department of mathematics;
quaid-i-azam university;
islamabad 44000;
pakistan;
nonlinear analysis and applied mathematics(naam)research group;
department of mathematics;
faculty of science;
king abdulaziz university;
jeddah 80203;
saudi arabia;
melting heat; Darcy-Forchheimer(D-F)porous medium; magnetohydrodynamics(MHD); Cattaneo-Christov(C-C)heat flux; fourth-grade fluid; optimal homotopy analysis method(OHAM);