The corresponding model have been formulated and solved. Three numerical examples have been considered to illustrate the model. Finally sensitivity analyses have been carried out taking one parameter at a time and other parameters as same.     

Keywords:

Inventory,deterioration,partially backlogged shortages,permissible delay in payment,

Refference:

1. Haley C.W., Higgins H.C., Inventory policy and trade credit financing, Manage.
Sci. 20 (1973) 464-471.
2. Goyal S.K., Economic order quantity under conditions of permissible delay in
payments, J. Oper. Res. Soc. 36 (1985) 35–38.
3. Aggarwal S.P., Jaggi C.K., Ordering policies of deteriorating items under
permissible delay in payments, J. Oper. Res. Soc. 46 (1995) 658–662.
4. Jamal A.M.M., Sarker B.R., S. Wang, An ordering policy for deteriorating
items with allowable shortages and permissible delay in payment, J. Oper. Res.
Soc. 48 (1997) 826-833.

5. Hwang H., Shinn S.W., Retailer’s pricing and lot sizing policy for exponentially
deteriorating products under the condition of permissible delay in payments,
Comp. Oper. Res. 24 (1997) 539–547.
6. Chang C. T., Ouyang L. Y., Teng J. T., An EOQ model for deteriorating items
under supplier credits linked to ordering quantity, Appl. Math. Model. 27
(2003) 983–996.
7. Abad P. L., Jaggi C. K., A joint approach for setting unit price and the length
Of the credit period for a seller when end demand is price sensitive, Int. J.
Prod. Econ. 83 (2003) 115–122.
8. Ouyang L. Y., Wu K. S., Yang C. T., A study on an inventory model for non
instantaneous deteriorating items with permissible delay in payments, Comp.
Ind. Eng. 51 (2006) 637–651.
9. Huang Y. F., An inventory model under two levels of trade credit and limited storage
space derived without derivatives, Appl. Math. Model. 30 (2006) 418 436.
10. Huang Y.F., Economic order quantity under conditionally permissible delay in
payments, Euro. J. Oper. Res. 176 (2007) 911– 924.
11. Huang Y. F., Optimal retailer’s replenishment decisions in the EPQ model
under two levels of trade credit policy, Euro. J. Oper. Res. 176 (2007) 1577–1591.
12. Das B., Maity K., Maiti M., A two warehouse supply-chain model under
possibility/ necessity/credibility measures, Math. Comp. Model. 46 (2007) 398–409.
13. Niu B., Xie J. X., A note on Two-warehouse inventory model with Deterioration
under FIFO dispatch policy, Euro. J. Oper. Res. 190 (2008) 571-577.
14. Rong M., Mahapatra N. K., Maiti M., A two warehouse inventory model for a
deteriorating item with partially/fully backlogged shortage and fuzzy lead time,
Euro. J. Oper. Res. 189 (2008) 59–75.
15. Dey J. K., Mondal S. K., Maiti M., Two storage inventory problem with
dynamic demand and interval valued lead-time over finite time horizon under
inflation and time-value of money, Euro. J. Oper. Res. 185 (2008) 170–194.
16. Hsieh T. P., Dye C. Y., Ouyang L.Y., Determining optimal lot size for a two
warehouse system with deterioration and shortages using net present value,
Euro. J. Oper. Res. 191 (2008) 182-192.
17. Maiti M. K., Fuzzy inventory model with two warehouses under possibility
measure on fuzzy goal, Euro. J. Oper. Res. 188 (2008) 746–774.
18. Jaggi C. K., and Verma P., Joint optimization of price and order quantity with
shortages for a two-warehouse system, Top (Spain), 16 (2008) 195-213.
19. Sana S. S., Chaudhuri K. S., A deterministic EOQ model with delays in
payments and price-discount offers, Euro. J. Oper. Res.184 (2008) 509–533.
20. Huang Y. F., Hsu K. H., An EOQ model under retailer partial trade credit
policy in supply chain, Int. J. Prod. Econ. 112 (2008) 655–664.
21. Ho C. H., Ouyang L.Y., Su C. H., Optimal pricing, shipment and payment
policy for an integrated supplier–buyer inventory model with two-part trade
credit, Euro. J. Oper. Res. 187 (2008) 496–510.
22. Lee C. C., Hsu S. L., A two-warehouse production model for deteriorating
inventory items with time-dependent demands, Euro. J. Oper. Res. 194 (2009)
700–710.
23. Jaggi C. K., Aggarwal K. K., Verma P., Inventory and pricing strategies for
deteriorating items with limited capacity and time proportional backlogging
rate, Int. J. Oper. Res. 8(3) (2010) 331-354.
24. Jaggi C. K., Khanna A., Supply chain models for deteriorating items with
stock-dependent consumption rate and shortages under inflation and
permissible delay in payment, Int. J. Math. Opera. Res. 2(4) (2010) 491-514.
25. Jaggi C. K., Kausar A., Retailer’s ordering policy in a supply chain when demand
is price and credit period dependent, Int. J. Strat. Dec. Sci. 2(4) (2011) 61-74.
26. Bhunia A. K., Shaikh A. A., A two warehouse inventory model for deteriorating
items with time dependent partial backlogging and variable demand dependent on
marketing strategy and time, International Journal of Inventory Control and
Management, 1 (2011), 95-110.
27 Bhunia A. K., Pal P., Chattopadhyay S., Medya B. K., An inventory model of
two-warehouse system with variable demand dependent on instantaneous
displayed stock and marketing decisions via hybrid RCGA, Int. J. Ind. Eng.
Comput. 2(2) (2011) 351-368.
28. Jaggi C. K., Khanna A., Verma P., Two-warehouse partially backlogging
inventory model for deteriorating items with linear trend in demand under
inflationary conditions, Int. J. Syst. Sci. 42(7) (2011) 1185-1196.
29. Jaggi C. K., Mittal M., Retailer’s ordering policy for deteriorating items with
initial inspection and allowable shortages under the condition of permissible
delay in payments, Int. J. Appl. Ind. Eng. 1(1) (2012) 64-79.
30. Yang H. L., (2012), ‘Two-warehouse partial backlogging inventory models with
three-parameter weibull .distribution deterioration under inflation’ International
Journal of Production Economics, 138, 107-116.

31. Bhunia A. K., and Shaikh A. A., Maiti A. K., Maiti M., A two warehouse
deterministic inventory model for deteriorating items with a linear trend in time
dependent demand over finite time horizon by Elitist Real-Coded Genetic Algorithm,
International Journal Industrial Engineering and Computations, 4(2013), 241-258
32. Bhunia A. K., Shaikh A. A., Gupta R. K., A study on two-warehouse partially
backlogged deteriorating inventory models under inflation via particle swarm
optimization, International Journal of System Science. (to appear) 2013.
33. Yang H. L., Chang C. T., A two-warehouse partial backlogging inventory model for
deteriorating items with permissible delay in payment under inflation’, Applied
Mathematical Modelling, 37(2013), 2717-2726.
34. Chung K. J., Huang T. S., The optimal retailer’s ordering policies for
deteriorating items with limited storage capacity under trade credit financing,
Int. J. Prod. Econ. 106 (2007) 127–145.
35. Liang Y., Zhou F., A two-warehouse inventory model for deteriorating items
under conditionally permissible delay in payment, Appl. Math. Model. 35
(2011) 2221-2231.
36. Bhunia A. K., Jaggi C. K., Sharma A., Sharma R., A two warehouse inventory
model for deteriorating items under permissible delay in payment with partial
backlogging, Applied Mathematics and Computation, 232(2014), 1125-1137.
37. Shah N. H., Patel A. R., Lou K. R., Optimal ordering and pricing policy for
price sensitive stock-dependent demand under progressive payment scheme,
International Journal Industrial Engineering Computations, 2(2011), 523-532.

View Download